symengine_conversions

gistfile1.txt

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#if defined(WIN32) || defined(MS_WINDOWS)
#define _USE_MATH_DEFINES
#endif
#include <math.h>
#define __PYX_HAVE__sage__symbolic__symengine_conversions
#define __PYX_HAVE_API__sage__symbolic__symengine_conversions
#include "string.h"
#include "stdio.h"
#include "gmp.h"
#include "ccobject.h"
#include "sage/libs/ntl/ntlwrap.cpp"
#include "sage/libs/ntl/ntlwrap.h"
#include "stdint.h"
#include "pythread.h"
#include "mpfr.h"
#include <symengine/symengine_rcp.h>
#include <symengine/basic.h>
#include <symengine/symbol.h>
#include <symengine/number.h>
#include <symengine/integer.h>
#include <symengine/rational.h>
#include <symengine/complex.h>
#include <symengine/real_double.h>
#include <symengine/complex_double.h>
#include <symengine/constants.h>
#include <symengine/add.h>
#include <symengine/mul.h>
#include <symengine/pow.h>
#include <symengine/functions.h>
#include <symengine/real_mpfr.h>
#include <symengine/complex_mpc.h>
#include <symengine/matrix.h>
#include <symengine/ntheory.h>
#include <symengine/visitor.h>
#include <symengine/eval_double.h>
#include <symengine/eval_mpfr.h>
#include <symengine/eval_mpc.h>
#include <symengine/symengine_rcp.h>
#include <symengine/basic.h>
#include <symengine/symbol.h>
#include <symengine/number.h>
#include <symengine/integer.h>
#include <symengine/rational.h>
#include <symengine/complex.h>
#include <symengine/real_double.h>
#include <symengine/complex_double.h>
#include <symengine/constants.h>
#include <symengine/add.h>
#include <symengine/mul.h>
#include <symengine/pow.h>
#include <symengine/functions.h>
#include <symengine/real_mpfr.h>
#include <symengine/complex_mpc.h>
#include <symengine/matrix.h>
#include <symengine/ntheory.h>
#include <symengine/visitor.h>
#include <symengine/eval_double.h>
#include <symengine/eval_mpfr.h>
#include <symengine/eval_mpc.h>
#include "pari/pari.h"
#include "mpc.h"
#include <string>
#include "ios"
#include "new"
#include "stdexcept"
#include "typeinfo"
#include <utility>
#include <map>
#include <vector>
#include "gmpxx.h"
#include <set>
#ifdef _OPENMP
#include <omp.h>
#endif /* _OPENMP */

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                PyExc_ValueError,
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                default_encoding_c);
            goto bad;
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bad:
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}
#endif
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
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#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
static char* __PYX_DEFAULT_STRING_ENCODING;
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bad:
    Py_XDECREF(default_encoding);
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  #define unlikely(x) (x)
#endif /* __GNUC__ */

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static PyObject *__pyx_b;
static PyObject *__pyx_empty_tuple;
static PyObject *__pyx_empty_bytes;
static int __pyx_lineno;
static int __pyx_clineno = 0;
static const char * __pyx_cfilenm= __FILE__;
static const char *__pyx_filename;

#if !defined(CYTHON_CCOMPLEX)
  #if defined(__cplusplus)
    #define CYTHON_CCOMPLEX 1
  #elif defined(_Complex_I)
    #define CYTHON_CCOMPLEX 1
  #else
    #define CYTHON_CCOMPLEX 0
  #endif
#endif
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    #include <complex>
  #else
    #include <complex.h>
  #endif
#endif
#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
  #undef _Complex_I
  #define _Complex_I 1.0fj
#endif


static const char *__pyx_f[] = {
  "sage/symbolic/symengine_conversions.pyx",
  "sage/structure/element.pxd",
  "type.pxd",
  "bool.pxd",
  "complex.pxd",
  "sage/structure/sage_object.pxd",
  "sage/structure/generators.pxd",
  "sage/structure/category_object.pxd",
  "sage/structure/coerce_dict.pxd",
  "sage/structure/parent_old.pxd",
  "sage/structure/parent_base.pxd",
  "sage/structure/parent_gens.pxd",
  "sage/rings/ring.pxd",
  "sage/structure/parent.pxd",
  "sage/categories/map.pxd",
  "sage/categories/morphism.pxd",
  "sage/rings/integer.pxd",
  "sage/rings/rational.pxd",
  "sage/rings/real_mpfr.pxd",
  "sage/rings/complex_mpc.pxd",
  "symengine_wrapper.pxd",
};
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    typedef ::std::complex< double > __pyx_t_double_complex;
  #else
    typedef double _Complex __pyx_t_double_complex;
  #endif
#else
    typedef struct { double real, imag; } __pyx_t_double_complex;
#endif


/*--- Type declarations ---*/
struct __pyx_obj_4sage_9structure_11sage_object_SageObject;
struct __pyx_obj_4sage_9structure_10generators_Generators;
struct __pyx_obj_4sage_9structure_10generators_Generators_finite;
struct __pyx_obj_4sage_9structure_10generators_Generators_list;
struct __pyx_obj_4sage_9structure_10generators_Generators_naturals;
struct __pyx_obj_4sage_9structure_10generators_Generators_none;
struct __pyx_obj_4sage_9structure_10generators_Generators_lazy_all;
struct __pyx_obj_4sage_9structure_15category_object_CategoryObject;
struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict;
struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict;
struct __pyx_obj_4sage_9structure_6parent_Parent;
struct __pyx_obj_4sage_9structure_10parent_old_Parent;
struct __pyx_obj_4sage_9structure_11parent_base_ParentWithBase;
struct __pyx_obj_4sage_9structure_11parent_gens_ParentWithGens;
struct __pyx_obj_4sage_9structure_11parent_gens_ParentWithMultiplicativeAbelianGens;
struct __pyx_obj_4sage_9structure_11parent_gens_ParentWithAdditiveAbelianGens;
struct __pyx_obj_4sage_5rings_4ring_Ring;
struct __pyx_obj_4sage_5rings_4ring_CommutativeRing;
struct __pyx_obj_4sage_5rings_4ring_IntegralDomain;
struct __pyx_obj_4sage_5rings_4ring_DedekindDomain;
struct __pyx_obj_4sage_5rings_4ring_PrincipalIdealDomain;
struct __pyx_obj_4sage_5rings_4ring_EuclideanDomain;
struct __pyx_obj_4sage_5rings_4ring_Field;
struct __pyx_obj_4sage_5rings_4ring_Algebra;
struct __pyx_obj_4sage_5rings_4ring_CommutativeAlgebra;
struct __pyx_obj_4sage_9structure_7element_Element;
struct __pyx_obj_4sage_9structure_7element_ElementWithCachedMethod;
struct __pyx_obj_4sage_9structure_7element_ModuleElement;
struct __pyx_obj_4sage_9structure_7element_MonoidElement;
struct __pyx_obj_4sage_9structure_7element_MultiplicativeGroupElement;
struct __pyx_obj_4sage_9structure_7element_AdditiveGroupElement;
struct __pyx_obj_4sage_9structure_7element_RingElement;
struct __pyx_obj_4sage_9structure_7element_CommutativeRingElement;
struct __pyx_obj_4sage_9structure_7element_IntegralDomainElement;
struct __pyx_obj_4sage_9structure_7element_DedekindDomainElement;
struct __pyx_obj_4sage_9structure_7element_PrincipalIdealDomainElement;
struct __pyx_obj_4sage_9structure_7element_EuclideanDomainElement;
struct __pyx_obj_4sage_9structure_7element_FieldElement;
struct __pyx_obj_4sage_9structure_7element_AlgebraElement;
struct __pyx_obj_4sage_9structure_7element_CommutativeAlgebraElement;
struct __pyx_obj_4sage_9structure_7element_CommutativeAlgebra;
struct __pyx_obj_4sage_9structure_7element_InfinityElement;
struct __pyx_obj_4sage_9structure_7element_Vector;
struct __pyx_obj_4sage_9structure_7element_Matrix;
struct __pyx_obj_4sage_9structure_7element_CoercionModel;
struct __pyx_obj_4sage_10categories_3map_Map;
struct __pyx_obj_4sage_10categories_3map_Section;
struct __pyx_obj_4sage_10categories_3map_FormalCompositeMap;
struct __pyx_obj_4sage_10categories_8morphism_Morphism;
struct __pyx_obj_4sage_10categories_8morphism_SetMorphism;
struct __pyx_obj_4sage_5rings_7integer_Integer;
struct __pyx_obj_4sage_5rings_7integer_int_to_Z;
struct __pyx_obj_4sage_5rings_8rational_Rational;
struct __pyx_obj_4sage_5rings_9real_mpfr_RealField_class;
struct __pyx_obj_4sage_5rings_9real_mpfr_RealNumber;
struct __pyx_obj_4sage_5rings_11complex_mpc_MPComplexNumber;
struct __pyx_obj_4sage_5rings_11complex_mpc_MPComplexField_class;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Basic;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Number;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Integer;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Rational;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Complex;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_RealDouble;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ComplexDouble;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_RealMPFR;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ComplexMPC;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Add;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Mul;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Pow;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Function;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Sin;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Cos;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Tan;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Cot;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Csc;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Sec;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ASin;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ACos;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ATan;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ACot;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ACsc;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ASec;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_FunctionSymbol;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_FunctionWrapper;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Abs;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Derivative;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Subs;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_MatrixBase;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_DenseMatrix;
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Log;
struct __pyx_opt_args_4sage_9structure_6parent_6Parent_init_coerce;
struct __pyx_opt_args_4sage_9structure_6parent_6Parent_get_action;
struct __pyx_opt_args_4sage_9structure_6parent_6Parent_discover_action;

/* "parent.pxd":35
 * 
 *     # Called from the __init__ method to set up coercion.
 *     cdef int init_coerce(self, bint warn=*) except -1             # <<<<<<<<<<<<<<
 * 
 *     # returns whether or not there is a Morphism from S to self
 */
struct __pyx_opt_args_4sage_9structure_6parent_6Parent_init_coerce {
  int __pyx_n;
  int warn;
};

/* "parent.pxd":52
 *     # returns the Action by/on self on/by S
 *     # corresponding to op and self_on_left
 *     cpdef get_action(self, S, op=*, bint self_on_left=*, self_el=*, S_el=*)             # <<<<<<<<<<<<<<
 *     cpdef _get_action_(self, S, op, bint self_on_left)
 * 
 */
struct __pyx_opt_args_4sage_9structure_6parent_6Parent_get_action {
  int __pyx_n;
  PyObject *op;
  int self_on_left;
  PyObject *self_el;
  PyObject *S_el;
};

/* "parent.pxd":66
 *     cdef discover_coerce_map_from(self, S)
 *     cdef discover_convert_map_from(self, S)
 *     cdef discover_action(self, S, op, bint self_on_left, self_el=*, S_el=*)             # <<<<<<<<<<<<<<
 * 
 *     # List consisting of Morphisms (from anything to self)
 */
struct __pyx_opt_args_4sage_9structure_6parent_6Parent_discover_action {
  int __pyx_n;
  PyObject *self_el;
  PyObject *S_el;
};
struct __pyx_opt_args_4sage_10categories_3map_3Map__call_with_args;

/* "map.pxd":13
 *     # these methods require x is an element of domain, and returns an element with parent codomain
 *     cpdef Element _call_(self, x)
 *     cpdef Element _call_with_args(self, x, args=*, kwds=*)             # <<<<<<<<<<<<<<
 * 
 *     cdef public domain    # will be either a weakref or a constant map
 */
struct __pyx_opt_args_4sage_10categories_3map_3Map__call_with_args {
  int __pyx_n;
  PyObject *args;
  PyObject *kwds;
};
struct __pyx_opt_args_4sage_5rings_8rational_rational_power_parts;

/* "sage/rings/rational.pxd":6
 * cimport integer
 * 
 * cpdef rational_power_parts(a, b, factor_limit=?)             # <<<<<<<<<<<<<<
 * 
 * cdef class Rational(sage.structure.element.FieldElement):
 */
struct __pyx_opt_args_4sage_5rings_8rational_rational_power_parts {
  int __pyx_n;
  PyObject *factor_limit;
};
struct __pyx_opt_args_4sage_5rings_9real_mpfr_RealField;

/* "sage/rings/real_mpfr.pxd":28
 *     cdef RealNumber abs(RealNumber self)
 * 
 * cpdef RealField(int prec=*, int sci_not=*, rnd=*)             # <<<<<<<<<<<<<<
 */
struct __pyx_opt_args_4sage_5rings_9real_mpfr_RealField {
  int __pyx_n;
  int prec;
  int sci_not;
  PyObject *rnd;
};

/* "sage_object.pxd":5
 * 
 * 
 * cdef class SageObject:             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_11sage_object_SageObject {
  PyObject_HEAD
};


/* "sage/structure/generators.pxd":3
 * from sage.structure.sage_object cimport SageObject
 * 
 * cdef class Generators(SageObject):             # <<<<<<<<<<<<<<
 * 
 *     cdef readonly _obj
 */
struct __pyx_obj_4sage_9structure_10generators_Generators {
  struct __pyx_obj_4sage_9structure_11sage_object_SageObject __pyx_base;
  struct __pyx_vtabstruct_4sage_9structure_10generators_Generators *__pyx_vtab;
  PyObject *_obj;
  PyObject *_index_set;
  PyObject *_category;
};


/* "sage/structure/generators.pxd":16
 *     cpdef list(self)
 * 
 * cdef class Generators_finite(Generators):             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t _n
 * 
 */
struct __pyx_obj_4sage_9structure_10generators_Generators_finite {
  struct __pyx_obj_4sage_9structure_10generators_Generators __pyx_base;
  Py_ssize_t _n;
};


/* "sage/structure/generators.pxd":19
 *     cdef Py_ssize_t _n
 * 
 * cdef class Generators_list(Generators_finite):             # <<<<<<<<<<<<<<
 *     cdef _List
 * 
 */
struct __pyx_obj_4sage_9structure_10generators_Generators_list {
  struct __pyx_obj_4sage_9structure_10generators_Generators_finite __pyx_base;
  PyObject *_List;
};


/* "sage/structure/generators.pxd":22
 *     cdef _List
 * 
 * cdef class Generators_naturals(Generators):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_10generators_Generators_naturals {
  struct __pyx_obj_4sage_9structure_10generators_Generators __pyx_base;
};


/* "sage/structure/generators.pxd":25
 *     pass
 * 
 * cdef class Generators_none(Generators):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_10generators_Generators_none {
  struct __pyx_obj_4sage_9structure_10generators_Generators __pyx_base;
};


/* "sage/structure/generators.pxd":28
 *     pass
 * 
 * cdef class Generators_lazy_all(Generators):             # <<<<<<<<<<<<<<
 *     cdef _f
 *     cdef int _compute_gens(self) except -1
 */
struct __pyx_obj_4sage_9structure_10generators_Generators_lazy_all {
  struct __pyx_obj_4sage_9structure_10generators_Generators __pyx_base;
  PyObject *_f;
};


/* "sage/structure/category_object.pxd":16
 * cpdef inline check_default_category(default_category, category)
 * 
 * cdef class CategoryObject(SageObject):             # <<<<<<<<<<<<<<
 *     cdef _generators
 *     cdef _category
 */
struct __pyx_obj_4sage_9structure_15category_object_CategoryObject {
  struct __pyx_obj_4sage_9structure_11sage_object_SageObject __pyx_base;
  PyObject *_generators;
  PyObject *_category;
  PyObject *_base;
  PyObject *_names;
  PyObject *_factory_data;
  PyObject *__weakref__;
  long _hash_value;
};


