solutionMatrix -- display the relations linear in the c- and o-variables as a matrix

Synopsis

Usage:

(solutionMat,restVars) = solutionMatrix(relLin)
Inputs:
- relLin, a matrix, row matrix containing all relations which are linear in the c- and o-variables
Outputs:
- solutionMat, a matrix, a matrix representing these linear relation
- restVars, a matrix, a row matrix containing the unknown c- and o-variables

Description

Differentiating the linear relations with respect to the $c$- and $o$-variables, we obtain a matrix whose coefficients depend only on the $a$-variables and are either linear or quadratic. All in all, the matrix is of the form $$ \begin{pmatrix} 0 & l_1 \\ l_2 & q \end{pmatrix} $$ where the entries of $l_1$, $l_2$ are linear in the $a$-variables and the entries of $q$ are quadratic.

i1 : kk = ZZ/197;

i2 : s = "1111";

i3 : (relLin,relPfaf,d1',d2,Ms) = setupGodeaux(kk,s);

i4 : (solutionMat,restVars) = solutionMatrix(relLin);

i5 : (betti solutionMat,betti restVars)

              0  1         0  1
o5 = (total: 42 32, total: 1 32)
         -6: 30  .      0: 1  .
         -5:  . 20      1: . 12
         -4: 12  .      2: .  .
         -3:  . 12      3: . 20

o5 : Sequence

Ways to use `solutionMatrix` :

"solutionMatrix(Matrix)"

For the programmer

The object solutionMatrix is a method function.

solutionMatrix -- display the relations linear in the c- and o-variables as a matrix

Synopsis

Description

Ways to use solutionMatrix :

For the programmer

Ways to use `solutionMatrix` :