On Tuesday, September 15, 2015 at 3:14:36 PM UTC-7, vdelecroix wrote:
>
> More or less indeed... If I would specify var('x', domain=GF(3)) then I
> would expect x^3 to be simplified in x. Which is what polynomial are not
> doing. To my mind, Sage is clearly lacking this feature.
>
This just means you want to work on the polynomial quotient ring
GF(p)[x1,...,xn]/<x1^p-x1,...,xn^p-xn>
For p=2 this is a BooleanPolynomialRing, which should have a pretty
efficient implementation. For other p you can construct the thing yourself.
sage: R.<x,y>=GF(3)[]
sage: I=R.ideal(x^3-x,y^3-y)
sage: Q.<X,Y>=R.quo(I)
sage: (X+Y)^9
X + Y
sage: (X+Y)^10
X^2 - X*Y + Y^2
No guarantees about efficiency!
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