ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 02 Mar 2020 15:27:09 +0100Iterate over multivariate polynomials over finite fieldshttps://ask.sagemath.org/question/50136/iterate-over-multivariate-polynomials-over-finite-fields/Say we have a finite field, e.g. $F_4$, and consider the $n$-ary polynomials $R=F_4[x_1,\dots,x_n]$ over this field.
I want to iterate over all these polynomials in $R$. Since the polynomials are over a finite field there are only finitely many different polynomials (considered as functions $F_4^n \to F_4$). How can I do this?
For $n=1$ I could do
R.<x> = PolynomialRing(GF(4))
S.<a> = R.quo(sage.rings.ideal.FieldIdeal(R))
S.is_finite()
Then I could iterate over $S$ and simply lift all the elements from $S$ back to $R$, i.e. s.lift(). The same thing however does not work for several polynomials:
R.<x,y> = PolynomialRing(GF(4))
S.<a,b> = R.quo(sage.rings.ideal.FieldIdeal(R))
S.is_finite()
yields the error
> AttributeError: 'super' object has no attribute 'is_finite'
As an alternative I could manually generate all multivariate polynomials with exponents less than the order of the field. However, this seems quite tedious and like a very "un-sage"/not algebraic way.philipp7Mon, 02 Mar 2020 15:27:09 +0100https://ask.sagemath.org/question/50136/Get coefficients of a polynomial in quotient ringhttps://ask.sagemath.org/question/24902/get-coefficients-of-a-polynomial-in-quotient-ring/Let say I have the following quotient ring:
F.<t> = PolynomialRing(GF(2), 'x').quotient(x^128 + x^7 + x^2 + x + 1);
Then I create a polynomial, for example t^128 which yields:
t^7 + t^2 + t + 1
Now how do I obtain the array of coefficients of this polynomial?
Or, similarly, how do I actually substitute 2 for t and evaluate this polynomial? The `subs` method doesn't work. (Probably the polynomial needs to be coerced to other ring with base field where 2 != 0).
NumberFourTue, 18 Nov 2014 13:04:35 +0100https://ask.sagemath.org/question/24902/