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_()


  • Ralf Stephan (2017-10)

class sage.interfaces.sympy.UndefSageHelper

Bases: object

Helper class to convert sympy function objects to sage functions


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

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


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

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.


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_()
sage.interfaces.sympy.sympy_set_to_list(set, vars)

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


Call some tests that were originally in SymPy.


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