/* "sage/structure/coerce_dict.pxd":7
 * 
 * @cython.final
 * cdef class MonoDict:             # <<<<<<<<<<<<<<
 *     cdef __weakref__
 *     cdef size_t mask
 */
struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict {
  PyObject_HEAD
  struct __pyx_vtabstruct_4sage_9structure_11coerce_dict_MonoDict *__pyx_vtab;
  PyObject *__weakref__;
  size_t mask;
  size_t used;
  size_t fill;
  struct __pyx_t_4sage_9structure_11coerce_dict_mono_cell *table;
  int weak_values;
  PyObject *eraser;
};


/* "sage/structure/coerce_dict.pxd":23
 * 
 * @cython.final
 * cdef class TripleDict:             # <<<<<<<<<<<<<<
 *     cdef __weakref__
 *     cdef size_t mask
 */
struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict {
  PyObject_HEAD
  struct __pyx_vtabstruct_4sage_9structure_11coerce_dict_TripleDict *__pyx_vtab;
  PyObject *__weakref__;
  size_t mask;
  size_t used;
  size_t fill;
  struct __pyx_t_4sage_9structure_11coerce_dict_triple_cell *table;
  int weak_values;
  PyObject *eraser;
};


/* "parent.pxd":12
 * from sage.structure.coerce_dict cimport MonoDict, TripleDict
 * 
 * cdef class Parent(category_object.CategoryObject):             # <<<<<<<<<<<<<<
 * 
 *     cdef public _element_constructor
 */
struct __pyx_obj_4sage_9structure_6parent_Parent {
  struct __pyx_obj_4sage_9structure_15category_object_CategoryObject __pyx_base;
  struct __pyx_vtabstruct_4sage_9structure_6parent_Parent *__pyx_vtab;
  PyObject *_element_constructor;
  PyObject *_convert_method_name;
  int _element_init_pass_parent;
  PyObject *__cached_methods;
  PyObject *_initial_coerce_list;
  PyObject *_initial_action_list;
  PyObject *_initial_convert_list;
  int _coercions_used;
  PyObject *_cache_an_element;
  PyObject *_coerce_from_list;
  PyObject *_registered_domains;
  struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *_coerce_from_hash;
  PyObject *_action_list;
  struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict *_action_hash;
  PyObject *_convert_from_list;
  struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *_convert_from_hash;
  PyObject *_embedding;
};


/* "parent_old.pxd":11
 * cimport parent
 * from sage.structure.coerce_dict cimport MonoDict
 * cdef class Parent(parent.Parent):             # <<<<<<<<<<<<<<
 * 
 *     # returns a Morphism from S to self, or None
 */
struct __pyx_obj_4sage_9structure_10parent_old_Parent {
  struct __pyx_obj_4sage_9structure_6parent_Parent __pyx_base;
  struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *_has_coerce_map_from;
};

struct __pyx_obj_4sage_9structure_11parent_base_ParentWithBase {
  struct __pyx_obj_4sage_9structure_10parent_old_Parent __pyx_base;
};


/* "sage/structure/parent_gens.pxd":15
 * cimport parent_base
 * 
 * cdef class ParentWithGens(parent_base.ParentWithBase):             # <<<<<<<<<<<<<<
 *     cdef public object _gens
 *     cdef public object _latex_names
 */
struct __pyx_obj_4sage_9structure_11parent_gens_ParentWithGens {
  struct __pyx_obj_4sage_9structure_11parent_base_ParentWithBase __pyx_base;
  PyObject *_gens;
  PyObject *_latex_names;
  PyObject *_list;
};


/* "sage/structure/parent_gens.pxd":21
 * 
 * 
 * cdef class ParentWithMultiplicativeAbelianGens(ParentWithGens):             # <<<<<<<<<<<<<<
 *     cdef public object _generator_orders
 * 
 */
struct __pyx_obj_4sage_9structure_11parent_gens_ParentWithMultiplicativeAbelianGens {
  struct __pyx_obj_4sage_9structure_11parent_gens_ParentWithGens __pyx_base;
  PyObject *_generator_orders;
};


/* "sage/structure/parent_gens.pxd":24
 *     cdef public object _generator_orders
 * 
 * cdef class ParentWithAdditiveAbelianGens(ParentWithGens):             # <<<<<<<<<<<<<<
 *     cdef public object _generator_orders
 */
struct __pyx_obj_4sage_9structure_11parent_gens_ParentWithAdditiveAbelianGens {
  struct __pyx_obj_4sage_9structure_11parent_gens_ParentWithGens __pyx_base;
  PyObject *_generator_orders;
};


/* "sage/rings/ring.pxd":5
 * cpdef bint _is_Field(x) except -2
 * 
 * cdef class Ring(ParentWithGens):             # <<<<<<<<<<<<<<
 *     cdef public object _zero_element
 *     cdef public object _one_element
 */
struct __pyx_obj_4sage_5rings_4ring_Ring {
  struct __pyx_obj_4sage_9structure_11parent_gens_ParentWithGens __pyx_base;
  PyObject *_zero_element;
  PyObject *_one_element;
  PyObject *_zero_ideal;
  PyObject *_unit_ideal;
  PyObject *__ideal_monoid;
};


/* "sage/rings/ring.pxd":13
 *     cdef _an_element_c_impl(self)
 * 
 * cdef class CommutativeRing(Ring):             # <<<<<<<<<<<<<<
 *     cdef public object __fraction_field
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_CommutativeRing {
  struct __pyx_obj_4sage_5rings_4ring_Ring __pyx_base;
  PyObject *__fraction_field;
};


/* "sage/rings/ring.pxd":16
 *     cdef public object __fraction_field
 * 
 * cdef class IntegralDomain(CommutativeRing):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_IntegralDomain {
  struct __pyx_obj_4sage_5rings_4ring_CommutativeRing __pyx_base;
};


/* "sage/rings/ring.pxd":19
 *     pass
 * 
 * cdef class DedekindDomain(IntegralDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_DedekindDomain {
  struct __pyx_obj_4sage_5rings_4ring_IntegralDomain __pyx_base;
};


/* "sage/rings/ring.pxd":23
 * 
 * 
 * cdef class PrincipalIdealDomain(IntegralDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_PrincipalIdealDomain {
  struct __pyx_obj_4sage_5rings_4ring_IntegralDomain __pyx_base;
};


/* "sage/rings/ring.pxd":26
 *     pass
 * 
 * cdef class EuclideanDomain(PrincipalIdealDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_EuclideanDomain {
  struct __pyx_obj_4sage_5rings_4ring_PrincipalIdealDomain __pyx_base;
};


/* "sage/rings/ring.pxd":29
 *     pass
 * 
 * cdef class Field(PrincipalIdealDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_Field {
  struct __pyx_obj_4sage_5rings_4ring_PrincipalIdealDomain __pyx_base;
};


/* "sage/rings/ring.pxd":32
 *     pass
 * 
 * cdef class Algebra(Ring):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_Algebra {
  struct __pyx_obj_4sage_5rings_4ring_Ring __pyx_base;
};


/* "sage/rings/ring.pxd":35
 *     pass
 * 
 * cdef class CommutativeAlgebra(CommutativeRing):             # <<<<<<<<<<<<<<
 *     pass
 */
struct __pyx_obj_4sage_5rings_4ring_CommutativeAlgebra {
  struct __pyx_obj_4sage_5rings_4ring_CommutativeRing __pyx_base;
};

struct __pyx_obj_4sage_9structure_7element_Element {
  struct __pyx_obj_4sage_9structure_11sage_object_SageObject __pyx_base;
  struct __pyx_vtabstruct_4sage_9structure_7element_Element *__pyx_vtab;
  struct __pyx_obj_4sage_9structure_6parent_Parent *_parent;
};


/* "sage/structure/element.pxd":47
 *     cpdef _acted_upon_(self, x, bint self_on_left)
 * 
 * cdef class ElementWithCachedMethod(Element):             # <<<<<<<<<<<<<<
 *     cdef public dict __cached_methods
 * 
 */
struct __pyx_obj_4sage_9structure_7element_ElementWithCachedMethod {
  struct __pyx_obj_4sage_9structure_7element_Element __pyx_base;
  PyObject *__cached_methods;
};


/* "sage/structure/element.pxd":50
 *     cdef public dict __cached_methods
 * 
 * cdef class ModuleElement(Element)       # forward declaration             # <<<<<<<<<<<<<<
 * 
 * cdef class RingElement(ModuleElement)   # forward declaration
 */
struct __pyx_obj_4sage_9structure_7element_ModuleElement {
  struct __pyx_obj_4sage_9structure_7element_Element __pyx_base;
};


/* "sage/structure/element.pxd":74
 *     cdef RingElement coerce_to_base_ring(self, x)
 * 
 * cdef class MonoidElement(Element):             # <<<<<<<<<<<<<<
 *     cpdef MonoidElement _mul_(self, MonoidElement right)
 * 
 */
struct __pyx_obj_4sage_9structure_7element_MonoidElement {
  struct __pyx_obj_4sage_9structure_7element_Element __pyx_base;
};


/* "sage/structure/element.pxd":77
 *     cpdef MonoidElement _mul_(self, MonoidElement right)
 * 
 * cdef class MultiplicativeGroupElement(MonoidElement):             # <<<<<<<<<<<<<<
 *     cpdef MultiplicativeGroupElement _div_(self, MultiplicativeGroupElement right)
 * 
 */
struct __pyx_obj_4sage_9structure_7element_MultiplicativeGroupElement {
  struct __pyx_obj_4sage_9structure_7element_MonoidElement __pyx_base;
};


/* "sage/structure/element.pxd":81
 * 
 * 
 * cdef class AdditiveGroupElement(ModuleElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_AdditiveGroupElement {
  struct __pyx_obj_4sage_9structure_7element_ModuleElement __pyx_base;
};


/* "sage/structure/element.pxd":52
 * cdef class ModuleElement(Element)       # forward declaration
 * 
 * cdef class RingElement(ModuleElement)   # forward declaration             # <<<<<<<<<<<<<<
 * 
 * cdef class ModuleElement(Element):
 */
struct __pyx_obj_4sage_9structure_7element_RingElement {
  struct __pyx_obj_4sage_9structure_7element_ModuleElement __pyx_base;
};


/* "sage/structure/element.pxd":94
 *     cdef RingElement _add_long(self, long n)
 * 
 * cdef class CommutativeRingElement(RingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_CommutativeRingElement {
  struct __pyx_obj_4sage_9structure_7element_RingElement __pyx_base;
};


/* "sage/structure/element.pxd":97
 *     pass
 * 
 * cdef class IntegralDomainElement(CommutativeRingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_IntegralDomainElement {
  struct __pyx_obj_4sage_9structure_7element_CommutativeRingElement __pyx_base;
};


/* "sage/structure/element.pxd":100
 *     pass
 * 
 * cdef class DedekindDomainElement(IntegralDomainElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_DedekindDomainElement {
  struct __pyx_obj_4sage_9structure_7element_IntegralDomainElement __pyx_base;
};


/* "sage/structure/element.pxd":103
 *     pass
 * 
 * cdef class PrincipalIdealDomainElement(DedekindDomainElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_PrincipalIdealDomainElement {
  struct __pyx_obj_4sage_9structure_7element_DedekindDomainElement __pyx_base;
};


/* "sage/structure/element.pxd":106
 *     pass
 * 
 * cdef class EuclideanDomainElement(PrincipalIdealDomainElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_EuclideanDomainElement {
  struct __pyx_obj_4sage_9structure_7element_PrincipalIdealDomainElement __pyx_base;
};


/* "sage/structure/element.pxd":109
 *     pass
 * 
 * cdef class FieldElement(CommutativeRingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_FieldElement {
  struct __pyx_obj_4sage_9structure_7element_CommutativeRingElement __pyx_base;
};


/* "sage/structure/element.pxd":112
 *     pass
 * 
 * cdef class AlgebraElement(RingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_AlgebraElement {
  struct __pyx_obj_4sage_9structure_7element_RingElement __pyx_base;
};


/* "sage/structure/element.pxd":115
 *     pass
 * 
 * cdef class CommutativeAlgebraElement(CommutativeRingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_CommutativeAlgebraElement {
  struct __pyx_obj_4sage_9structure_7element_CommutativeRingElement __pyx_base;
};


/* "sage/structure/element.pxd":118
 *     pass
 * 
 * cdef class CommutativeAlgebra(AlgebraElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_CommutativeAlgebra {
  struct __pyx_obj_4sage_9structure_7element_AlgebraElement __pyx_base;
};


/* "sage/structure/element.pxd":121
 *     pass
 * 
 * cdef class InfinityElement(RingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_InfinityElement {
  struct __pyx_obj_4sage_9structure_7element_RingElement __pyx_base;
};


/* "sage/structure/element.pxd":125
 * 
 * 
 * cdef class Vector(ModuleElement):             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t _degree
 * 
 */
struct __pyx_obj_4sage_9structure_7element_Vector {
  struct __pyx_obj_4sage_9structure_7element_ModuleElement __pyx_base;
  Py_ssize_t _degree;
};


/* "sage/structure/element.pxd":140
 * 
 * 
 * cdef class Matrix(ModuleElement):             # <<<<<<<<<<<<<<
 *     # All matrix classes must be written in Cython
 *     cdef Py_ssize_t _nrows
 */
struct __pyx_obj_4sage_9structure_7element_Matrix {
  struct __pyx_obj_4sage_9structure_7element_ModuleElement __pyx_base;
  Py_ssize_t _nrows;
  Py_ssize_t _ncols;
};


/* "sage/structure/element.pxd":155
 * 
 * 
 * cdef class CoercionModel:             # <<<<<<<<<<<<<<
 *     cpdef canonical_coercion(self, x, y)
 *     cpdef bin_op(self, x, y, op)
 */
struct __pyx_obj_4sage_9structure_7element_CoercionModel {
  PyObject_HEAD
  struct __pyx_vtabstruct_4sage_9structure_7element_CoercionModel *__pyx_vtab;
};


/* "map.pxd":4
 * from sage.structure.element cimport Element
 * 
 * cdef class Map(Element):             # <<<<<<<<<<<<<<
 *     cdef public int _coerce_cost # a rough measure of the cost of using this morphism in the coercion system.
 *                           # 10 by default, 100 if a DefaultCoercionMorphism, 10000 if inexact.
 */
struct __pyx_obj_4sage_10categories_3map_Map {
  struct __pyx_obj_4sage_9structure_7element_Element __pyx_base;
  int _coerce_cost;
  PyObject *domain;
  PyObject *codomain;
  struct __pyx_obj_4sage_9structure_6parent_Parent *_codomain;
  PyObject *_category_for;
  PyObject *_repr_type_str;
};


/* "map.pxd":23
 * 
 * 
 * cdef class Section(Map):             # <<<<<<<<<<<<<<
 *     cdef Map _inverse
 * 
 */
struct __pyx_obj_4sage_10categories_3map_Section {
  struct __pyx_obj_4sage_10categories_3map_Map __pyx_base;
  struct __pyx_obj_4sage_10categories_3map_Map *_inverse;
};


/* "map.pxd":26
 *     cdef Map _inverse
 * 
 * cdef class FormalCompositeMap(Map):             # <<<<<<<<<<<<<<
 *     cdef __list
 */
struct __pyx_obj_4sage_10categories_3map_FormalCompositeMap {
  struct __pyx_obj_4sage_10categories_3map_Map __pyx_base;
  PyObject *__pyx___list;
};


