Hey Guys, i am absolutely new to sage but want to use it for some algebraic calculations. Therefore i must generate the Polynomial ring R=(Z/nZ[x])/(xN−1) to calcuate some inverses and products of some polynomials in R.
I hope it's not a too stupid question and apologize for bothering you guys with this but i still hope someone can give me an answer :).
(ofc for some given n and N)
You should have a look at the documentation.
sage: A = Zmod(4)
sage: P = PolynomialRing(A, 'x')
sage: x = P.gen()
sage: R = R.quotient(x^7 - 1)
sage: xbar = R.gen()
sage: xbar ** 7
1
sage: 4 * xbar
0But note that computation of inverses does not work at all:
sage: 1 / xbar
Traceback (most recent call last):
...
NotImplementedError: The base ring (=Ring of integers modulo 4) is not a fieldfirst of thanks. i dont know why haven't found that documentation... is there no possibility to compute inverses?
Probably because Sage doesn't want to try to compute inverses when there is no guarantee there will be an inverse to a given element?
is there another computer algebra system that tries it even though its not a field?
Can you explain me what that "xbar" means?
xbar is just the name of the variable given by @vdelecroix As you can see, it is defined as R.gen() which means that it is the generator or the quitient ring of P by x^7 - 1, more precisely, it is the image of x under the quotient map.
Asked: 9 years ago
Seen: 720 times
Last updated: Oct 08 '15
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