jcrose

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These are replies submitted by jcrose

@Carl Love 

That worked, thank you Carl. Took about 4 minutes of processing.

But now there's a new problem. Alas, the result is fault as there should remain six non-zero rows.

I came up with an alternate 10x10 matrix, the coefficients still polynoms in the monomials a & b.

Here it is: https://www.dropbox.com/s/1c70btdnzzx4mkq/GLSPoly10rows.mw

Following the method you outlined kernel connection is lost during calculation. A firewall shouldn't be the problem, I just guess the computational load is just too heavy.

I came around this entry: https://groups.google.com/forum/#!topic/comp.soft-sys.math.maple/Cok6dBdMsbc

where Gröbner Bases are used for the solution. Unfortunatley I don't know anything about Gröbners bases. Would you be kind enough to help me forwards again? Thank you in advance.

From the entry:

"Unfortunately this is not the best code in Maple 10 for solving
polynomial systems.  It actually suffers from a bug in
LinearAlgebra:-Determinant, which is called from the subresultant
algorithm.

You might try the following (Maple 10 only):

F := {coefficients}:
vars := {e1,e2,...}:
infolevel[GroebnerBasis] := 4:

# this will compute a lexicographic Groebner basis
G := PolynomialIdeals:-GroebnerBasis(F, 'tord', 'plex', vars):

# this will efficiently split the system
P := Groebner:-Solve(G, [op(tord)]);

# this will hopefully solve the components
S := map(a->solve(a[1], {op(tord)}), P);

"

Please help me with this problem or hint me towards a solution to go after.

@Carl Love Thank you for your help, first of all.

Yes, you are right, polyGLS consists of polynoms which form a Matrix of coefficients. Citing from the paper: "Considering this as a homogeneous linear system in monomials of a and b this
will give expressions in the monomials a^3; a^2b; a^2; ab^2; ab; a; b^3; b^2; b; 1."

So the entries in polyGLS are the coefficients for the monomials, such that

polyGLS * [a^3; a^2b; a^2; ab^2; ab; a; b^3; b^2; b; 1].

It is also said that there exists a linear dependency between the rows thus reducing the rank of the matrix from 7 to 6. So after reducing polyGLS to the row recuced echolon form there should exist a zero-row.

 

 

 

 

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