/* "sage/categories/morphism.pxd":5
 * from map cimport Map
 * 
 * cdef class Morphism(Map):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_10categories_8morphism_Morphism {
  struct __pyx_obj_4sage_10categories_3map_Map __pyx_base;
};


/* "sage/categories/morphism.pxd":8
 *     pass
 * 
 * cdef class SetMorphism(Morphism):             # <<<<<<<<<<<<<<
 *     cdef object _function
 *     cpdef bint _eq_c_impl(left, Element right)
 */
struct __pyx_obj_4sage_10categories_8morphism_SetMorphism {
  struct __pyx_obj_4sage_10categories_8morphism_Morphism __pyx_base;
  PyObject *_function;
};


/* "sage/rings/integer.pxd":7
 * from sage.categories.morphism cimport Morphism
 * 
 * cdef class Integer(EuclideanDomainElement):             # <<<<<<<<<<<<<<
 *     cdef mpz_t value
 * 
 */
struct __pyx_obj_4sage_5rings_7integer_Integer {
  struct __pyx_obj_4sage_9structure_7element_EuclideanDomainElement __pyx_base;
  mpz_t value;
};


/* "sage/rings/integer.pxd":36
 * cdef Integer smallInteger(long value)
 * 
 * cdef class int_to_Z(Morphism):             # <<<<<<<<<<<<<<
 *     pass
 */
struct __pyx_obj_4sage_5rings_7integer_int_to_Z {
  struct __pyx_obj_4sage_10categories_8morphism_Morphism __pyx_base;
};


/* "sage/rings/rational.pxd":8
 * cpdef rational_power_parts(a, b, factor_limit=?)
 * 
 * cdef class Rational(sage.structure.element.FieldElement):             # <<<<<<<<<<<<<<
 *     cdef mpq_t value
 * 
 */
struct __pyx_obj_4sage_5rings_8rational_Rational {
  struct __pyx_obj_4sage_9structure_7element_FieldElement __pyx_base;
  mpq_t value;
};


/* "sage/rings/real_mpfr.pxd":12
 * cdef class RealNumber(sage.structure.element.RingElement)  # forward decl
 * 
 * cdef class RealField_class(sage.rings.ring.Field):             # <<<<<<<<<<<<<<
 *     cdef int __prec
 *     cdef bint sci_not
 */
struct __pyx_obj_4sage_5rings_9real_mpfr_RealField_class {
  struct __pyx_obj_4sage_5rings_4ring_Field __pyx_base;
  int __pyx___prec;
  int sci_not;
  mpfr_rnd_t rnd;
  PyObject *rnd_str;
};


/* "sage/rings/real_mpfr.pxd":10
 * 
 * 
 * cdef class RealNumber(sage.structure.element.RingElement)  # forward decl             # <<<<<<<<<<<<<<
 * 
 * cdef class RealField_class(sage.rings.ring.Field):
 */
struct __pyx_obj_4sage_5rings_9real_mpfr_RealNumber {
  struct __pyx_obj_4sage_9structure_7element_RingElement __pyx_base;
  mpfr_t value;
  char init;
};


/* "sage/rings/complex_mpc.pxd":5
 * cimport sage.rings.ring
 * 
 * cdef class MPComplexNumber(sage.structure.element.FieldElement):             # <<<<<<<<<<<<<<
 *     cdef mpc_t value
 *     cdef char init
 */
struct __pyx_obj_4sage_5rings_11complex_mpc_MPComplexNumber {
  struct __pyx_obj_4sage_9structure_7element_FieldElement __pyx_base;
  mpc_t value;
  char init;
};


/* "sage/rings/complex_mpc.pxd":10
 *     cdef MPComplexNumber _new(self)
 * 
 * cdef class MPComplexField_class(sage.rings.ring.Field):             # <<<<<<<<<<<<<<
 *     cdef readonly int __prec
 *     cdef mpc_rnd_t __rnd
 */
struct __pyx_obj_4sage_5rings_11complex_mpc_MPComplexField_class {
  struct __pyx_obj_4sage_5rings_4ring_Field __pyx_base;
  int __prec;
  mpc_rnd_t __pyx___rnd;
  PyObject *__pyx___rnd_str;
  PyObject *__pyx___real_field;
  PyObject *__pyx___imag_field;
};


/* "symengine/lib/symengine_wrapper.pxd":4
 * from symengine cimport RCP
 * 
 * cdef class Basic(object):             # <<<<<<<<<<<<<<
 *     cdef RCP[const symengine.Basic] thisptr
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Basic {
  PyObject_HEAD
  SymEngine::RCP<SymEngine::Basic const >  thisptr;
};


/* "symengine/lib/symengine_wrapper.pxd":7
 *     cdef RCP[const symengine.Basic] thisptr
 * 
 * cdef class Number(Basic):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Number {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Basic __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":10
 *     pass
 * 
 * cdef class Integer(Number):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Integer {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Number __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":13
 *     pass
 * 
 * cdef class Rational(Number):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Rational {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Number __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":16
 *     pass
 * 
 * cdef class Complex(Number):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Complex {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Number __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":19
 *     pass
 * 
 * cdef class RealDouble(Number):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_RealDouble {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Number __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":22
 *     pass
 * 
 * cdef class ComplexDouble(Number):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ComplexDouble {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Number __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":25
 *     pass
 * 
 * cdef class RealMPFR(Number):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_RealMPFR {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Number __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":28
 *     pass
 * 
 * cdef class ComplexMPC(Number):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ComplexMPC {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Number __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":31
 *     pass
 * 
 * cdef class Add(Basic):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Add {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Basic __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":34
 *     pass
 * 
 * cdef class Mul(Basic):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Mul {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Basic __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":37
 *     pass
 * 
 * cdef class Pow(Basic):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Pow {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Basic __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":40
 *     pass
 * 
 * cdef class Function(Basic):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Function {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Basic __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":43
 *     pass
 * 
 * cdef class TrigFunction(Basic):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Basic __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":46
 *     pass
 * 
 * cdef class Sin(TrigFunction):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Sin {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":49
 *     pass
 * 
 * cdef class Cos(TrigFunction):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Cos {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":52
 *     pass
 * 
 * cdef class Tan(TrigFunction):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Tan {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":55
 *     pass
 * 
 * cdef class Cot(TrigFunction):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Cot {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":58
 *     pass
 * 
 * cdef class Csc(TrigFunction):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Csc {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":61
 *     pass
 * 
 * cdef class Sec(TrigFunction):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Sec {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":64
 *     pass
 * 
 * cdef class ASin(TrigFunction):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ASin {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":67
 *     pass
 * 
 * cdef class ACos(TrigFunction):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ACos {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":70
 *     pass
 * 
 * cdef class ATan(TrigFunction):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ATan {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":73
 *     pass
 * 
 * cdef class ACot(TrigFunction):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ACot {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":76
 *     pass
 * 
 * cdef class ACsc(TrigFunction):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ACsc {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":79
 *     pass
 * 
 * cdef class ASec(TrigFunction):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ASec {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":82
 *     pass
 * 
 * cdef class FunctionSymbol(Function):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_FunctionSymbol {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Function __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":85
 *     pass
 * 
 * cdef class FunctionWrapper(FunctionSymbol):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_FunctionWrapper {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_FunctionSymbol __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":88
 *     pass
 * 
 * cdef class Abs(Function):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Abs {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Function __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":91
 *     pass
 * 
 * cdef class Derivative(Basic):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Derivative {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Basic __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":94
 *     pass
 * 
 * cdef class Subs(Basic):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Subs {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Basic __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":97
 *     pass
 * 
 * cdef class MatrixBase(object):             # <<<<<<<<<<<<<<
 *     cdef symengine.MatrixBase* thisptr
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_MatrixBase {
  PyObject_HEAD
  SymEngine::MatrixBase *thisptr;
};


/* "symengine/lib/symengine_wrapper.pxd":100
 *     cdef symengine.MatrixBase* thisptr
 * 
 * cdef class DenseMatrix(MatrixBase):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_DenseMatrix {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_MatrixBase __pyx_base;
};


/* "symengine/lib/symengine_wrapper.pxd":103
 *     pass
 * 
 * cdef class Log(Basic):             # <<<<<<<<<<<<<<
 *     pass
 */
struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Log {
  struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Basic __pyx_base;
};



/* "sage/structure/generators.pxd":3
 * from sage.structure.sage_object cimport SageObject
 * 
 * cdef class Generators(SageObject):             # <<<<<<<<<<<<<<
 * 
 *     cdef readonly _obj
 */

struct __pyx_vtabstruct_4sage_9structure_10generators_Generators {
  PyObject *(*get_from_index)(struct __pyx_obj_4sage_9structure_10generators_Generators *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*index_set)(struct __pyx_obj_4sage_9structure_10generators_Generators *, int __pyx_skip_dispatch);
  PyObject *(*category)(struct __pyx_obj_4sage_9structure_10generators_Generators *, int __pyx_skip_dispatch);
  PyObject *(*obj)(struct __pyx_obj_4sage_9structure_10generators_Generators *, int __pyx_skip_dispatch);
  PyObject *(*count)(struct __pyx_obj_4sage_9structure_10generators_Generators *, int __pyx_skip_dispatch);
  PyObject *(*list)(struct __pyx_obj_4sage_9structure_10generators_Generators *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_10generators_Generators *__pyx_vtabptr_4sage_9structure_10generators_Generators;


/* "sage/structure/generators.pxd":16
 *     cpdef list(self)
 * 
 * cdef class Generators_finite(Generators):             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t _n
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_10generators_Generators_finite {
  struct __pyx_vtabstruct_4sage_9structure_10generators_Generators __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_10generators_Generators_finite *__pyx_vtabptr_4sage_9structure_10generators_Generators_finite;


/* "sage/structure/generators.pxd":19
 *     cdef Py_ssize_t _n
 * 
 * cdef class Generators_list(Generators_finite):             # <<<<<<<<<<<<<<
 *     cdef _List
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_10generators_Generators_list {
  struct __pyx_vtabstruct_4sage_9structure_10generators_Generators_finite __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_10generators_Generators_list *__pyx_vtabptr_4sage_9structure_10generators_Generators_list;


/* "sage/structure/generators.pxd":22
 *     cdef _List
 * 
 * cdef class Generators_naturals(Generators):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_10generators_Generators_naturals {
  struct __pyx_vtabstruct_4sage_9structure_10generators_Generators __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_10generators_Generators_naturals *__pyx_vtabptr_4sage_9structure_10generators_Generators_naturals;


/* "sage/structure/generators.pxd":25
 *     pass
 * 
 * cdef class Generators_none(Generators):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_10generators_Generators_none {
  struct __pyx_vtabstruct_4sage_9structure_10generators_Generators __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_10generators_Generators_none *__pyx_vtabptr_4sage_9structure_10generators_Generators_none;


/* "sage/structure/generators.pxd":28
 *     pass
 * 
 * cdef class Generators_lazy_all(Generators):             # <<<<<<<<<<<<<<
 *     cdef _f
 *     cdef int _compute_gens(self) except -1
 */

struct __pyx_vtabstruct_4sage_9structure_10generators_Generators_lazy_all {
  struct __pyx_vtabstruct_4sage_9structure_10generators_Generators __pyx_base;
  int (*_compute_gens)(struct __pyx_obj_4sage_9structure_10generators_Generators_lazy_all *);
};
static struct __pyx_vtabstruct_4sage_9structure_10generators_Generators_lazy_all *__pyx_vtabptr_4sage_9structure_10generators_Generators_lazy_all;


/* "sage/structure/coerce_dict.pxd":7
 * 
 * @cython.final
 * cdef class MonoDict:             # <<<<<<<<<<<<<<
 *     cdef __weakref__
 *     cdef size_t mask
 */

struct __pyx_vtabstruct_4sage_9structure_11coerce_dict_MonoDict {
  struct __pyx_t_4sage_9structure_11coerce_dict_mono_cell *(*lookup)(struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *, PyObject *);
  PyObject *(*get)(struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *, PyObject *);
  PyObject *(*set)(struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *, PyObject *, PyObject *);
  int (*resize)(struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *);
};
static struct __pyx_vtabstruct_4sage_9structure_11coerce_dict_MonoDict *__pyx_vtabptr_4sage_9structure_11coerce_dict_MonoDict;


/* "sage/structure/coerce_dict.pxd":23
 * 
 * @cython.final
 * cdef class TripleDict:             # <<<<<<<<<<<<<<
 *     cdef __weakref__
 *     cdef size_t mask
 */

struct __pyx_vtabstruct_4sage_9structure_11coerce_dict_TripleDict {
  struct __pyx_t_4sage_9structure_11coerce_dict_triple_cell *(*lookup)(struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict *, PyObject *, PyObject *, PyObject *);
  PyObject *(*get)(struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict *, PyObject *, PyObject *, PyObject *);
  PyObject *(*set)(struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict *, PyObject *, PyObject *, PyObject *, PyObject *);
  int (*resize)(struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict *);
};
static struct __pyx_vtabstruct_4sage_9structure_11coerce_dict_TripleDict *__pyx_vtabptr_4sage_9structure_11coerce_dict_TripleDict;


/* "parent.pxd":12
 * from sage.structure.coerce_dict cimport MonoDict, TripleDict
 * 
 * cdef class Parent(category_object.CategoryObject):             # <<<<<<<<<<<<<<
 * 
 *     cdef public _element_constructor
 */

struct __pyx_vtabstruct_4sage_9structure_6parent_Parent {
  int (*is_coercion_cached)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  int (*is_conversion_cached)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*register_coercion)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*register_action)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*register_conversion)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*register_embedding)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  int (*_richcmp)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int, int __pyx_skip_dispatch);
  int (*_cmp_)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  int (*is_exact)(struct __pyx_obj_4sage_9structure_6parent_Parent *, int __pyx_skip_dispatch);
  int (*init_coerce)(struct __pyx_obj_4sage_9structure_6parent_Parent *, struct __pyx_opt_args_4sage_9structure_6parent_6Parent_init_coerce *__pyx_optional_args);
  int (*has_coerce_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*coerce_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_internal_coerce_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_coerce_map_from_)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*convert_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_internal_convert_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_convert_map_from_)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*get_action)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_4sage_9structure_6parent_6Parent_get_action *__pyx_optional_args);
  PyObject *(*_get_action_)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, PyObject *, int, int __pyx_skip_dispatch);
  PyObject *(*coerce)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*an_element)(struct __pyx_obj_4sage_9structure_6parent_Parent *, int __pyx_skip_dispatch);
  PyObject *(*_generic_convert_map)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*discover_coerce_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *);
  PyObject *(*discover_convert_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *);
  PyObject *(*discover_action)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, PyObject *, int, struct __pyx_opt_args_4sage_9structure_6parent_6Parent_discover_action *__pyx_optional_args);
};
static struct __pyx_vtabstruct_4sage_9structure_6parent_Parent *__pyx_vtabptr_4sage_9structure_6parent_Parent;


