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boblas

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6 years, 274 days
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These are questions asked by boblas

elimination monomial ordering...

boblas 15 Maple
elimination groebner monomial
November 05 2018
1 2

Hi!

I have the following problem: to create a special elimination ordering which is a weighted degree ordering suitable for elimination + pure lexicographic ordering. Let me provide an example. Assume my variables are x,y,z,t,u,v and I want to eliminate x,y,z. For this purpose, I define the weight vector [1,1,1,0,0,0] and compare monomials wrt corresponding weighted degree. If such degrees are equal, I compare monomials by pure lexicographic ordering. This is exactly what I need. How to obtain such monomial ordering by the package Groebner? I have tried monomial orderings defined by matrices using command  'matrix'(M,vars) but it seems it does not work for 30 variables.

Any suggestion? Thanks in advance.

mod 2 multivariate factorization...

boblas 15 Maple
modular factorization multivariate
October 03 2018
2 4
I have just found that the standard routine of Maple for performing mod 2 multivariate factorization, that is
Factor(p) mod 2
takes a very long computing time (I stopped after a long while) for the polynomial

p := K[4]*(K[4]^2*K[5]*K[6]^3*K[7]^2+K[4]*K[5]^2*K[6]^4*K[7]+K[4]^3*K[6]^2*K[7]^2+K[4]^2*K[5]*K[6]^3*K[7]+K[4]^2*K[5]*K[6]^2*K[7]^2+K[4]*K[5]^3*K[6]^3+K[5]^3*K[6]^4+K[4]^2*K[5]^3*K[6]+K[4]^2*K[5]^2*K[6]^2+K[4]^3*K[5]^2+K[4]^2*K[5]^3);

Note that the factorization of this polynomial is very fast on other computer algebra systems. Since mod 2 multivariate factorization (in fact, normalization of mod 2 multivariate rational functions) is essential for some algorithms that I'm currently implementing in Maple, I would ask if you know how to improve (bug, additional parameters?) the function Factor or if there are other functions, packages in Maple which implement a more feasible mod 2 multivariate factorization.

Many thanks in advance.

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