Evaluation of polynomial coefficient rings in free algebras

[stumpc5]

Steps To Reproduce

sage: version()
'SageMath version 10.5.beta5, Release Date: 2024-09-22'
sage: Pyab.<a,b> = FreeAlgebra(QQ,2)
sage: f = 2*a - 2*b + a*b - b*a
sage: f
2*a - 2*b + a*b - b*a
sage: for mon,coeff in f:
....:     print(coeff, coeff.parent(), mon, coeff*mon)
2 Rational Field a None
-2 Rational Field b None
1 Rational Field a*b a*b
-1 Rational Field b*a None

sage: for mon,coeff in f:
....:     print(coeff,coeff.parent(),mon, Pyab(coeff) * mon)
....: 
2 Rational Field a 2*a
-2 Rational Field b -2*b
1 Rational Field a*b a*b
-1 Rational Field b*a -b*a

Expected Behavior

Multiplying coefficients with monomials correctly

Actual Behavior

Does it correctly, in the example, only for the coefficient 1, not for \pm 2, -1.

Additional Information

No response

Environment

• OS: Ubuntu 24.04
• Sage Version: 10.5.beta5

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[mantepse]

This is only very surprising behaviour, not a bug:

sage: for mon, coeff in f:
....:     print(mon.parent(), coeff.parent())
....:     
Free monoid on 2 generators (a, b) Rational Field
Free monoid on 2 generators (a, b) Rational Field
Free monoid on 2 generators (a, b) Rational Field
Free monoid on 2 generators (a, b) Rational Field

What you want is

sage: [c * Pyab(m) for m, c in f]
[2*a, -2*b, a*b, -b*a]

[mantepse]

As an aside, I cannot reproduce the report, which is a bit odd. With the same sage version, I get

sage: for mon,coeff in f:
....:     print(coeff, coeff.parent(), mon, coeff*mon)
....:     
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[4], line 2
      1 for mon,coeff in f:
----> 2     print(coeff, coeff.parent(), mon, coeff*mon)

File ~/sage-trac/src/sage/rings/rational.pyx:2443, in sage.rings.rational.Rational.__mul__()
   2441         return x
   2442 
-> 2443     return coercion_model.bin_op(left, right, operator.mul)
   2444 
   2445 cpdef _mul_(self, right):

File ~/sage-trac/src/sage/structure/coerce.pyx:1282, in sage.structure.coerce.CoercionModel.bin_op()
   1280     # We should really include the underlying error.
   1281     # This causes so much headache.
-> 1282     raise bin_op_exception(op, x, y)
   1283 
   1284 cpdef canonical_coercion(self, x, y):

TypeError: unsupported operand parent(s) for *: 'Rational Field' and 'Free monoid on 2 generators (a, b)'