/* "parent_old.pxd":11
 * cimport parent
 * from sage.structure.coerce_dict cimport MonoDict
 * cdef class Parent(parent.Parent):             # <<<<<<<<<<<<<<
 * 
 *     # returns a Morphism from S to self, or None
 */

struct __pyx_vtabstruct_4sage_9structure_10parent_old_Parent {
  struct __pyx_vtabstruct_4sage_9structure_6parent_Parent __pyx_base;
  PyObject *(*coerce_map_from_c)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*coerce_map_from_c_impl)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *);
  PyObject *(*get_action_c)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *, PyObject *, int, int __pyx_skip_dispatch);
  PyObject *(*get_action_c_impl)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *, PyObject *, int);
  PyObject *(*has_coerce_map_from_c)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*has_coerce_map_from_c_impl)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *);
  PyObject *(*_coerce_c)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_coerce_c_impl)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *);
  PyObject *(*_coerce_self_c)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *);
  PyObject *(*_an_element_c_impl)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *);
  PyObject *(*_an_element_c)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_10parent_old_Parent *__pyx_vtabptr_4sage_9structure_10parent_old_Parent;


struct __pyx_vtabstruct_4sage_9structure_11parent_base_ParentWithBase {
  struct __pyx_vtabstruct_4sage_9structure_10parent_old_Parent __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_11parent_base_ParentWithBase *__pyx_vtabptr_4sage_9structure_11parent_base_ParentWithBase;


/* "sage/structure/parent_gens.pxd":15
 * cimport parent_base
 * 
 * cdef class ParentWithGens(parent_base.ParentWithBase):             # <<<<<<<<<<<<<<
 *     cdef public object _gens
 *     cdef public object _latex_names
 */

struct __pyx_vtabstruct_4sage_9structure_11parent_gens_ParentWithGens {
  struct __pyx_vtabstruct_4sage_9structure_11parent_base_ParentWithBase __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_11parent_gens_ParentWithGens *__pyx_vtabptr_4sage_9structure_11parent_gens_ParentWithGens;


/* "sage/structure/parent_gens.pxd":21
 * 
 * 
 * cdef class ParentWithMultiplicativeAbelianGens(ParentWithGens):             # <<<<<<<<<<<<<<
 *     cdef public object _generator_orders
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_11parent_gens_ParentWithMultiplicativeAbelianGens {
  struct __pyx_vtabstruct_4sage_9structure_11parent_gens_ParentWithGens __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_11parent_gens_ParentWithMultiplicativeAbelianGens *__pyx_vtabptr_4sage_9structure_11parent_gens_ParentWithMultiplicativeAbelianGens;


/* "sage/structure/parent_gens.pxd":24
 *     cdef public object _generator_orders
 * 
 * cdef class ParentWithAdditiveAbelianGens(ParentWithGens):             # <<<<<<<<<<<<<<
 *     cdef public object _generator_orders
 */

struct __pyx_vtabstruct_4sage_9structure_11parent_gens_ParentWithAdditiveAbelianGens {
  struct __pyx_vtabstruct_4sage_9structure_11parent_gens_ParentWithGens __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_11parent_gens_ParentWithAdditiveAbelianGens *__pyx_vtabptr_4sage_9structure_11parent_gens_ParentWithAdditiveAbelianGens;


/* "sage/rings/ring.pxd":5
 * cpdef bint _is_Field(x) except -2
 * 
 * cdef class Ring(ParentWithGens):             # <<<<<<<<<<<<<<
 *     cdef public object _zero_element
 *     cdef public object _one_element
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_Ring {
  struct __pyx_vtabstruct_4sage_9structure_11parent_gens_ParentWithGens __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_Ring *__pyx_vtabptr_4sage_5rings_4ring_Ring;


/* "sage/rings/ring.pxd":13
 *     cdef _an_element_c_impl(self)
 * 
 * cdef class CommutativeRing(Ring):             # <<<<<<<<<<<<<<
 *     cdef public object __fraction_field
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeRing {
  struct __pyx_vtabstruct_4sage_5rings_4ring_Ring __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeRing *__pyx_vtabptr_4sage_5rings_4ring_CommutativeRing;


/* "sage/rings/ring.pxd":16
 *     cdef public object __fraction_field
 * 
 * cdef class IntegralDomain(CommutativeRing):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_IntegralDomain {
  struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeRing __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_IntegralDomain *__pyx_vtabptr_4sage_5rings_4ring_IntegralDomain;


/* "sage/rings/ring.pxd":19
 *     pass
 * 
 * cdef class DedekindDomain(IntegralDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_DedekindDomain {
  struct __pyx_vtabstruct_4sage_5rings_4ring_IntegralDomain __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_DedekindDomain *__pyx_vtabptr_4sage_5rings_4ring_DedekindDomain;


/* "sage/rings/ring.pxd":23
 * 
 * 
 * cdef class PrincipalIdealDomain(IntegralDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_PrincipalIdealDomain {
  struct __pyx_vtabstruct_4sage_5rings_4ring_IntegralDomain __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_PrincipalIdealDomain *__pyx_vtabptr_4sage_5rings_4ring_PrincipalIdealDomain;


/* "sage/rings/ring.pxd":26
 *     pass
 * 
 * cdef class EuclideanDomain(PrincipalIdealDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_EuclideanDomain {
  struct __pyx_vtabstruct_4sage_5rings_4ring_PrincipalIdealDomain __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_EuclideanDomain *__pyx_vtabptr_4sage_5rings_4ring_EuclideanDomain;


/* "sage/rings/ring.pxd":29
 *     pass
 * 
 * cdef class Field(PrincipalIdealDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_Field {
  struct __pyx_vtabstruct_4sage_5rings_4ring_PrincipalIdealDomain __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_Field *__pyx_vtabptr_4sage_5rings_4ring_Field;


/* "sage/rings/ring.pxd":32
 *     pass
 * 
 * cdef class Algebra(Ring):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_Algebra {
  struct __pyx_vtabstruct_4sage_5rings_4ring_Ring __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_Algebra *__pyx_vtabptr_4sage_5rings_4ring_Algebra;


/* "sage/rings/ring.pxd":35
 *     pass
 * 
 * cdef class CommutativeAlgebra(CommutativeRing):             # <<<<<<<<<<<<<<
 *     pass
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeAlgebra {
  struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeRing __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeAlgebra *__pyx_vtabptr_4sage_5rings_4ring_CommutativeAlgebra;


struct __pyx_vtabstruct_4sage_9structure_7element_Element {
  PyObject *(*_richcmp_)(struct __pyx_obj_4sage_9structure_7element_Element *, struct __pyx_obj_4sage_9structure_7element_Element *, int, int __pyx_skip_dispatch);
  int (*_cmp_)(struct __pyx_obj_4sage_9structure_7element_Element *, struct __pyx_obj_4sage_9structure_7element_Element *, int __pyx_skip_dispatch);
  PyObject *(*_richcmp)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *, int);
  int (*_cmp)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *);
  PyObject *(*_set_parent_c)(struct __pyx_obj_4sage_9structure_7element_Element *, struct __pyx_obj_4sage_9structure_6parent_Parent *);
  PyObject *(*base_extend)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_act_on_)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *, int, int __pyx_skip_dispatch);
  PyObject *(*_acted_upon_)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *, int, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_Element *__pyx_vtabptr_4sage_9structure_7element_Element;


/* "sage/structure/element.pxd":47
 *     cpdef _acted_upon_(self, x, bint self_on_left)
 * 
 * cdef class ElementWithCachedMethod(Element):             # <<<<<<<<<<<<<<
 *     cdef public dict __cached_methods
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_ElementWithCachedMethod {
  struct __pyx_vtabstruct_4sage_9structure_7element_Element __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_ElementWithCachedMethod *__pyx_vtabptr_4sage_9structure_7element_ElementWithCachedMethod;


/* "sage/structure/element.pxd":50
 *     cdef public dict __cached_methods
 * 
 * cdef class ModuleElement(Element)       # forward declaration             # <<<<<<<<<<<<<<
 * 
 * cdef class RingElement(ModuleElement)   # forward declaration
 */

struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_Element __pyx_base;
  struct __pyx_obj_4sage_9structure_7element_ModuleElement *(*_add_)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, struct __pyx_obj_4sage_9structure_7element_ModuleElement *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_ModuleElement *(*_sub_)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, struct __pyx_obj_4sage_9structure_7element_ModuleElement *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_ModuleElement *(*_neg_)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_ModuleElement *(*_lmul_)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, struct __pyx_obj_4sage_9structure_7element_RingElement *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_ModuleElement *(*_rmul_)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, struct __pyx_obj_4sage_9structure_7element_RingElement *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_ModuleElement *(*_mul_long)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, long);
  struct __pyx_obj_4sage_9structure_7element_ModuleElement *(*_iadd_)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, struct __pyx_obj_4sage_9structure_7element_ModuleElement *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_ModuleElement *(*_isub_)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, struct __pyx_obj_4sage_9structure_7element_ModuleElement *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_ModuleElement *(*_ilmul_)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, struct __pyx_obj_4sage_9structure_7element_RingElement *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_RingElement *(*coerce_to_base_ring)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, PyObject *);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement *__pyx_vtabptr_4sage_9structure_7element_ModuleElement;


/* "sage/structure/element.pxd":52
 * cdef class ModuleElement(Element)       # forward declaration
 * 
 * cdef class RingElement(ModuleElement)   # forward declaration             # <<<<<<<<<<<<<<
 * 
 * cdef class ModuleElement(Element):
 */

struct __pyx_vtabstruct_4sage_9structure_7element_RingElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement __pyx_base;
  struct __pyx_obj_4sage_9structure_7element_RingElement *(*_mul_)(struct __pyx_obj_4sage_9structure_7element_RingElement *, struct __pyx_obj_4sage_9structure_7element_RingElement *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_RingElement *(*_div_)(struct __pyx_obj_4sage_9structure_7element_RingElement *, struct __pyx_obj_4sage_9structure_7element_RingElement *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_RingElement *(*_imul_)(struct __pyx_obj_4sage_9structure_7element_RingElement *, struct __pyx_obj_4sage_9structure_7element_RingElement *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_RingElement *(*_idiv_)(struct __pyx_obj_4sage_9structure_7element_RingElement *, struct __pyx_obj_4sage_9structure_7element_RingElement *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_RingElement *(*_add_long)(struct __pyx_obj_4sage_9structure_7element_RingElement *, long);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_RingElement *__pyx_vtabptr_4sage_9structure_7element_RingElement;


/* "sage/structure/element.pxd":74
 *     cdef RingElement coerce_to_base_ring(self, x)
 * 
 * cdef class MonoidElement(Element):             # <<<<<<<<<<<<<<
 *     cpdef MonoidElement _mul_(self, MonoidElement right)
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_MonoidElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_Element __pyx_base;
  struct __pyx_obj_4sage_9structure_7element_MonoidElement *(*_mul_)(struct __pyx_obj_4sage_9structure_7element_MonoidElement *, struct __pyx_obj_4sage_9structure_7element_MonoidElement *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_MonoidElement *__pyx_vtabptr_4sage_9structure_7element_MonoidElement;


/* "sage/structure/element.pxd":77
 *     cpdef MonoidElement _mul_(self, MonoidElement right)
 * 
 * cdef class MultiplicativeGroupElement(MonoidElement):             # <<<<<<<<<<<<<<
 *     cpdef MultiplicativeGroupElement _div_(self, MultiplicativeGroupElement right)
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_MultiplicativeGroupElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_MonoidElement __pyx_base;
  struct __pyx_obj_4sage_9structure_7element_MultiplicativeGroupElement *(*_div_)(struct __pyx_obj_4sage_9structure_7element_MultiplicativeGroupElement *, struct __pyx_obj_4sage_9structure_7element_MultiplicativeGroupElement *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_MultiplicativeGroupElement *__pyx_vtabptr_4sage_9structure_7element_MultiplicativeGroupElement;


/* "sage/structure/element.pxd":81
 * 
 * 
 * cdef class AdditiveGroupElement(ModuleElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_AdditiveGroupElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_AdditiveGroupElement *__pyx_vtabptr_4sage_9structure_7element_AdditiveGroupElement;


/* "sage/structure/element.pxd":94
 *     cdef RingElement _add_long(self, long n)
 * 
 * cdef class CommutativeRingElement(RingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeRingElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_RingElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeRingElement *__pyx_vtabptr_4sage_9structure_7element_CommutativeRingElement;


/* "sage/structure/element.pxd":97
 *     pass
 * 
 * cdef class IntegralDomainElement(CommutativeRingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_IntegralDomainElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeRingElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_IntegralDomainElement *__pyx_vtabptr_4sage_9structure_7element_IntegralDomainElement;


/* "sage/structure/element.pxd":100
 *     pass
 * 
 * cdef class DedekindDomainElement(IntegralDomainElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_DedekindDomainElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_IntegralDomainElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_DedekindDomainElement *__pyx_vtabptr_4sage_9structure_7element_DedekindDomainElement;


/* "sage/structure/element.pxd":103
 *     pass
 * 
 * cdef class PrincipalIdealDomainElement(DedekindDomainElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_PrincipalIdealDomainElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_DedekindDomainElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_PrincipalIdealDomainElement *__pyx_vtabptr_4sage_9structure_7element_PrincipalIdealDomainElement;


/* "sage/structure/element.pxd":106
 *     pass
 * 
 * cdef class EuclideanDomainElement(PrincipalIdealDomainElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_EuclideanDomainElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_PrincipalIdealDomainElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_EuclideanDomainElement *__pyx_vtabptr_4sage_9structure_7element_EuclideanDomainElement;


/* "sage/structure/element.pxd":109
 *     pass
 * 
 * cdef class FieldElement(CommutativeRingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_FieldElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeRingElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_FieldElement *__pyx_vtabptr_4sage_9structure_7element_FieldElement;


/* "sage/structure/element.pxd":112
 *     pass
 * 
 * cdef class AlgebraElement(RingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_AlgebraElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_RingElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_AlgebraElement *__pyx_vtabptr_4sage_9structure_7element_AlgebraElement;


/* "sage/structure/element.pxd":115
 *     pass
 * 
 * cdef class CommutativeAlgebraElement(CommutativeRingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeAlgebraElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeRingElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeAlgebraElement *__pyx_vtabptr_4sage_9structure_7element_CommutativeAlgebraElement;


/* "sage/structure/element.pxd":118
 *     pass
 * 
 * cdef class CommutativeAlgebra(AlgebraElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeAlgebra {
  struct __pyx_vtabstruct_4sage_9structure_7element_AlgebraElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeAlgebra *__pyx_vtabptr_4sage_9structure_7element_CommutativeAlgebra;


/* "sage/structure/element.pxd":121
 *     pass
 * 
 * cdef class InfinityElement(RingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_InfinityElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_RingElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_InfinityElement *__pyx_vtabptr_4sage_9structure_7element_InfinityElement;


/* "sage/structure/element.pxd":125
 * 
 * 
 * cdef class Vector(ModuleElement):             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t _degree
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_Vector {
  struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement __pyx_base;
  struct __pyx_obj_4sage_9structure_7element_Element *(*_dot_product_)(struct __pyx_obj_4sage_9structure_7element_Vector *, struct __pyx_obj_4sage_9structure_7element_Vector *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_Element *(*_dot_product_coerce_)(struct __pyx_obj_4sage_9structure_7element_Vector *, struct __pyx_obj_4sage_9structure_7element_Vector *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_Vector *(*_pairwise_product_)(struct __pyx_obj_4sage_9structure_7element_Vector *, struct __pyx_obj_4sage_9structure_7element_Vector *, int __pyx_skip_dispatch);
  int (*is_sparse_c)(struct __pyx_obj_4sage_9structure_7element_Vector *);
  int (*is_dense_c)(struct __pyx_obj_4sage_9structure_7element_Vector *);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_Vector *__pyx_vtabptr_4sage_9structure_7element_Vector;


