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`.
        """
        # 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.

Shekharrajak

# examples how we can use factor to reduce number of imageset :

# current master branch
In [110]: solveset(4*sin(x)**3  + 2*sin(x)**2 - 2*sin(x) - 1)  # ------------ eq(1)
Out[110]: 
⎧        7⋅π        ⎫   ⎧        11⋅π        ⎫   ⎧        5⋅π        ⎫   ⎧        3⋅π        ⎫   ⎧        7⋅π        ⎫   ⎧        π        ⎫
⎨2⋅n⋅π + ─── | n ∊ ℤ⎬ ∪ ⎨2⋅n⋅π + ──── | n ∊ ℤ⎬ ∪ ⎨2⋅n⋅π + ─── | n ∊ ℤ⎬ ∪ ⎨2⋅n⋅π + ─── | n ∊ ℤ⎬ ∪ ⎨2⋅n⋅π + ─── | n ∊ ℤ⎬ ∪ ⎨2⋅n⋅π + ─ | n ∊ ℤ⎬
⎩         6         ⎭   ⎩         6          ⎭   ⎩         4         ⎭   ⎩         4         ⎭   ⎩         4         ⎭   ⎩        4        ⎭

In [123]: solveset((4*sin(x)**3  + 2*sin(x)**2 - 2*sin(x) - 1).rewrite(exp))

Shekharrajak

def reduce_imageset(soln):
    """
    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
    sort the negative and positive expression.
    and using interpolate defined in polys/polyfuncs.py
    generates a function in `n`, which can return all the

Shekharrajak

In [ ]: solveset(2*sin(x) - 1<0,x, S.Reals)
Out[ ]: 
⎛    π⎞   ⎛5⋅π   ⎞
⎜-∞, ─⎟ ∪ ⎜───, ∞⎟
⎝    6⎠   ⎝ 6    ⎠