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I apologize for my terrible formatting (I am new to this site), but I am having an issue with the reduce() method for FractionFieldElement. In a Jupyter notebook I executed the following code

S = FractionField(QQ['t'])

S.inject_variables()

R = PolynomialRing(FractionField(QQ['t']),'x',3)

R.inject_variables()

(((x0^2-x1^2)/(x0-x1)).reduce())

but this returned an object with NoneType, rather than a fraction field element or ring element. What am I doing wrong?

I apologize for my terrible formatting (I am new to this site), but I am having an issue with the reduce() reduce() method for FractionFieldElement. FractionFieldElement. In a Jupyter notebook I executed the following code

sage: S = FractionField(QQ['t'])
 
S.inject_variables()
 
FractionField(QQ['t'])
sage: S.inject_variables()
sage: R = PolynomialRing(FractionField(QQ['t']),'x',3)PolynomialRing(FractionField(QQ['t']),'x',3)
sage: R.inject_variables()
sage: (((x0^2-x1^2)/(x0-x1)).reduce())
 
R.inject_variables()
 
(((x0^2-x1^2)/(x0-x1)).reduce())