/* "sage/structure/element.pxd":140
 * 
 * 
 * cdef class Matrix(ModuleElement):             # <<<<<<<<<<<<<<
 *     # All matrix classes must be written in Cython
 *     cdef Py_ssize_t _nrows
 */

struct __pyx_vtabstruct_4sage_9structure_7element_Matrix {
  struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement __pyx_base;
  struct __pyx_obj_4sage_9structure_7element_Vector *(*_vector_times_matrix_)(struct __pyx_obj_4sage_9structure_7element_Matrix *, struct __pyx_obj_4sage_9structure_7element_Vector *);
  struct __pyx_obj_4sage_9structure_7element_Vector *(*_matrix_times_vector_)(struct __pyx_obj_4sage_9structure_7element_Matrix *, struct __pyx_obj_4sage_9structure_7element_Vector *);
  struct __pyx_obj_4sage_9structure_7element_Matrix *(*_matrix_times_matrix_)(struct __pyx_obj_4sage_9structure_7element_Matrix *, struct __pyx_obj_4sage_9structure_7element_Matrix *);
  int (*is_sparse_c)(struct __pyx_obj_4sage_9structure_7element_Matrix *);
  int (*is_dense_c)(struct __pyx_obj_4sage_9structure_7element_Matrix *);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_Matrix *__pyx_vtabptr_4sage_9structure_7element_Matrix;


/* "sage/structure/element.pxd":155
 * 
 * 
 * cdef class CoercionModel:             # <<<<<<<<<<<<<<
 *     cpdef canonical_coercion(self, x, y)
 *     cpdef bin_op(self, x, y, op)
 */

struct __pyx_vtabstruct_4sage_9structure_7element_CoercionModel {
  PyObject *(*canonical_coercion)(struct __pyx_obj_4sage_9structure_7element_CoercionModel *, PyObject *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*bin_op)(struct __pyx_obj_4sage_9structure_7element_CoercionModel *, PyObject *, PyObject *, PyObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_CoercionModel *__pyx_vtabptr_4sage_9structure_7element_CoercionModel;


/* "map.pxd":4
 * from sage.structure.element cimport Element
 * 
 * cdef class Map(Element):             # <<<<<<<<<<<<<<
 *     cdef public int _coerce_cost # a rough measure of the cost of using this morphism in the coercion system.
 *                           # 10 by default, 100 if a DefaultCoercionMorphism, 10000 if inexact.
 */

struct __pyx_vtabstruct_4sage_10categories_3map_Map {
  struct __pyx_vtabstruct_4sage_9structure_7element_Element __pyx_base;
  PyObject *(*_update_slots)(struct __pyx_obj_4sage_10categories_3map_Map *, PyObject *);
  PyObject *(*_extra_slots)(struct __pyx_obj_4sage_10categories_3map_Map *, PyObject *);
  struct __pyx_obj_4sage_9structure_7element_Element *(*_call_)(struct __pyx_obj_4sage_10categories_3map_Map *, PyObject *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_Element *(*_call_with_args)(struct __pyx_obj_4sage_10categories_3map_Map *, PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_4sage_10categories_3map_3Map__call_with_args *__pyx_optional_args);
};
static struct __pyx_vtabstruct_4sage_10categories_3map_Map *__pyx_vtabptr_4sage_10categories_3map_Map;


/* "map.pxd":23
 * 
 * 
 * cdef class Section(Map):             # <<<<<<<<<<<<<<
 *     cdef Map _inverse
 * 
 */

struct __pyx_vtabstruct_4sage_10categories_3map_Section {
  struct __pyx_vtabstruct_4sage_10categories_3map_Map __pyx_base;
};
static struct __pyx_vtabstruct_4sage_10categories_3map_Section *__pyx_vtabptr_4sage_10categories_3map_Section;


/* "map.pxd":26
 *     cdef Map _inverse
 * 
 * cdef class FormalCompositeMap(Map):             # <<<<<<<<<<<<<<
 *     cdef __list
 */

struct __pyx_vtabstruct_4sage_10categories_3map_FormalCompositeMap {
  struct __pyx_vtabstruct_4sage_10categories_3map_Map __pyx_base;
};
static struct __pyx_vtabstruct_4sage_10categories_3map_FormalCompositeMap *__pyx_vtabptr_4sage_10categories_3map_FormalCompositeMap;


/* "sage/categories/morphism.pxd":5
 * from map cimport Map
 * 
 * cdef class Morphism(Map):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_10categories_8morphism_Morphism {
  struct __pyx_vtabstruct_4sage_10categories_3map_Map __pyx_base;
};
static struct __pyx_vtabstruct_4sage_10categories_8morphism_Morphism *__pyx_vtabptr_4sage_10categories_8morphism_Morphism;


/* "sage/categories/morphism.pxd":8
 *     pass
 * 
 * cdef class SetMorphism(Morphism):             # <<<<<<<<<<<<<<
 *     cdef object _function
 *     cpdef bint _eq_c_impl(left, Element right)
 */

struct __pyx_vtabstruct_4sage_10categories_8morphism_SetMorphism {
  struct __pyx_vtabstruct_4sage_10categories_8morphism_Morphism __pyx_base;
  int (*_eq_c_impl)(struct __pyx_obj_4sage_10categories_8morphism_SetMorphism *, struct __pyx_obj_4sage_9structure_7element_Element *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_10categories_8morphism_SetMorphism *__pyx_vtabptr_4sage_10categories_8morphism_SetMorphism;


/* "sage/rings/integer.pxd":7
 * from sage.categories.morphism cimport Morphism
 * 
 * cdef class Integer(EuclideanDomainElement):             # <<<<<<<<<<<<<<
 *     cdef mpz_t value
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_7integer_Integer {
  struct __pyx_vtabstruct_4sage_9structure_7element_EuclideanDomainElement __pyx_base;
  void (*_to_ZZ)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct ZZ *);
  void (*set_from_mpz)(struct __pyx_obj_4sage_5rings_7integer_Integer *, __mpz_struct *);
  PyObject *(*hash_c)(struct __pyx_obj_4sage_5rings_7integer_Integer *);
  PyObject *(*_pari_)(struct __pyx_obj_4sage_5rings_7integer_Integer *, int __pyx_skip_dispatch);
  PyObject *(*_shift_helper)(struct __pyx_obj_4sage_5rings_7integer_Integer *, PyObject *, int, int __pyx_skip_dispatch);
  PyObject *(*_and)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
  PyObject *(*_or)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
  PyObject *(*_xor)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
  size_t (*_exact_log_log2_iter)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *, int __pyx_skip_dispatch);
  size_t (*_exact_log_mpfi_log)(struct __pyx_obj_4sage_5rings_7integer_Integer *, PyObject *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_RingElement *(*_valuation)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *, int __pyx_skip_dispatch);
  PyObject *(*_val_unit)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
  struct __pyx_obj_4sage_5rings_7integer_Integer *(*_divide_knowing_divisible_by)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
  int (*_is_power_of)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
  int (*_pseudoprime_is_prime)(struct __pyx_obj_4sage_5rings_7integer_Integer *, PyObject *);
  PyObject *(*_reduce_set)(struct __pyx_obj_4sage_5rings_7integer_Integer *, PyObject *);
};
static struct __pyx_vtabstruct_4sage_5rings_7integer_Integer *__pyx_vtabptr_4sage_5rings_7integer_Integer;


/* "sage/rings/integer.pxd":36
 * cdef Integer smallInteger(long value)
 * 
 * cdef class int_to_Z(Morphism):             # <<<<<<<<<<<<<<
 *     pass
 */

struct __pyx_vtabstruct_4sage_5rings_7integer_int_to_Z {
  struct __pyx_vtabstruct_4sage_10categories_8morphism_Morphism __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_7integer_int_to_Z *__pyx_vtabptr_4sage_5rings_7integer_int_to_Z;


/* "sage/rings/rational.pxd":8
 * cpdef rational_power_parts(a, b, factor_limit=?)
 * 
 * cdef class Rational(sage.structure.element.FieldElement):             # <<<<<<<<<<<<<<
 *     cdef mpq_t value
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_8rational_Rational {
  struct __pyx_vtabstruct_4sage_9structure_7element_FieldElement __pyx_base;
  PyObject *(*__pyx___set_value)(struct __pyx_obj_4sage_5rings_8rational_Rational *, PyObject *, unsigned int);
  void (*set_from_mpq)(struct __pyx_obj_4sage_5rings_8rational_Rational *, __mpq_struct *);
  PyObject *(*_lshift)(struct __pyx_obj_4sage_5rings_8rational_Rational *, long);
  PyObject *(*_rshift)(struct __pyx_obj_4sage_5rings_8rational_Rational *, long);
  PyObject *(*_val_unit)(struct __pyx_obj_4sage_5rings_8rational_Rational *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
};
static struct __pyx_vtabstruct_4sage_5rings_8rational_Rational *__pyx_vtabptr_4sage_5rings_8rational_Rational;


/* "sage/rings/real_mpfr.pxd":10
 * 
 * 
 * cdef class RealNumber(sage.structure.element.RingElement)  # forward decl             # <<<<<<<<<<<<<<
 * 
 * cdef class RealField_class(sage.rings.ring.Field):
 */

struct __pyx_vtabstruct_4sage_5rings_9real_mpfr_RealNumber {
  struct __pyx_vtabstruct_4sage_9structure_7element_RingElement __pyx_base;
  struct __pyx_obj_4sage_5rings_9real_mpfr_RealNumber *(*_new)(struct __pyx_obj_4sage_5rings_9real_mpfr_RealNumber *);
  PyObject *(*_set)(struct __pyx_obj_4sage_5rings_9real_mpfr_RealNumber *, PyObject *, int);
  PyObject *(*_set_from_GEN_REAL)(struct __pyx_obj_4sage_5rings_9real_mpfr_RealNumber *, GEN);
  struct __pyx_obj_4sage_5rings_9real_mpfr_RealNumber *(*abs)(struct __pyx_obj_4sage_5rings_9real_mpfr_RealNumber *);
};
static struct __pyx_vtabstruct_4sage_5rings_9real_mpfr_RealNumber *__pyx_vtabptr_4sage_5rings_9real_mpfr_RealNumber;


/* "sage/rings/real_mpfr.pxd":12
 * cdef class RealNumber(sage.structure.element.RingElement)  # forward decl
 * 
 * cdef class RealField_class(sage.rings.ring.Field):             # <<<<<<<<<<<<<<
 *     cdef int __prec
 *     cdef bint sci_not
 */

struct __pyx_vtabstruct_4sage_5rings_9real_mpfr_RealField_class {
  struct __pyx_vtabstruct_4sage_5rings_4ring_Field __pyx_base;
  struct __pyx_obj_4sage_5rings_9real_mpfr_RealNumber *(*_new)(struct __pyx_obj_4sage_5rings_9real_mpfr_RealField_class *);
};
static struct __pyx_vtabstruct_4sage_5rings_9real_mpfr_RealField_class *__pyx_vtabptr_4sage_5rings_9real_mpfr_RealField_class;


/* "sage/rings/complex_mpc.pxd":5
 * cimport sage.rings.ring
 * 
 * cdef class MPComplexNumber(sage.structure.element.FieldElement):             # <<<<<<<<<<<<<<
 *     cdef mpc_t value
 *     cdef char init
 */

struct __pyx_vtabstruct_4sage_5rings_11complex_mpc_MPComplexNumber {
  struct __pyx_vtabstruct_4sage_9structure_7element_FieldElement __pyx_base;
  struct __pyx_obj_4sage_5rings_11complex_mpc_MPComplexNumber *(*_new)(struct __pyx_obj_4sage_5rings_11complex_mpc_MPComplexNumber *);
};
static struct __pyx_vtabstruct_4sage_5rings_11complex_mpc_MPComplexNumber *__pyx_vtabptr_4sage_5rings_11complex_mpc_MPComplexNumber;


/* "sage/rings/complex_mpc.pxd":10
 *     cdef MPComplexNumber _new(self)
 * 
 * cdef class MPComplexField_class(sage.rings.ring.Field):             # <<<<<<<<<<<<<<
 *     cdef readonly int __prec
 *     cdef mpc_rnd_t __rnd
 */

struct __pyx_vtabstruct_4sage_5rings_11complex_mpc_MPComplexField_class {
  struct __pyx_vtabstruct_4sage_5rings_4ring_Field __pyx_base;
  struct __pyx_obj_4sage_5rings_11complex_mpc_MPComplexNumber *(*_new)(struct __pyx_obj_4sage_5rings_11complex_mpc_MPComplexField_class *);
  PyObject *(*_an_element_)(struct __pyx_obj_4sage_5rings_11complex_mpc_MPComplexField_class *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_5rings_11complex_mpc_MPComplexField_class *__pyx_vtabptr_4sage_5rings_11complex_mpc_MPComplexField_class;

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/* Module declarations from 'libc.string' */

/* Module declarations from 'libc.stdio' */

/* Module declarations from 'sage.libs.gmp.types' */

/* Module declarations from '__builtin__' */

/* Module declarations from 'cpython.type' */
static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0;

/* Module declarations from 'cpython.version' */

/* Module declarations from 'cpython.exc' */

/* Module declarations from 'cpython.module' */

/* Module declarations from 'cpython.mem' */

/* Module declarations from 'cpython.tuple' */

/* Module declarations from 'cpython.list' */

/* Module declarations from 'cpython.sequence' */

/* Module declarations from 'cpython.mapping' */

/* Module declarations from 'cpython.iterator' */

/* Module declarations from 'cpython.number' */

/* Module declarations from 'cpython.int' */

/* Module declarations from '__builtin__' */

/* Module declarations from 'cpython.bool' */
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/* Module declarations from 'cpython.long' */

/* Module declarations from 'cpython.float' */

/* Module declarations from '__builtin__' */

/* Module declarations from 'cpython.complex' */
static PyTypeObject *__pyx_ptype_7cpython_7complex_complex = 0;

/* Module declarations from 'cpython.string' */

/* Module declarations from 'cpython.unicode' */

/* Module declarations from 'cpython.dict' */

/* Module declarations from 'cpython.instance' */

/* Module declarations from 'cpython.function' */

/* Module declarations from 'cpython.method' */

/* Module declarations from 'cpython.weakref' */

/* Module declarations from 'cpython.getargs' */

/* Module declarations from 'cpython.pythread' */

/* Module declarations from 'cpython.pystate' */

/* Module declarations from 'cpython.cobject' */

/* Module declarations from 'cpython.oldbuffer' */

/* Module declarations from 'cpython.set' */

/* Module declarations from 'cpython.buffer' */

/* Module declarations from 'cpython.bytes' */

/* Module declarations from 'cpython.pycapsule' */

/* Module declarations from 'cpython' */

/* Module declarations from 'cpython.object' */

/* Module declarations from 'cpython.ref' */

/* Module declarations from 'cpython.slice' */

/* Module declarations from 'sage.libs.ntl.ntl_ZZ_decl' */

/* Module declarations from 'sage.libs.ntl.ntl_lzz_p_decl' */

/* Module declarations from 'sage.libs.ntl.ntl_lzz_pX_decl' */

/* Module declarations from 'sage.libs.ntl.ntl_ZZ_p_decl' */

/* Module declarations from 'sage.libs.ntl.ntl_vec_ZZ_p_decl' */

/* Module declarations from 'sage.libs.ntl.ntl_ZZX_decl' */

/* Module declarations from 'sage.libs.ntl.ntl_ZZ_pContext_decl' */

/* Module declarations from 'sage.libs.ntl.ntl_ZZ_pX_decl' */

/* Module declarations from 'sage.libs.ntl.ntl_lzz_pContext_decl' */

/* Module declarations from 'sage.libs.ntl.ntl_ZZ_pEContext_decl' */

/* Module declarations from 'sage.libs.ntl.ntl_ZZ_pE_decl' */

/* Module declarations from 'sage.libs.ntl.ntl_vec_ZZ_pE_decl' */

/* Module declarations from 'sage.libs.ntl.ntl_ZZ_pEX_decl' */

/* Module declarations from 'sage.libs.ntl.convert' */
static void (*__pyx_f_4sage_4libs_3ntl_7convert_ZZ_to_mpz)(__mpz_struct *, struct ZZ *); /*proto*/
static void (*__pyx_f_4sage_4libs_3ntl_7convert_mpz_to_ZZ)(struct ZZ *, mpz_srcptr); /*proto*/

