I am attempting to compute some sets of rational functions. Unfortunately, it seems that elements of a fraction field are only reduced to unit multiples of numerator and denominator. Multiplying the numerator and denominator by the same unit gives equal elements, but they hash to different things.
I can separate each rational function into numerator and denominator, rescale them and reconstruct the fraction, but is there a simpler way?
R.<w>=PolynomialRing(ZZ)
K=FractionField(R)
test = (K(-1)/K(-w))
test.reduce()
print(test)
-1/-w
{1/w, -1/-w}
'SageMath version 10.0.beta3, Release Date: 2023-03-02'
Compiled this morning on OSX 12.6.3