Make all symbols commutative in a sympy expression

Question

Say you have a number of non commutative symbols within a sympy expression, something like

a, c = sympy.symbols('a c', commutative=False)
b = sympy.Symbol('b')
expr = a * c + b * c

What is the preferred way to make all symbols in the expression commutative, so that, for example, sympy.simplify(allcommutative(expr)) = c * (a + b)?

In this answer it is stated that there is no way to change the commutativity of a symbol after creation without replacing a symbol, but maybe there is an easy way to change in blocks all symbols of an expression like this?

Saucer

Why were they created as noncommutative if they're supposed to be commutative? – Esperanzaespial

@Esperanzaespial legit question of course. My reason is that I want to force a specific ordering in the printed expression, and setting the symbols as non commutative was the easiest way I found to achieve that. – Saucer

Answer 1

If you want Eq(expr, c * (a + b)) to evaluate to True, you'll need to replace symbols by other symbols that commute. For example:

replacements = {s: sympy.Dummy(s.name) for s in expr.free_symbols}
sympy.Eq(expr, c * (a + b)).xreplace(replacements).simplify()

This returns True.

Eck

this is the kind of this I was thinking of, yes. I guess there is no better way then. Thanks – Saucer

@Saucer Yeah, I wish I could make x commutative by saying x.is_commutative=True, but I get AttributeError: can't set attribute. – Siskind

Why doesn't calling a, c = sympy.symbols('a c', commutative=False) later work? It seems expressions involving those symbols are set in stone (as subs doesn't work on them). – Siskind

@Siskind Sympy objects are immutable. Check out the "common pitfalls" section of the docs. – Eck

Answer 2

Two comments:

1. noncommutatives will factor (though they respect the side that the nc expr appears on)
2. although you have a robust answer, a simple answer that will often be good enough is to just sympify the string version of the expression

Both are shown below:

>>> import sympy
>>> a, c = sympy.symbols('a c', commutative=False)
>>> b = sympy.Symbol('b')
>>> expr = a * c + b * c
>>> factor(expr)
(b + a)*c
>>> S(str(_))
c*(a + b)

Dramatics