/* Module declarations from 'libc.stdint' */

/* Module declarations from 'sage.structure.sage_object' */
static PyTypeObject *__pyx_ptype_4sage_9structure_11sage_object_SageObject = 0;
static CYTHON_INLINE int __pyx_f_4sage_9structure_11sage_object_rich_to_bool(int, int); /*proto*/

/* Module declarations from 'sage.structure.generators' */
static PyTypeObject *__pyx_ptype_4sage_9structure_10generators_Generators = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_10generators_Generators_finite = 0;
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/* Module declarations from 'sage.structure.category_object' */
static PyTypeObject *__pyx_ptype_4sage_9structure_15category_object_CategoryObject = 0;

/* Module declarations from 'cython' */

/* Module declarations from 'sage.structure.coerce_dict' */
static PyTypeObject *__pyx_ptype_4sage_9structure_11coerce_dict_MonoDict = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_11coerce_dict_TripleDict = 0;

/* Module declarations from 'sage.structure' */

/* Module declarations from 'sage.structure.parent_old' */
static PyTypeObject *__pyx_ptype_4sage_9structure_10parent_old_Parent = 0;

/* Module declarations from 'sage.structure.parent_base' */
static PyTypeObject *__pyx_ptype_4sage_9structure_11parent_base_ParentWithBase = 0;

/* Module declarations from 'sage.structure.parent_gens' */
static PyTypeObject *__pyx_ptype_4sage_9structure_11parent_gens_ParentWithGens = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_11parent_gens_ParentWithMultiplicativeAbelianGens = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_11parent_gens_ParentWithAdditiveAbelianGens = 0;

/* Module declarations from 'sage.rings.ring' */
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_Ring = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_CommutativeRing = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_IntegralDomain = 0;
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static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_EuclideanDomain = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_Field = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_Algebra = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_CommutativeAlgebra = 0;

/* Module declarations from 'sage.rings' */

/* Module declarations from 'sage' */

/* Module declarations from 'sage.structure.parent' */
static PyTypeObject *__pyx_ptype_4sage_9structure_6parent_Parent = 0;

/* Module declarations from 'sage.structure.element' */
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_Element = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_ElementWithCachedMethod = 0;
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static PyTypeObject *__pyx_ptype_4sage_9structure_7element_AlgebraElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_CommutativeAlgebraElement = 0;
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static PyTypeObject *__pyx_ptype_4sage_9structure_7element_InfinityElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_Vector = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_Matrix = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_CoercionModel = 0;

/* Module declarations from 'sage.categories.map' */
static PyTypeObject *__pyx_ptype_4sage_10categories_3map_Map = 0;
static PyTypeObject *__pyx_ptype_4sage_10categories_3map_Section = 0;
static PyTypeObject *__pyx_ptype_4sage_10categories_3map_FormalCompositeMap = 0;

/* Module declarations from 'sage.categories.morphism' */
static PyTypeObject *__pyx_ptype_4sage_10categories_8morphism_Morphism = 0;
static PyTypeObject *__pyx_ptype_4sage_10categories_8morphism_SetMorphism = 0;

/* Module declarations from 'sage.rings.integer' */
static PyTypeObject *__pyx_ptype_4sage_5rings_7integer_Integer = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_7integer_int_to_Z = 0;

/* Module declarations from 'sage.rings.rational' */
static PyTypeObject *__pyx_ptype_4sage_5rings_8rational_Rational = 0;

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/* Module declarations from 'sage.rings.real_mpfr' */
static PyTypeObject *__pyx_ptype_4sage_5rings_9real_mpfr_RealNumber = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_9real_mpfr_RealField_class = 0;

/* Module declarations from 'sage.libs.mpc' */

/* Module declarations from 'sage.rings.complex_mpc' */
static PyTypeObject *__pyx_ptype_4sage_5rings_11complex_mpc_MPComplexNumber = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_11complex_mpc_MPComplexField_class = 0;

/* Module declarations from 'libcpp' */

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/* Module declarations from 'libcpp.map' */

/* Module declarations from 'libcpp.vector' */

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/* Module declarations from 'symengine.lib.symengine_wrapper' */
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Basic = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Number = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Integer = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Rational = 0;
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static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_ComplexDouble = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_RealMPFR = 0;
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static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Add = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Mul = 0;
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static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_TrigFunction = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Sin = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Cos = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Tan = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Cot = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Csc = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Sec = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_ASin = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_ACos = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_ATan = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_ACot = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_ACsc = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_ASec = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_FunctionSymbol = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_FunctionWrapper = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Abs = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Derivative = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Subs = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_MatrixBase = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_DenseMatrix = 0;
static PyTypeObject *__pyx_ptype_9symengine_3lib_17symengine_wrapper_Log = 0;

/* Module declarations from 'sage.symbolic.symengine_conversions' */
#define __Pyx_MODULE_NAME "sage.symbolic.symengine_conversions"
int __pyx_module_is_main_sage__symbolic__symengine_conversions = 0;

