Thomas D. Dean on Sat, 19 Nov 2022 18:53:37 +0100


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Re: Obtaining the coefficient matrix of multivariable homogeneous linear equation system. 

On 11/19/22 04:58, Charles Greathouse wrote:



    ? A     = [a,b;c,d];
    ? basis = [matrix(2,2,k,l,k==i&&l==j)|i<-[1..2];j<-[1..2]]
    %2 = [[1,0;0,0],[0,1;0,0],[0,0;1,0],[0,0;0,1]]
    ? C     = [A * B - B * A  | B<-basis]
    %3 = [[0,-b;c,0],[-c,a-d;0,c],[b,0;-a+d,-b],[0,b;-c,0]]
    ? D     = Mat([concat(Vec(c))  | c<-C]~)
    %4 = [0,-c,b,0;-b,a-d,0,b;c,0,-a+d,-c;0,c,-b,0]
    ? matker(D)
    %5 = [1/c*a-d/c,1;1/c*b,0;1,0;0,1]

    Cheers,
    Bill.



Ubuntu 20.04 latest gp.
I get an error with this code. The value of D is not the same order and is enclosed with brackets. 




> /usr/local/bin/gp

Reading GPRC: /home/tomdean/.gprc

GPRC Done.



        GP/PARI CALCULATOR Version 2.16.0 (development 28175-12b43bac1)

          amd64 running linux (x86-64/GMP-6.2.1 kernel) 64-bit version
compiled: Nov 19 2022, gcc version 9.4.0 (Ubuntu 9.4.0-1ubuntu1~20.04.1) 

                           threading engine: pthread

                 (readline v8.0 enabled, extended help enabled)



                     Copyright (C) 2000-2022 The PARI Group
PARI/GP is free software, covered by the GNU General Public License, and comes 

WITHOUT ANY WARRANTY WHATSOEVER.



Type ? for help, \q to quit.

Type ?18 for how to get moral (and possibly technical) support.



parisizemax = 4000002048, primelimit = 1000000, nbthreads = 4

? A     = [a,b;c,d];

? basis = [matrix(2,2,k,l,k==i&&l==j)|i<-[1..2];j<-[1..2]]

%2 = [[1, 0; 0, 0], [0, 1; 0, 0], [0, 0; 1, 0], [0, 0; 0, 1]]

? C     = [A * B - B * A  | B<-basis]

%3 = [[0, -b; c, 0], [-c, a - d; 0, c], [b, 0; -a + d, -b], [0, b; -c, 0]]

? D     = Mat([concat(Vec(c))  | c<-C]~)

%4 =

[     [0, c, -b, 0]~]



[ [-c, 0, a - d, c]~]



[[b, -a + d, 0, -b]~]



[     [0, -c, b, 0]~]



? matker(D)

  ***   at top-level: matker(D)

  ***                 ^---------

  *** matker: forbidden division t_INT / t_COL (4 elts).

  ***   Break loop: type 'break' to go back to GP prompt

break> break



? E = [0,-c,b,0;-b,a-d,0,b;c,0,-a+d,-c;0,c,-b,0]

%5 =

[ 0    -c      b  0]



[-b a - d      0  b]



[ c     0 -a + d -c]



[ 0     c     -b  0]



? matker(E)

%6 =

[1/c*a - d/c 1]



[      1/c*b 0]



[          1 0]



[          0 1]


Tom Dean