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.Fri, 30 Mar 2018 03:56:50 +0200Does anyone know how to implement a simple XL Algorithm in sage?https://ask.sagemath.org/question/41818/does-anyone-know-how-to-implement-a-simple-xl-algorithm-in-sage/I need to implement the XL algorithm in sage, which i can use to solve over-determined systems of polynomial equations (more equations than variables). Any help on how to do this?
Thu, 29 Mar 2018 14:45:45 +0200https://ask.sagemath.org/question/41818/does-anyone-know-how-to-implement-a-simple-xl-algorithm-in-sage/Comment by dan_fulea for <p>I need to implement the XL algorithm in sage, which i can use to solve over-determined systems of polynomial equations (more equations than variables). Any help on how to do this? </p>
https://ask.sagemath.org/question/41818/does-anyone-know-how-to-implement-a-simple-xl-algorithm-in-sage/?comment=41820#post-id-41820Is this relevant:
[http://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/multi_polynomial_sequence.html](http://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/multi_polynomial_sequence.html)
Here, there is a line...
*Using these building blocks we can implement a simple XL algorithm easily:*Thu, 29 Mar 2018 15:07:57 +0200https://ask.sagemath.org/question/41818/does-anyone-know-how-to-implement-a-simple-xl-algorithm-in-sage/?comment=41820#post-id-41820Comment by Dalvir for <p>I need to implement the XL algorithm in sage, which i can use to solve over-determined systems of polynomial equations (more equations than variables). Any help on how to do this? </p>
https://ask.sagemath.org/question/41818/does-anyone-know-how-to-implement-a-simple-xl-algorithm-in-sage/?comment=41822#post-id-41822I have had a look at that but i don't really understand what is going on there because it doesn't seem to provide a solution, also i need to do it for a polynomial system. They define a polynomial system with the following
`sr = mq.SR(1,1,1,4, gf2=True, polybori=True, order='lex')`
`F,s = sr.polynomial_system() `and i don't really get what kind of polynomial system has actually been implemented there :/Thu, 29 Mar 2018 15:40:59 +0200https://ask.sagemath.org/question/41818/does-anyone-know-how-to-implement-a-simple-xl-algorithm-in-sage/?comment=41822#post-id-41822Comment by dan_fulea for <p>I need to implement the XL algorithm in sage, which i can use to solve over-determined systems of polynomial equations (more equations than variables). Any help on how to do this? </p>
https://ask.sagemath.org/question/41818/does-anyone-know-how-to-implement-a-simple-xl-algorithm-in-sage/?comment=41827#post-id-41827The structure in encapsulated. To see the $36$ polynomials in `F`:
for pol in F: print pol
There are `20` variables in `F.variables()`. So there are $\binom{20}2=190$ monomials $ab$, where $a,b$ are variables, $a\ne b$.
Then we build `F2 = Sequence(map(mul, cartesian_product_iterator((monomials, F))))`. The cartesian product of all monomials $ab$ and all `pol`s $f$ has then $190\cdot 36$ elements, we map them via `mul` getting all$ab\;f$ of this shape.
The tricky `F2.coefficient_matrix(sparse=False)` isolates the corresponding matrix, try `F2.coefficient_matrix?` to see in examples how this works.
From here, standard linear algebra gets the hands on it...
This example may not be related to the own problem, but then we have to know this other problem / situation.Fri, 30 Mar 2018 03:56:50 +0200https://ask.sagemath.org/question/41818/does-anyone-know-how-to-implement-a-simple-xl-algorithm-in-sage/?comment=41827#post-id-41827