/* Implementation of 'sage.symbolic.symengine_conversions' */
static PyObject *__pyx_builtin_AttributeError;
static PyObject *__pyx_pf_4sage_8symbolic_21symengine_conversions_convert_to_integer(CYTHON_UNUSED PyObject *__pyx_self, struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Integer *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_4sage_8symbolic_21symengine_conversions_2convert_to_rational(CYTHON_UNUSED PyObject *__pyx_self, struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Rational *__pyx_v_i); /* proto */
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  __pyx_vtabptr_4sage_5rings_4ring_DedekindDomain = (struct __pyx_vtabstruct_4sage_5rings_4ring_DedekindDomain*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_4ring_DedekindDomain->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_4ring_DedekindDomain)) {__pyx_filename = __pyx_f[12]; __pyx_lineno = 19; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_5rings_4ring_PrincipalIdealDomain = __Pyx_ImportType("sage.rings.ring", "PrincipalIdealDomain", sizeof(struct __pyx_obj_4sage_5rings_4ring_PrincipalIdealDomain), 1); if (unlikely(!__pyx_ptype_4sage_5rings_4ring_PrincipalIdealDomain)) {__pyx_filename = __pyx_f[12]; __pyx_lineno = 23; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_5rings_4ring_PrincipalIdealDomain = (struct __pyx_vtabstruct_4sage_5rings_4ring_PrincipalIdealDomain*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_4ring_PrincipalIdealDomain->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_4ring_PrincipalIdealDomain)) {__pyx_filename = __pyx_f[12]; __pyx_lineno = 23; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_5rings_4ring_EuclideanDomain = __Pyx_ImportType("sage.rings.ring", "EuclideanDomain", sizeof(struct __pyx_obj_4sage_5rings_4ring_EuclideanDomain), 1); if (unlikely(!__pyx_ptype_4sage_5rings_4ring_EuclideanDomain)) {__pyx_filename = __pyx_f[12]; __pyx_lineno = 26; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_5rings_4ring_EuclideanDomain = (struct __pyx_vtabstruct_4sage_5rings_4ring_EuclideanDomain*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_4ring_EuclideanDomain->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_4ring_EuclideanDomain)) {__pyx_filename = __pyx_f[12]; __pyx_lineno = 26; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_5rings_4ring_Field = __Pyx_ImportType("sage.rings.ring", "Field", sizeof(struct __pyx_obj_4sage_5rings_4ring_Field), 1); if (unlikely(!__pyx_ptype_4sage_5rings_4ring_Field)) {__pyx_filename = __pyx_f[12]; __pyx_lineno = 29; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_5rings_4ring_Field = (struct __pyx_vtabstruct_4sage_5rings_4ring_Field*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_4ring_Field->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_4ring_Field)) {__pyx_filename = __pyx_f[12]; __pyx_lineno = 29; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_5rings_4ring_Algebra = __Pyx_ImportType("sage.rings.ring", "Algebra", sizeof(struct __pyx_obj_4sage_5rings_4ring_Algebra), 1); if (unlikely(!__pyx_ptype_4sage_5rings_4ring_Algebra)) {__pyx_filename = __pyx_f[12]; __pyx_lineno = 32; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_5rings_4ring_Algebra = (struct __pyx_vtabstruct_4sage_5rings_4ring_Algebra*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_4ring_Algebra->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_4ring_Algebra)) {__pyx_filename = __pyx_f[12]; __pyx_lineno = 32; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_5rings_4ring_CommutativeAlgebra = __Pyx_ImportType("sage.rings.ring", "CommutativeAlgebra", sizeof(struct __pyx_obj_4sage_5rings_4ring_CommutativeAlgebra), 1); if (unlikely(!__pyx_ptype_4sage_5rings_4ring_CommutativeAlgebra)) {__pyx_filename = __pyx_f[12]; __pyx_lineno = 35; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_5rings_4ring_CommutativeAlgebra = (struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeAlgebra*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_4ring_CommutativeAlgebra->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_4ring_CommutativeAlgebra)) {__pyx_filename = __pyx_f[12]; __pyx_lineno = 35; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_6parent_Parent = __Pyx_ImportType("sage.structure.parent", "Parent", sizeof(struct __pyx_obj_4sage_9structure_6parent_Parent), 1); if (unlikely(!__pyx_ptype_4sage_9structure_6parent_Parent)) {__pyx_filename = __pyx_f[13]; __pyx_lineno = 12; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_6parent_Parent = (struct __pyx_vtabstruct_4sage_9structure_6parent_Parent*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_6parent_Parent->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_6parent_Parent)) {__pyx_filename = __pyx_f[13]; __pyx_lineno = 12; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_Element = __Pyx_ImportType("sage.structure.element", "Element", sizeof(struct __pyx_obj_4sage_9structure_7element_Element), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_Element)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 35; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_Element = (struct __pyx_vtabstruct_4sage_9structure_7element_Element*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_Element->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_Element)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 35; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_ElementWithCachedMethod = __Pyx_ImportType("sage.structure.element", "ElementWithCachedMethod", sizeof(struct __pyx_obj_4sage_9structure_7element_ElementWithCachedMethod), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_ElementWithCachedMethod)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 47; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_ElementWithCachedMethod = (struct __pyx_vtabstruct_4sage_9structure_7element_ElementWithCachedMethod*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_ElementWithCachedMethod->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_ElementWithCachedMethod)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 47; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_ModuleElement = __Pyx_ImportType("sage.structure.element", "ModuleElement", sizeof(struct __pyx_obj_4sage_9structure_7element_ModuleElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_ModuleElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 50; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_ModuleElement = (struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_ModuleElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_ModuleElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 50; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_RingElement = __Pyx_ImportType("sage.structure.element", "RingElement", sizeof(struct __pyx_obj_4sage_9structure_7element_RingElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_RingElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 52; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_RingElement = (struct __pyx_vtabstruct_4sage_9structure_7element_RingElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_RingElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_RingElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 52; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_MonoidElement = __Pyx_ImportType("sage.structure.element", "MonoidElement", sizeof(struct __pyx_obj_4sage_9structure_7element_MonoidElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_MonoidElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 74; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_MonoidElement = (struct __pyx_vtabstruct_4sage_9structure_7element_MonoidElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_MonoidElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_MonoidElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 74; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_MultiplicativeGroupElement = __Pyx_ImportType("sage.structure.element", "MultiplicativeGroupElement", sizeof(struct __pyx_obj_4sage_9structure_7element_MultiplicativeGroupElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_MultiplicativeGroupElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 77; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_MultiplicativeGroupElement = (struct __pyx_vtabstruct_4sage_9structure_7element_MultiplicativeGroupElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_MultiplicativeGroupElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_MultiplicativeGroupElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 77; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_AdditiveGroupElement = __Pyx_ImportType("sage.structure.element", "AdditiveGroupElement", sizeof(struct __pyx_obj_4sage_9structure_7element_AdditiveGroupElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_AdditiveGroupElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 81; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_AdditiveGroupElement = (struct __pyx_vtabstruct_4sage_9structure_7element_AdditiveGroupElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_AdditiveGroupElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_AdditiveGroupElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 81; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_CommutativeRingElement = __Pyx_ImportType("sage.structure.element", "CommutativeRingElement", sizeof(struct __pyx_obj_4sage_9structure_7element_CommutativeRingElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_CommutativeRingElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 94; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_CommutativeRingElement = (struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeRingElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_CommutativeRingElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_CommutativeRingElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 94; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_IntegralDomainElement = __Pyx_ImportType("sage.structure.element", "IntegralDomainElement", sizeof(struct __pyx_obj_4sage_9structure_7element_IntegralDomainElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_IntegralDomainElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 97; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_IntegralDomainElement = (struct __pyx_vtabstruct_4sage_9structure_7element_IntegralDomainElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_IntegralDomainElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_IntegralDomainElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 97; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_DedekindDomainElement = __Pyx_ImportType("sage.structure.element", "DedekindDomainElement", sizeof(struct __pyx_obj_4sage_9structure_7element_DedekindDomainElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_DedekindDomainElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 100; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_DedekindDomainElement = (struct __pyx_vtabstruct_4sage_9structure_7element_DedekindDomainElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_DedekindDomainElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_DedekindDomainElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 100; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_PrincipalIdealDomainElement = __Pyx_ImportType("sage.structure.element", "PrincipalIdealDomainElement", sizeof(struct __pyx_obj_4sage_9structure_7element_PrincipalIdealDomainElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_PrincipalIdealDomainElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 103; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_PrincipalIdealDomainElement = (struct __pyx_vtabstruct_4sage_9structure_7element_PrincipalIdealDomainElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_PrincipalIdealDomainElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_PrincipalIdealDomainElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 103; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_EuclideanDomainElement = __Pyx_ImportType("sage.structure.element", "EuclideanDomainElement", sizeof(struct __pyx_obj_4sage_9structure_7element_EuclideanDomainElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_EuclideanDomainElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 106; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_EuclideanDomainElement = (struct __pyx_vtabstruct_4sage_9structure_7element_EuclideanDomainElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_EuclideanDomainElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_EuclideanDomainElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 106; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_FieldElement = __Pyx_ImportType("sage.structure.element", "FieldElement", sizeof(struct __pyx_obj_4sage_9structure_7element_FieldElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_FieldElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 109; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_FieldElement = (struct __pyx_vtabstruct_4sage_9structure_7element_FieldElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_FieldElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_FieldElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 109; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_AlgebraElement = __Pyx_ImportType("sage.structure.element", "AlgebraElement", sizeof(struct __pyx_obj_4sage_9structure_7element_AlgebraElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_AlgebraElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 112; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_AlgebraElement = (struct __pyx_vtabstruct_4sage_9structure_7element_AlgebraElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_AlgebraElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_AlgebraElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 112; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_CommutativeAlgebraElement = __Pyx_ImportType("sage.structure.element", "CommutativeAlgebraElement", sizeof(struct __pyx_obj_4sage_9structure_7element_CommutativeAlgebraElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_CommutativeAlgebraElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 115; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_CommutativeAlgebraElement = (struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeAlgebraElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_CommutativeAlgebraElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_CommutativeAlgebraElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 115; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_CommutativeAlgebra = __Pyx_ImportType("sage.structure.element", "CommutativeAlgebra", sizeof(struct __pyx_obj_4sage_9structure_7element_CommutativeAlgebra), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_CommutativeAlgebra)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 118; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_CommutativeAlgebra = (struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeAlgebra*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_CommutativeAlgebra->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_CommutativeAlgebra)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 118; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_InfinityElement = __Pyx_ImportType("sage.structure.element", "InfinityElement", sizeof(struct __pyx_obj_4sage_9structure_7element_InfinityElement), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_InfinityElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 121; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_InfinityElement = (struct __pyx_vtabstruct_4sage_9structure_7element_InfinityElement*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_InfinityElement->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_InfinityElement)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 121; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_Vector = __Pyx_ImportType("sage.structure.element", "Vector", sizeof(struct __pyx_obj_4sage_9structure_7element_Vector), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_Vector)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 125; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_Vector = (struct __pyx_vtabstruct_4sage_9structure_7element_Vector*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_Vector->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_Vector)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 125; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_Matrix = __Pyx_ImportType("sage.structure.element", "Matrix", sizeof(struct __pyx_obj_4sage_9structure_7element_Matrix), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_Matrix)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 140; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_Matrix = (struct __pyx_vtabstruct_4sage_9structure_7element_Matrix*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_Matrix->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_Matrix)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 140; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_9structure_7element_CoercionModel = __Pyx_ImportType("sage.structure.element", "CoercionModel", sizeof(struct __pyx_obj_4sage_9structure_7element_CoercionModel), 1); if (unlikely(!__pyx_ptype_4sage_9structure_7element_CoercionModel)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 155; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_9structure_7element_CoercionModel = (struct __pyx_vtabstruct_4sage_9structure_7element_CoercionModel*)__Pyx_GetVtable(__pyx_ptype_4sage_9structure_7element_CoercionModel->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_9structure_7element_CoercionModel)) {__pyx_filename = __pyx_f[1]; __pyx_lineno = 155; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_10categories_3map_Map = __Pyx_ImportType("sage.categories.map", "Map", sizeof(struct __pyx_obj_4sage_10categories_3map_Map), 1); if (unlikely(!__pyx_ptype_4sage_10categories_3map_Map)) {__pyx_filename = __pyx_f[14]; __pyx_lineno = 4; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_10categories_3map_Map = (struct __pyx_vtabstruct_4sage_10categories_3map_Map*)__Pyx_GetVtable(__pyx_ptype_4sage_10categories_3map_Map->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_10categories_3map_Map)) {__pyx_filename = __pyx_f[14]; __pyx_lineno = 4; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_10categories_3map_Section = __Pyx_ImportType("sage.categories.map", "Section", sizeof(struct __pyx_obj_4sage_10categories_3map_Section), 1); if (unlikely(!__pyx_ptype_4sage_10categories_3map_Section)) {__pyx_filename = __pyx_f[14]; __pyx_lineno = 23; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_10categories_3map_Section = (struct __pyx_vtabstruct_4sage_10categories_3map_Section*)__Pyx_GetVtable(__pyx_ptype_4sage_10categories_3map_Section->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_10categories_3map_Section)) {__pyx_filename = __pyx_f[14]; __pyx_lineno = 23; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_10categories_3map_FormalCompositeMap = __Pyx_ImportType("sage.categories.map", "FormalCompositeMap", sizeof(struct __pyx_obj_4sage_10categories_3map_FormalCompositeMap), 1); if (unlikely(!__pyx_ptype_4sage_10categories_3map_FormalCompositeMap)) {__pyx_filename = __pyx_f[14]; __pyx_lineno = 26; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_10categories_3map_FormalCompositeMap = (struct __pyx_vtabstruct_4sage_10categories_3map_FormalCompositeMap*)__Pyx_GetVtable(__pyx_ptype_4sage_10categories_3map_FormalCompositeMap->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_10categories_3map_FormalCompositeMap)) {__pyx_filename = __pyx_f[14]; __pyx_lineno = 26; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_10categories_8morphism_Morphism = __Pyx_ImportType("sage.categories.morphism", "Morphism", sizeof(struct __pyx_obj_4sage_10categories_8morphism_Morphism), 1); if (unlikely(!__pyx_ptype_4sage_10categories_8morphism_Morphism)) {__pyx_filename = __pyx_f[15]; __pyx_lineno = 5; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_10categories_8morphism_Morphism = (struct __pyx_vtabstruct_4sage_10categories_8morphism_Morphism*)__Pyx_GetVtable(__pyx_ptype_4sage_10categories_8morphism_Morphism->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_10categories_8morphism_Morphism)) {__pyx_filename = __pyx_f[15]; __pyx_lineno = 5; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_10categories_8morphism_SetMorphism = __Pyx_ImportType("sage.categories.morphism", "SetMorphism", sizeof(struct __pyx_obj_4sage_10categories_8morphism_SetMorphism), 1); if (unlikely(!__pyx_ptype_4sage_10categories_8morphism_SetMorphism)) {__pyx_filename = __pyx_f[15]; __pyx_lineno = 8; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_10categories_8morphism_SetMorphism = (struct __pyx_vtabstruct_4sage_10categories_8morphism_SetMorphism*)__Pyx_GetVtable(__pyx_ptype_4sage_10categories_8morphism_SetMorphism->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_10categories_8morphism_SetMorphism)) {__pyx_filename = __pyx_f[15]; __pyx_lineno = 8; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_5rings_7integer_Integer = __Pyx_ImportType("sage.rings.integer", "Integer", sizeof(struct __pyx_obj_4sage_5rings_7integer_Integer), 1); if (unlikely(!__pyx_ptype_4sage_5rings_7integer_Integer)) {__pyx_filename = __pyx_f[16]; __pyx_lineno = 7; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_5rings_7integer_Integer = (struct __pyx_vtabstruct_4sage_5rings_7integer_Integer*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_7integer_Integer->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_7integer_Integer)) {__pyx_filename = __pyx_f[16]; __pyx_lineno = 7; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_5rings_7integer_int_to_Z = __Pyx_ImportType("sage.rings.integer", "int_to_Z", sizeof(struct __pyx_obj_4sage_5rings_7integer_int_to_Z), 1); if (unlikely(!__pyx_ptype_4sage_5rings_7integer_int_to_Z)) {__pyx_filename = __pyx_f[16]; __pyx_lineno = 36; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_5rings_7integer_int_to_Z = (struct __pyx_vtabstruct_4sage_5rings_7integer_int_to_Z*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_7integer_int_to_Z->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_7integer_int_to_Z)) {__pyx_filename = __pyx_f[16]; __pyx_lineno = 36; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_5rings_8rational_Rational = __Pyx_ImportType("sage.rings.rational", "Rational", sizeof(struct __pyx_obj_4sage_5rings_8rational_Rational), 1); if (unlikely(!__pyx_ptype_4sage_5rings_8rational_Rational)) {__pyx_filename = __pyx_f[17]; __pyx_lineno = 8; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_5rings_8rational_Rational = (struct __pyx_vtabstruct_4sage_5rings_8rational_Rational*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_8rational_Rational->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_8rational_Rational)) {__pyx_filename = __pyx_f[17]; __pyx_lineno = 8; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_5rings_9real_mpfr_RealNumber = __Pyx_ImportType("sage.rings.real_mpfr", "RealNumber", sizeof(struct __pyx_obj_4sage_5rings_9real_mpfr_RealNumber), 1); if (unlikely(!__pyx_ptype_4sage_5rings_9real_mpfr_RealNumber)) {__pyx_filename = __pyx_f[18]; __pyx_lineno = 10; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_5rings_9real_mpfr_RealNumber = (struct __pyx_vtabstruct_4sage_5rings_9real_mpfr_RealNumber*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_9real_mpfr_RealNumber->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_9real_mpfr_RealNumber)) {__pyx_filename = __pyx_f[18]; __pyx_lineno = 10; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_5rings_9real_mpfr_RealField_class = __Pyx_ImportType("sage.rings.real_mpfr", "RealField_class", sizeof(struct __pyx_obj_4sage_5rings_9real_mpfr_RealField_class), 1); if (unlikely(!__pyx_ptype_4sage_5rings_9real_mpfr_RealField_class)) {__pyx_filename = __pyx_f[18]; __pyx_lineno = 12; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_5rings_9real_mpfr_RealField_class = (struct __pyx_vtabstruct_4sage_5rings_9real_mpfr_RealField_class*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_9real_mpfr_RealField_class->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_9real_mpfr_RealField_class)) {__pyx_filename = __pyx_f[18]; __pyx_lineno = 12; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_5rings_11complex_mpc_MPComplexNumber = __Pyx_ImportType("sage.rings.complex_mpc", "MPComplexNumber", sizeof(struct __pyx_obj_4sage_5rings_11complex_mpc_MPComplexNumber), 1); if (unlikely(!__pyx_ptype_4sage_5rings_11complex_mpc_MPComplexNumber)) {__pyx_filename = __pyx_f[19]; __pyx_lineno = 5; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_5rings_11complex_mpc_MPComplexNumber = (struct __pyx_vtabstruct_4sage_5rings_11complex_mpc_MPComplexNumber*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_11complex_mpc_MPComplexNumber->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_11complex_mpc_MPComplexNumber)) {__pyx_filename = __pyx_f[19]; __pyx_lineno = 5; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4sage_5rings_11complex_mpc_MPComplexField_class = __Pyx_ImportType("sage.rings.complex_mpc", "MPComplexField_class", sizeof(struct __pyx_obj_4sage_5rings_11complex_mpc_MPComplexField_class), 1); if (unlikely(!__pyx_ptype_4sage_5rings_11complex_mpc_MPComplexField_class)) {__pyx_filename = __pyx_f[19]; __pyx_lineno = 10; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_vtabptr_4sage_5rings_11complex_mpc_MPComplexField_class = (struct __pyx_vtabstruct_4sage_5rings_11complex_mpc_MPComplexField_class*)__Pyx_GetVtable(__pyx_ptype_4sage_5rings_11complex_mpc_MPComplexField_class->tp_dict); if (unlikely(!__pyx_vtabptr_4sage_5rings_11complex_mpc_MPComplexField_class)) {__pyx_filename = __pyx_f[19]; __pyx_lineno = 10; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Basic = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Basic", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Basic), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Basic)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 4; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Number = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Number", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Number), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Number)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 7; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Integer = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Integer", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Integer), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Integer)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 10; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Rational = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Rational", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Rational), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Rational)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 13; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Complex = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Complex", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Complex), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Complex)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 16; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_RealDouble = __Pyx_ImportType("symengine.lib.symengine_wrapper", "RealDouble", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_RealDouble), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_RealDouble)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 19; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_ComplexDouble = __Pyx_ImportType("symengine.lib.symengine_wrapper", "ComplexDouble", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ComplexDouble), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_ComplexDouble)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 22; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_RealMPFR = __Pyx_ImportType("symengine.lib.symengine_wrapper", "RealMPFR", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_RealMPFR), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_RealMPFR)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 25; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_ComplexMPC = __Pyx_ImportType("symengine.lib.symengine_wrapper", "ComplexMPC", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ComplexMPC), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_ComplexMPC)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 28; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Add = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Add", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Add), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Add)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 31; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Mul = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Mul", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Mul), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Mul)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 34; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Pow = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Pow", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Pow), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Pow)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 37; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Function = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Function", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Function), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Function)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 40; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_TrigFunction = __Pyx_ImportType("symengine.lib.symengine_wrapper", "TrigFunction", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_TrigFunction), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_TrigFunction)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 43; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Sin = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Sin", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Sin), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Sin)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 46; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Cos = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Cos", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Cos), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Cos)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 49; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Tan = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Tan", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Tan), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Tan)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 52; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Cot = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Cot", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Cot), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Cot)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 55; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Csc = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Csc", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Csc), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Csc)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 58; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_Sec = __Pyx_ImportType("symengine.lib.symengine_wrapper", "Sec", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_Sec), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_Sec)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 61; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_ASin = __Pyx_ImportType("symengine.lib.symengine_wrapper", "ASin", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ASin), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_ASin)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 64; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_ACos = __Pyx_ImportType("symengine.lib.symengine_wrapper", "ACos", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ACos), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_ACos)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 67; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_ATan = __Pyx_ImportType("symengine.lib.symengine_wrapper", "ATan", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ATan), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_ATan)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 70; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_ACot = __Pyx_ImportType("symengine.lib.symengine_wrapper", "ACot", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ACot), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_ACot)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 73; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_ACsc = __Pyx_ImportType("symengine.lib.symengine_wrapper", "ACsc", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ACsc), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_ACsc)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 76; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_ASec = __Pyx_ImportType("symengine.lib.symengine_wrapper", "ASec", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_ASec), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_ASec)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 79; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_9symengine_3lib_17symengine_wrapper_FunctionSymbol = __Pyx_ImportType("symengine.lib.symengine_wrapper", "FunctionSymbol", sizeof(struct __pyx_obj_9symengine_3lib_17symengine_wrapper_FunctionSymbol), 1); if (unlikely(!__pyx_ptype_9symengine_3lib_17symengine_wrapper_FunctionSymbol)) {__pyx_filename = __pyx_f[20]; __pyx_lineno = 82; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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    if (code_line <= entries[mid].code_line) {
        return mid;
    } else {
        return mid + 1;
    }
}
static PyCodeObject *__pyx_find_code_object(int code_line) {
    PyCodeObject* code_object;
    int pos;
    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
        return NULL;
    }
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
        return NULL;
    }
    code_object = __pyx_code_cache.entries[pos].code_object;
    Py_INCREF(code_object);
    return code_object;
}
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
    int pos, i;
    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
    if (unlikely(!code_line)) {
        return;
    }
    if (unlikely(!entries)) {
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
        if (likely(entries)) {
            __pyx_code_cache.entries = entries;
            __pyx_code_cache.max_count = 64;
            __pyx_code_cache.count = 1;
            entries[0].code_line = code_line;
            entries[0].code_object = code_object;
            Py_INCREF(code_object);
        }
        return;
    }
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
        PyCodeObject* tmp = entries[pos].code_object;
        entries[pos].code_object = code_object;
        Py_DECREF(tmp);
        return;
    }
    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
        int new_max = __pyx_code_cache.max_count + 64;
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
            __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));
        if (unlikely(!entries)) {
            return;
        }
        __pyx_code_cache.entries = entries;
        __pyx_code_cache.max_count = new_max;
    }
    for (i=__pyx_code_cache.count; i>pos; i--) {
        entries[i] = entries[i-1];
    }
    entries[pos].code_line = code_line;
    entries[pos].code_object = code_object;
    __pyx_code_cache.count++;
    Py_INCREF(code_object);
}

