SymPy –> Sage conversion

The file consists of _sage_() methods that are added lazily to the respective SymPy objects. Any call of the _sympy_() method of a symbolic expression will trigger the addition. See sage.symbolic.expression_conversion.SymPyConverter for the conversion to SymPy.

Only Function objects where the names differ need their own _sage()_ method. There are several functions with differing name that have an alias in Sage that is the same as the name in SymPy, so no explicit translation is needed for them:

sage: from sympy import Symbol, Si, Ci, Shi, Chi, sign
sage: sx = Symbol('x')
sage: assert sin_integral(x)._sympy_() == Si(sx)
sage: assert sin_integral(x) == Si(sx)._sage_()
sage: assert sinh_integral(x)._sympy_() == Shi(sx)
sage: assert sinh_integral(x) == Shi(sx)._sage_()
sage: assert cos_integral(x)._sympy_() == Ci(sx)
sage: assert cos_integral(x) == Ci(sx)._sage_()
sage: assert cosh_integral(x)._sympy_() == Chi(sx)
sage: assert cosh_integral(x) == Chi(sx)._sage_()
sage: assert sgn(x)._sympy_() == sign(sx)
sage: assert sgn(x) == sign(sx)._sage_()

>>> from sage.all import *
>>> from sympy import Symbol, Si, Ci, Shi, Chi, sign
>>> sx = Symbol('x')
>>> assert sin_integral(x)._sympy_() == Si(sx)
>>> assert sin_integral(x) == Si(sx)._sage_()
>>> assert sinh_integral(x)._sympy_() == Shi(sx)
>>> assert sinh_integral(x) == Shi(sx)._sage_()
>>> assert cos_integral(x)._sympy_() == Ci(sx)
>>> assert cos_integral(x) == Ci(sx)._sage_()
>>> assert cosh_integral(x)._sympy_() == Chi(sx)
>>> assert cosh_integral(x) == Chi(sx)._sage_()
>>> assert sgn(x)._sympy_() == sign(sx)
>>> assert sgn(x) == sign(sx)._sage_()

from sympy import Symbol, Si, Ci, Shi, Chi, sign
sx = Symbol('x')
assert sin_integral(x)._sympy_() == Si(sx)
assert sin_integral(x) == Si(sx)._sage_()
assert sinh_integral(x)._sympy_() == Shi(sx)
assert sinh_integral(x) == Shi(sx)._sage_()
assert cos_integral(x)._sympy_() == Ci(sx)
assert cos_integral(x) == Ci(sx)._sage_()
assert cosh_integral(x)._sympy_() == Chi(sx)
assert cosh_integral(x) == Chi(sx)._sage_()
assert sgn(x)._sympy_() == sign(sx)
assert sgn(x) == sign(sx)._sage_()

AUTHORS:

  • Ralf Stephan (2017-10)

class sage.interfaces.sympy.UndefSageHelper[source]

Bases: object

Helper class to convert sympy function objects to sage functions

EXAMPLES:

sage: from sympy import Function
sage: f = function('f')
sage: F = Function('f')
sage: assert f._sympy_() == F
sage: assert f == F._sage_()

>>> from sage.all import *
>>> from sympy import Function
>>> f = function('f')
>>> F = Function('f')
>>> assert f._sympy_() == F
>>> assert f == F._sage_()

from sympy import Function
f = function('f')
F = Function('f')
assert f._sympy_() == F
assert f == F._sage_()
sage.interfaces.sympy.check_expression(expr, var_symbols, only_from_sympy=False)[source]

Do eval(expr) both in Sage and SymPy and other checks.

EXAMPLES:

sage: from sage.interfaces.sympy import check_expression
sage: check_expression("1.123*x", "x")

>>> from sage.all import *
>>> from sage.interfaces.sympy import check_expression
>>> check_expression("1.123*x", "x")

from sage.interfaces.sympy import check_expression
check_expression("1.123*x", "x")
sage.interfaces.sympy.sympy_init(*args, **kwargs)[source]

Add _sage_() methods to SymPy objects where needed.

This gets called with every call to Expression._sympy_() so there is only need to call it if you bypass _sympy_() to create SymPy objects. Note that SymPy objects have _sage_() methods hard installed but having them inside Sage as one file makes them easier to maintain for Sage developers.

EXAMPLES:

sage: from sage.interfaces.sympy import sympy_init
sage: from sympy import Symbol, Abs
sage: sympy_init()
sage: assert abs(x) == Abs(Symbol('x'))._sage_()

>>> from sage.all import *
>>> from sage.interfaces.sympy import sympy_init
>>> from sympy import Symbol, Abs
>>> sympy_init()
>>> assert abs(x) == Abs(Symbol('x'))._sage_()

from sage.interfaces.sympy import sympy_init
from sympy import Symbol, Abs
sympy_init()
assert abs(x) == Abs(Symbol('x'))._sage_()
sage.interfaces.sympy.sympy_set_to_list(set, vars)[source]

Convert all set objects that can be returned by SymPy’s solvers.

sage.interfaces.sympy.test_all()[source]

Call some tests that were originally in SymPy.

EXAMPLES:

sage: from sage.interfaces.sympy import test_all
sage: test_all()

>>> from sage.all import *
>>> from sage.interfaces.sympy import test_all
>>> test_all()

from sage.interfaces.sympy import test_all
test_all()