I am using sage to find some basis elements in a CombinatorialFreeModule
that have some nice properties. To do this I work in a large polynomial
ring and solve a corresponding system of equations. The algebra that I am
working in is itself defined over a polynomial ring, say ZZ[h, q, ,q^-1,
u0, u1] and I am getting solutions to my matrix equations that look like:
[[(-h)/(-h), 0, h/(-h),0],
[0, ((-h*q^-1 + h*q)*u0 + (-h*q^-1 + h*q)*u1)/((-h*q^-1 + h*q)*u0 + (-h*q^-1
+ h*q)*u1), 0, 0],
[0, 0, 0, h^2*u0*u1/(h^2*u0*u1)]]
These coefficients simplify quite drastically to:
[[1, 0, 1, 0],
[0, 1, 0, 0],
[0, 0, 0, 1]]
Is there a way to make sage do this reduction? Everything that I have tried
so far as failed. If I take the (1,1) entry above to be a then it's parent
is
sage: a.parent()
Fraction Field of Multivariate Polynomial Ring in c0, c1, c2, c3 over
Multivariate Laurent Polynomial Ring in u0, u1 over Univariate Laurent
Polynomial Ring in q over Univariate Laurent Polynomial Ring in h over
Integer Ring
So I get errors when I try things like:
sage: a.reduce()
---------------------------------------------------------------------------
ArithmeticError Traceback (most recent call last)
...
ArithmeticError: unable to reduce because gcd algorithm not implemented on
input
Andrew
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