Spracherkennung für: .g vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
#! @Chapter Examples and Tests
#! @Section Solving (Homogeneous) Linear Systems
#! @Example
LoadPackage( "LinearAlgebraForCAP", false );
#! true
QQ := HomalgFieldOfRationals();;
QQ_mat := MatrixCategory( QQ );
#! Category of matrices over Q
t := TensorUnit( QQ_mat );
#! <A vector space object over Q of dimension
1>
id_t := IdentityMorphism( t );
#! <An identity morphism in Category of matrices over Q>
1*(
11)*
7 +
2*(
12)*
8 +
3*(
13)*
9;
#!
620
4*(
11)*
3 +
5*(
12)*
4 +
6*(
13)*
1;
#!
450
alpha := [ [
1/QQ * id_t,
2/QQ * id_t,
3/QQ * id_t ], [
4/QQ * id_t,
5/QQ * id_t,
6/QQ * id_t ] ];;
beta := [ [
7/QQ * id_t,
8/QQ * id_t,
9/QQ * id_t ], [
3/QQ * id_t,
4/QQ * id_t,
1/QQ * id_t ] ];;
gamma := [
620/QQ * id_t,
450/QQ * id_t ];;
MereExistenceOfSolutionOfLinearSystemInAbCategory(
QQ_mat, alpha, beta, gamma );
#! true
MereExistenceOfUniqueSolutionOfLinearSystemInAbCategory(
QQ_mat, alpha, beta, gamma );
#! false
x := SolveLinearSystemInAbCategory( QQ_mat, alpha, beta, gamma );;
(
1*
7)/QQ * x[
1] + (
2*
8)/QQ * x[
2] + (
3*
9)/QQ * x[
3] = gamma[
1];
#! true
(
4*
3)/QQ * x[
1] + (
5*
4)/QQ * x[
2] + (
6*
1)/QQ * x[
3] = gamma[
2];
#! true
MereExistenceOfUniqueSolutionOfHomogeneousLinearSystemInAbCategory(
QQ_mat, alpha, beta );
#! false
B := BasisOfSolutionsOfHomogeneousLinearSystemInLinearCategory(
QQ_mat, alpha, beta );;
Length( B );
#!
1
(
1*
7)/QQ * B[
1][
1] + (
2*
8)/QQ * B[
1][
2] + (
3*
9)/QQ * B[
1][
3] =
0/QQ * id_t;
#! true
(
4*
3)/QQ * B[
1][
1] + (
5*
4)/QQ * B[
1][
2] + (
6*
1)/QQ * B[
1][
3] =
0/QQ * id_t;
#! true
2*(
11)*
5 +
3*(
12)*
7 +
9*(
13)*
2;
#!
596
Add( alpha, [
2/QQ * id_t,
3/QQ * id_t,
9/QQ * id_t ] );;
Add( beta, [
5/QQ * id_t,
7/QQ * id_t,
2/QQ * id_t ] );;
Add( gamma,
596/QQ * id_t );;
MereExistenceOfSolutionOfLinearSystemInAbCategory(
QQ_mat, alpha, beta, gamma );
#! true
MereExistenceOfUniqueSolutionOfLinearSystemInAbCategory(
QQ_mat, alpha, beta, gamma );
#! true
x := SolveLinearSystemInAbCategory( QQ_mat, alpha, beta, gamma );;
(
1*
7)/QQ * x[
1] + (
2*
8)/QQ * x[
2] + (
3*
9)/QQ * x[
3] = gamma[
1];
#! true
(
4*
3)/QQ * x[
1] + (
5*
4)/QQ * x[
2] + (
6*
1)/QQ * x[
3] = gamma[
2];
#! true
(
2*
5)/QQ * x[
1] + (
3*
7)/QQ * x[
2] + (
9*
2)/QQ * x[
3] = gamma[
3];
#! true
MereExistenceOfUniqueSolutionOfHomogeneousLinearSystemInAbCategory(
QQ_mat, alpha, beta );
#! true
B := BasisOfSolutionsOfHomogeneousLinearSystemInLinearCategory(
QQ_mat, alpha, beta );;
Length( B );
#!
0
alpha := [ [
2/QQ * id_t,
3/QQ * id_t ] ];;
delta := [ [
3/QQ * id_t,
3/QQ * id_t ] ];;
B := BasisOfSolutionsOfHomogeneousDoubleLinearSystemInLinearCategory( alpha, delta );
;
Length( B );
#! 1
mor1 := PreCompose( alpha[1][1], B[1][1] ) + PreCompose( alpha[1][2], B[1][2] );
#! <A morphism in Category of matrices over Q>
mor2 := PreCompose( B[1][1], delta[1][1] ) + PreCompose( B[1][2], delta[1][2] );
#! <A morphism in Category of matrices over Q>
mor1 = mor2;
#! true
#! @EndExample
