Coverage for sympy/polys/rationaltools.py : 58%

"""Tools for manipulation of rational expressions. """ 

from __future__ import print_function, division 

from sympy.core import Basic, Add, sympify 

from sympy.core.compatibility import iterable 

from sympy.core.exprtools import gcd_terms 

from sympy.utilities import public 

@public 

def together(expr, deep=False): 

""" 

Denest and combine rational expressions using symbolic methods. 

This function takes an expression or a container of expressions 

and puts it (them) together by denesting and combining rational 

subexpressions. No heroic measures are taken to minimize degree 

of the resulting numerator and denominator. To obtain completely 

reduced expression use :func:`cancel`. However, :func:`together` 

can preserve as much as possible of the structure of the input 

expression in the output (no expansion is performed). 

A wide variety of objects can be put together including lists, 

tuples, sets, relational objects, integrals and others. It is 

also possible to transform interior of function applications, 

by setting ``deep`` flag to ``True``. 

By definition, :func:`together` is a complement to :func:`apart`, 

so ``apart(together(expr))`` should return expr unchanged. Note 

however, that :func:`together` uses only symbolic methods, so 

it might be necessary to use :func:`cancel` to perform algebraic 

simplification and minimise degree of the numerator and denominator. 

Examples 

======== 

>>> from sympy import together, exp 

>>> from sympy.abc import x, y, z 

>>> together(1/x + 1/y) 

(x + y)/(x*y) 

>>> together(1/x + 1/y + 1/z) 

(x*y + x*z + y*z)/(x*y*z) 

>>> together(1/(x*y) + 1/y**2) 

(x + y)/(x*y**2) 

>>> together(1/(1 + 1/x) + 1/(1 + 1/y)) 

(x*(y + 1) + y*(x + 1))/((x + 1)*(y + 1)) 

>>> together(exp(1/x + 1/y)) 

exp(1/y + 1/x) 

>>> together(exp(1/x + 1/y), deep=True) 

exp((x + y)/(x*y)) 

>>> together(1/exp(x) + 1/(x*exp(x))) 

(x + 1)*exp(-x)/x 

>>> together(1/exp(2*x) + 1/(x*exp(3*x))) 

(x*exp(x) + 1)*exp(-3*x)/x 

""" 

def _together(expr): 

if isinstance(expr, Basic): 

if expr.is_Atom or (expr.is_Function and not deep): 

return expr 

elif expr.is_Add: 

return gcd_terms(list(map(_together, Add.make_args(expr)))) 

elif expr.is_Pow: 

base = _together(expr.base) 

if deep: 

exp = _together(expr.exp) 

else: 

exp = expr.exp 

return expr.__class__(base, exp) 

else: 

return expr.__class__(*[ _together(arg) for arg in expr.args ]) 

elif iterable(expr): 

return expr.__class__([ _together(ex) for ex in expr ]) 

return expr 

return _together(sympify(expr))