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
print(test == K(1/w))
True
s = set([K(1/w), test])
print(s)
{1/w, -1/-w}
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