#include "compile.h"
#include "frameobject.h"
#include "traceback.h"
static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
            const char *funcname, int c_line,
            int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyObject *py_srcfile = 0;
    PyObject *py_funcname = 0;
    #if PY_MAJOR_VERSION < 3
    py_srcfile = PyString_FromString(filename);
    #else
    py_srcfile = PyUnicode_FromString(filename);
    #endif
    if (!py_srcfile) goto bad;
    if (c_line) {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #else
        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #endif
    }
    else {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromString(funcname);
        #else
        py_funcname = PyUnicode_FromString(funcname);
        #endif
    }
    if (!py_funcname) goto bad;
    py_code = __Pyx_PyCode_New(
        0,
        0,
        0,
        0,
        0,
        __pyx_empty_bytes, /*PyObject *code,*/
        __pyx_empty_tuple, /*PyObject *consts,*/
        __pyx_empty_tuple, /*PyObject *names,*/
        __pyx_empty_tuple, /*PyObject *varnames,*/
        __pyx_empty_tuple, /*PyObject *freevars,*/
        __pyx_empty_tuple, /*PyObject *cellvars,*/
        py_srcfile,   /*PyObject *filename,*/
        py_funcname,  /*PyObject *name,*/
        py_line,
        __pyx_empty_bytes  /*PyObject *lnotab*/
    );
    Py_DECREF(py_srcfile);
    Py_DECREF(py_funcname);
    return py_code;
bad:
    Py_XDECREF(py_srcfile);
    Py_XDECREF(py_funcname);
    return NULL;
}
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyFrameObject *py_frame = 0;
    py_code = __pyx_find_code_object(c_line ? c_line : py_line);
    if (!py_code) {
        py_code = __Pyx_CreateCodeObjectForTraceback(
            funcname, c_line, py_line, filename);
        if (!py_code) goto bad;
        __pyx_insert_code_object(c_line ? c_line : py_line, py_code);
    }
    py_frame = PyFrame_New(
        PyThreadState_GET(), /*PyThreadState *tstate,*/
        py_code,             /*PyCodeObject *code,*/
        __pyx_d,      /*PyObject *globals,*/
        0                    /*PyObject *locals*/
    );
    if (!py_frame) goto bad;
    py_frame->f_lineno = py_line;
    PyTraceBack_Here(py_frame);
bad:
    Py_XDECREF(py_code);
    Py_XDECREF(py_frame);
}

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_mpfr_prec_t(mpfr_prec_t value) {
    const mpfr_prec_t neg_one = (mpfr_prec_t) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(mpfr_prec_t) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(mpfr_prec_t) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
        } else if (sizeof(mpfr_prec_t) <= sizeof(unsigned long long)) {
            return PyLong_FromUnsignedLongLong((unsigned long long) value);
        }
    } else {
        if (sizeof(mpfr_prec_t) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(mpfr_prec_t) <= sizeof(long long)) {
            return PyLong_FromLongLong((long long) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(mpfr_prec_t),
                                     little, !is_unsigned);
    }
}

#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      return ::std::complex< double >(x, y);
    }
  #else
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      return x + y*(__pyx_t_double_complex)_Complex_I;
    }
  #endif
#else
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      __pyx_t_double_complex z;
      z.real = x;
      z.imag = y;
      return z;
    }
#endif

#if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eq(__pyx_t_double_complex a, __pyx_t_double_complex b) {
       return (a.real == b.real) && (a.imag == b.imag);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real + b.real;
        z.imag = a.imag + b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real - b.real;
        z.imag = a.imag - b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real * b.real - a.imag * b.imag;
        z.imag = a.real * b.imag + a.imag * b.real;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        double denom = b.real * b.real + b.imag * b.imag;
        z.real = (a.real * b.real + a.imag * b.imag) / denom;
        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__pyx_t_double_complex a) {
        __pyx_t_double_complex z;
        z.real = -a.real;
        z.imag = -a.imag;
        return z;
    }
    static CYTHON_INLINE int __Pyx_c_is_zero(__pyx_t_double_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__pyx_t_double_complex a) {
        __pyx_t_double_complex z;
        z.real =  a.real;
        z.imag = -a.imag;
        return z;
    }
    #if 1
        static CYTHON_INLINE double __Pyx_c_abs(__pyx_t_double_complex z) {
          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
            return sqrt(z.real*z.real + z.imag*z.imag);
          #else
            return hypot(z.real, z.imag);
          #endif
        }
        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow(__pyx_t_double_complex a, __pyx_t_double_complex b) {
            __pyx_t_double_complex z;
            double r, lnr, theta, z_r, z_theta;
            if (b.imag == 0 && b.real == (int)b.real) {
                if (b.real < 0) {
                    double denom = a.real * a.real + a.imag * a.imag;
                    a.real = a.real / denom;
                    a.imag = -a.imag / denom;
                    b.real = -b.real;
                }
                switch ((int)b.real) {
                    case 0:
                        z.real = 1;
                        z.imag = 0;
                        return z;
                    case 1:
                        return a;
                    case 2:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(a, a);
                    case 3:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, a);
                    case 4:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_abs(a);
                theta = atan2(a.imag, a.real);
            }
            lnr = log(r);
            z_r = exp(lnr * b.real - theta * b.imag);
            z_theta = theta * b.real + lnr * b.imag;
            z.real = z_r * cos(z_theta);
            z.imag = z_r * sin(z_theta);
            return z;
        }
    #endif
#endif

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
    const long neg_one = (long) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(long) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
        } else if (sizeof(long) <= sizeof(unsigned long long)) {
            return PyLong_FromUnsignedLongLong((unsigned long long) value);
        }
    } else {
        if (sizeof(long) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(long long)) {
            return PyLong_FromLongLong((long long) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(long),
                                     little, !is_unsigned);
    }
}

#define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)       \
    {                                                                     \
        func_type value = func_value;                                     \
        if (sizeof(target_type) < sizeof(func_type)) {                    \
            if (unlikely(value != (func_type) (target_type) value)) {     \
                func_type zero = 0;                                       \
                if (is_unsigned && unlikely(value < zero))                \
                    goto raise_neg_overflow;                              \
                else                                                      \
                    goto raise_overflow;                                  \
            }                                                             \
        }                                                                 \
        return (target_type) value;                                       \
    }

#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
  #include "longintrepr.h"
 #endif
#endif

static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
    const long neg_one = (long) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(long) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (long) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(long, digit, ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
            if (sizeof(long) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT(long, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(long) <= sizeof(unsigned long long)) {
                __PYX_VERIFY_RETURN_INT(long, unsigned long long, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +(((PyLongObject*)x)->ob_digit[0]));
                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (sizeof(long) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT(long, long, PyLong_AsLong(x))
            } else if (sizeof(long) <= sizeof(long long)) {
                __PYX_VERIFY_RETURN_INT(long, long long, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            long val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (long) -1;
        }
    } else {
        long val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (long) -1;
        val = __Pyx_PyInt_As_long(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to long");
    return (long) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to long");
    return (long) -1;
}

static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
    const int neg_one = (int) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(int) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (int) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(int, digit, ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
            if (sizeof(int) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT(int, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(int) <= sizeof(unsigned long long)) {
                __PYX_VERIFY_RETURN_INT(int, unsigned long long, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +(((PyLongObject*)x)->ob_digit[0]));
                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (sizeof(int) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT(int, long, PyLong_AsLong(x))
            } else if (sizeof(int) <= sizeof(long long)) {
                __PYX_VERIFY_RETURN_INT(int, long long, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            int val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (int) -1;
        }
    } else {
        int val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (int) -1;
        val = __Pyx_PyInt_As_int(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to int");
    return (int) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to int");
    return (int) -1;
}

static int __Pyx_check_binary_version(void) {
    char ctversion[4], rtversion[4];
    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
        char message[200];
        PyOS_snprintf(message, sizeof(message),
                      "compiletime version %s of module '%.100s' "
                      "does not match runtime version %s",
                      ctversion, __Pyx_MODULE_NAME, rtversion);
        return PyErr_WarnEx(NULL, message, 1);
    }
    return 0;
}

#ifndef __PYX_HAVE_RT_ImportModule
#define __PYX_HAVE_RT_ImportModule
static PyObject *__Pyx_ImportModule(const char *name) {
    PyObject *py_name = 0;
    PyObject *py_module = 0;
    py_name = __Pyx_PyIdentifier_FromString(name);
    if (!py_name)
        goto bad;
    py_module = PyImport_Import(py_name);
    Py_DECREF(py_name);
    return py_module;
bad:
    Py_XDECREF(py_name);
    return 0;
}
#endif

#ifndef __PYX_HAVE_RT_ImportType
#define __PYX_HAVE_RT_ImportType
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
    size_t size, int strict)
{
    PyObject *py_module = 0;
    PyObject *result = 0;
    PyObject *py_name = 0;
    char warning[200];
    Py_ssize_t basicsize;
#ifdef Py_LIMITED_API
    PyObject *py_basicsize;
#endif
    py_module = __Pyx_ImportModule(module_name);
    if (!py_module)
        goto bad;
    py_name = __Pyx_PyIdentifier_FromString(class_name);
    if (!py_name)
        goto bad;
    result = PyObject_GetAttr(py_module, py_name);
    Py_DECREF(py_name);
    py_name = 0;
    Py_DECREF(py_module);
    py_module = 0;
    if (!result)
        goto bad;
    if (!PyType_Check(result)) {
        PyErr_Format(PyExc_TypeError,
            "%.200s.%.200s is not a type object",
            module_name, class_name);
        goto bad;
    }
#ifndef Py_LIMITED_API
    basicsize = ((PyTypeObject *)result)->tp_basicsize;
#else
    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
    if (!py_basicsize)
        goto bad;
    basicsize = PyLong_AsSsize_t(py_basicsize);
    Py_DECREF(py_basicsize);
    py_basicsize = 0;
    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
        goto bad;
#endif
    if (!strict && (size_t)basicsize > size) {
        PyOS_snprintf(warning, sizeof(warning),
            "%s.%s size changed, may indicate binary incompatibility",
            module_name, class_name);
        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
    }
    else if ((size_t)basicsize != size) {
        PyErr_Format(PyExc_ValueError,
            "%.200s.%.200s has the wrong size, try recompiling",
            module_name, class_name);
        goto bad;
    }
    return (PyTypeObject *)result;
bad:
    Py_XDECREF(py_module);
    Py_XDECREF(result);
    return NULL;
}
#endif

#ifndef __PYX_HAVE_RT_ImportFunction
#define __PYX_HAVE_RT_ImportFunction
static int __Pyx_ImportFunction(PyObject *module, const char *funcname, void (**f)(void), const char *sig) {
    PyObject *d = 0;
    PyObject *cobj = 0;
    union {
        void (*fp)(void);
        void *p;
    } tmp;
    d = PyObject_GetAttrString(module, (char *)"__pyx_capi__");
    if (!d)
        goto bad;
    cobj = PyDict_GetItemString(d, funcname);
    if (!cobj) {
        PyErr_Format(PyExc_ImportError,
            "%.200s does not export expected C function %.200s",
                PyModule_GetName(module), funcname);
        goto bad;
    }
#if PY_VERSION_HEX >= 0x02070000
    if (!PyCapsule_IsValid(cobj, sig)) {
        PyErr_Format(PyExc_TypeError,
            "C function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
             PyModule_GetName(module), funcname, sig, PyCapsule_GetName(cobj));
        goto bad;
    }
    tmp.p = PyCapsule_GetPointer(cobj, sig);
#else
    {const char *desc, *s1, *s2;
    desc = (const char *)PyCObject_GetDesc(cobj);
    if (!desc)
        goto bad;
    s1 = desc; s2 = sig;
    while (*s1 != '\0' && *s1 == *s2) { s1++; s2++; }
    if (*s1 != *s2) {
        PyErr_Format(PyExc_TypeError,
            "C function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
             PyModule_GetName(module), funcname, sig, desc);
        goto bad;
    }
    tmp.p = PyCObject_AsVoidPtr(cobj);}
#endif
    *f = tmp.fp;
    if (!(*f))
        goto bad;
    Py_DECREF(d);
    return 0;
bad:
    Py_XDECREF(d);
    return -1;
}
#endif

static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
    while (t->p) {
        #if PY_MAJOR_VERSION < 3
        if (t->is_unicode) {
            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
        } else if (t->intern) {
            *t->p = PyString_InternFromString(t->s);
        } else {
            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
        }
        #else
        if (t->is_unicode | t->is_str) {
            if (t->intern) {
                *t->p = PyUnicode_InternFromString(t->s);
            } else if (t->encoding) {
                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
            } else {
                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
            }
        } else {
            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
        }
        #endif
        if (!*t->p)
            return -1;
        ++t;
    }
    return 0;
}

static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
}
static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject* o) {
    Py_ssize_t ignore;
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
}
static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
    if (
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
            __Pyx_sys_getdefaultencoding_not_ascii &&
#endif
            PyUnicode_Check(o)) {
#if PY_VERSION_HEX < 0x03030000
        char* defenc_c;
        PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
        if (!defenc) return NULL;
        defenc_c = PyBytes_AS_STRING(defenc);
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        {
            char* end = defenc_c + PyBytes_GET_SIZE(defenc);
            char* c;
            for (c = defenc_c; c < end; c++) {
                if ((unsigned char) (*c) >= 128) {
                    PyUnicode_AsASCIIString(o);
                    return NULL;
                }
            }
        }
#endif
        *length = PyBytes_GET_SIZE(defenc);
        return defenc_c;
#else
        if (__Pyx_PyUnicode_READY(o) == -1) return NULL;
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        if (PyUnicode_IS_ASCII(o)) {
            *length = PyUnicode_GET_LENGTH(o);
            return PyUnicode_AsUTF8(o);
        } else {
            PyUnicode_AsASCIIString(o);
            return NULL;
        }
#else
        return PyUnicode_AsUTF8AndSize(o, length);
#endif
#endif
    } else
#endif
#if !CYTHON_COMPILING_IN_PYPY
    if (PyByteArray_Check(o)) {
        *length = PyByteArray_GET_SIZE(o);
        return PyByteArray_AS_STRING(o);
    } else
#endif
    {
        char* result;
        int r = PyBytes_AsStringAndSize(o, &result, length);
        if (unlikely(r < 0)) {
            return NULL;
        } else {
            return result;
        }
    }
}
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
   int is_true = x == Py_True;
   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
   else return PyObject_IsTrue(x);
}
static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x) {
  PyNumberMethods *m;
  const char *name = NULL;
  PyObject *res = NULL;
#if PY_MAJOR_VERSION < 3
  if (PyInt_Check(x) || PyLong_Check(x))
#else
  if (PyLong_Check(x))
#endif
    return Py_INCREF(x), x;
  m = Py_TYPE(x)->tp_as_number;
#if PY_MAJOR_VERSION < 3
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Int(x);
  }
  else if (m && m->nb_long) {
    name = "long";
    res = PyNumber_Long(x);
  }
#else
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Long(x);
  }
#endif
  if (res) {
#if PY_MAJOR_VERSION < 3
    if (!PyInt_Check(res) && !PyLong_Check(res)) {
#else
    if (!PyLong_Check(res)) {
#endif
      PyErr_Format(PyExc_TypeError,
                   "__%.4s__ returned non-%.4s (type %.200s)",
                   name, name, Py_TYPE(res)->tp_name);
      Py_DECREF(res);
      return NULL;
    }
  }
  else if (!PyErr_Occurred()) {
    PyErr_SetString(PyExc_TypeError,
                    "an integer is required");
  }
  return res;
}
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
  Py_ssize_t ival;
  PyObject *x;
#if PY_MAJOR_VERSION < 3
  if (likely(PyInt_CheckExact(b)))
      return PyInt_AS_LONG(b);
#endif
  if (likely(PyLong_CheckExact(b))) {
    #if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
     #if CYTHON_USE_PYLONG_INTERNALS
       switch (Py_SIZE(b)) {
       case -1: return -(sdigit)((PyLongObject*)b)->ob_digit[0];
       case  0: return 0;
       case  1: return ((PyLongObject*)b)->ob_digit[0];
       }
     #endif
    #endif
    return PyLong_AsSsize_t(b);
  }
  x = PyNumber_Index(b);
  if (!x) return -1;
  ival = PyInt_AsSsize_t(x);
  Py_DECREF(x);
  return ival;
}
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
    return PyInt_FromSize_t(ival);
}


#endif /* Py_PYTHON_H */