Shekharrajak

def substitution(system, symbols, result=[{}], known_symbols=[],
                 exclude=[], all_symbols=None):
    r""" Solves the `system` using substitution method.
    A helper function for `nonlinsolve`. This will be called from
    `nonlinsolve` when any equation(s) is non polynomial equation.

    Parameters
    ==========

    system : list of equations

Shekharrajak

def _solve_using_known_values(result, solver):
        """Solves the system using already known solution
        (result contains the dict <symbol: value>).
        solver is `solveset_complex` or `solveset_real`.
        """

        # stores imageset <expr: imageset(Lambda(n, expr), base)>.
        soln_imageset = {}
        total_solveset_call_inner = 0
        total_conditionset_inner = 0

Shekharrajak

def _extract_main_soln(sol, soln_imageset):
            """separate the Complements, Intersections, ImageSet lambda expr
            and it's base_set.
            """
            # if there is union, then need to check
            # complement, intersection, Imageset
            # order should not be changed.
            if isinstance(sol, Complement):
                # extract solution and complement
                complements[sym] = sol.args[1]

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def _solve_using_known_values(result, solver):
        """Solves the system using already known solution
        (result contains the dict <symbol: value>).
        solver is `solveset_complex` or `solveset_real`.
        """
        # helper functions

        def _append_new_soln(sol, rnew, newresult, imgset_info):
            """If rnew (A dict <symbol: soln> ) contains valid soln
            append it to newresult list.

Shekharrajak

##############################################################################
# ------------------------------nonlinsolve ---------------------------------#
##############################################################################


def substitution(system, symbols, result=[{}], known_symbols=[],
                 exclude=[], all_symbols=None):
    r""" Solves the `system` using substitution method.
    A helper function for `nonlinsolve`. This will be called from
    `nonlinsolve` when any equation(s) is non polynomial equation.

Shekharrajak

# used in class Set(Basic):sets.py file

def _union_simplify(self, other):
        """
        Try to reduce number of imageset in the args. Helper method for
        ImageSet `_union `. It helps to get simpler imageset or
        union of imageset.
        First extract the expression of imageset and store in separate list
        (self_expr for self and final_list for other). If there is any expr in
        self_list have difference of pi or -pi with any final_expr expr. then

Shekharrajak

##############################################################################
# ------------------------------nonlinsolve ---------------------------------#
##############################################################################


def substitution(system, symbols=None, result=[{}], known_symbols=[],
                 exclude=[], all_symbols=None):
    r""" Solves the `system` using substitution method.

Shekharrajak

##############################################################################
# ------------------------------nonlinsolve ---------------------------------#
##############################################################################


def substitution(system, symbols=None, result=[{}], known_symbols=[], exclude=[],
                 all_symbols=None):
    r""" Solves the `system` using substitution method.
    A helper function for     `nonlinsolve`. This will be called from
    `nonlinsolve` when any equation(s)     is non polynomial equation.

Shekharrajak

def solveset_univariate_trig_inequality(expr, gen, relational=True):
    """Solves a real univariate inequality.

    Examples
    ========

    >>> from sympy.solvers.inequalities import solveset_univariate_trig_inequality
    >>> from sympy.core.symbol import Symbol
    >>> x = Symbol('x')
    >>> solveset((2*cos(x)+1)/(2*cos(x)-1) > 0, x, S.Reals)

Shekharrajak

def reduce_imageset(new_imgset, imgset = S.EmptySet):
    """
    Try to reduce number of imageset in the args.
    It is mostly helper to _solve_trig method defined in
    solvers/solveset.py.

    First extract the expression of imageset and put in list in new_list
    (for new_imgset expr) and final_list(for imgset expr). If there is any
    expr in new_list have difference of pi or -pi with any final_list expr.