I would like to advertise https://trac.sagemath.org/ticket/31077, which I
think it is a rather troubling bug. It occurs when expanding a symbolic
expression, which happens to be a rational function. I narrowed down the
bug to a call to pynac, I do not know, however, whether the bug occurs
within pynac or in the communication between pynac and sage. The smallest
example I currently know of is reproduced below.
I don't know who could help, which is why I am advertising here.
Best wishes,
Martin
sage: var("A B C x")
sage: p = A^2*B^2*C^3*x^2 + A^2*B^2*C^2*x^3 + A^2*B^2*C^2*x^2 + A^2*C^3*x^3
+ A^5*B^2 + A^2*B^2*C^3 + A^3*B^2*C*x + A^2*B^2*C^2*x + A^3*B^2*x^2 +
A^4*x^3 + A^3*C*x^3 + A^4*C^2 + A^2*B^2*C^2 + A^3*C^3 + A^3*B^2*x +
B^2*C^3*x + A^3*C*x^2 + A^2*C^2*x^2 + A*C^3*x^2 + A*C^2*x^3 + C^3*x^3 +
A^3*B^2 + A^2*B*C^2 + A*B*C^3 + A*B*C^2*x + B^2*C^2*x + A^3*x^2 + C^3*x^2 +
A^2*x^3 + B^2*x^3 + A*C*x^3 + C^2*x^3 + A^4 + A^3*C + A^2*C^2 + B^2*C^2 +
A*C^3 + B*C^3 + A^2*B*x + A*B*C*x + A*C*x^2 + B*C*x^2 + C^2*x^2 + A^2*B +
B^2*C + B*C^2 + C^3 + A*B*x + A*x^2 + C*x^2 + x^3 + A^2 + B^2 + A*C + B*C +
C^2 + B*x + x^2 + B + C + x + 1 sage: G = (((A + B + x) * (A + B^2 + 1) * p
+ (A + B + 1)/x)*(A+1))
sage: G.expand().is_polynomial(x) != G.is_polynomial(x)
True
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