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These are answers submitted by gepo

Actually, we can just use

if (poly1=poly2)

to complete the job.

A quick question: why "gcdexrpoly" and "rpoly" cannot be found in Maple Resources. Thanks
well, it is not actually a rational number, for alias(a=RootOf(1+z^31+z^23+z^11+z^7+z^2+z^32)); a is primitive root of a galois field.
I found a tricky problem when using your method: f := a00*x^123+a45*x^233+a02*x^123+a67*x^156+a47*x^67; C := [coeffs(f,x,'M')]: # coefficients M := [M]: # monomials I got what "M" is: [x^233, x^67, x^123, x^156] which is not sorted from low degree to high degree. As a result, the corresponding coefficients are not sorted. I am wondering whether there is a way to fix it. Thanks a lot. Gepo
Got it. This function works really good. Thanks.
Well, it is not exactly what I want. Following your method, I got: M := [x^123, x^233, x^156, x^234]. But what I want is the coefficients of "f", not only the power of "x". Thank you though.
I am pretty sure Maple can handle bigger numbers than 32-bit ones. and the problem is not to compute the values of alpha^12345678987654321; alpha is actually an special element in Galois field GF(2^32). From properties of Galois field, alpha^12345678987654321 should be a polynomial with degree less than 32, something like (not exactly): x^31+x^25+x^17+x^15+x^11+x^7+x^5+x^2+x+1. thanks.
thanks. Another question: if they are different, can I see the differences? A:=[x^2+x+1,x-1]; B:=[x^2+x+1]; how can I compute A-B? Thanks Gepo

What I want to do actually is I do not want to substitute a variable whose value has been already known, just keeping the variable as it is.

For example,






I want to store all these equations into a list, like L:=[a0:=b0,a1:=a0+b1,a2:=a1+c0,result:=a0+a1+a2];

Well, this is not a easy task, because Maple will automatically substitue variables whose values are known.

For example, the above "L" will become:



Any suggestions?





thanks, it works.

Thanks, that makes sense.

By way , do you know whcih one runs faster, F4 or F5, for general problems?


Thanks a lot


Actually, I have read this slides which is to show how to reduce the matrix. This part is not hard. I just not clear what are the rules to choose multiple syzygies. thanks
I am pretty understanding Buchburger's algorithm and now I am studying F4 algorithm since everyone says it runs fast. When I studied F4, I found things were not easy. Before I am diving in thinking about linear algebra, I need to understand the algorithm well. My final goal is to implement it with C. Do you have some examples to explain the F4 algorithm or do you have a pseudocode of F4 or useful documents? thanks in advance. gepo
works. Thank you so much.
got it . using Inverse(matrixname) mod 2;
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