Singular

4.11.1 matrix declarations

Syntax:

matrix name[rows][cols] = list_of_poly_expressions ;
matrix name = matrix_expression ;

Purpose:

defines a matrix (of polynomials).

The given poly_list fills up the matrix beginning with the first row from the left to the right, then the second row and so on. If the poly_list contains less than rows*cols elements, the matrix is filled up with zeros; if it contains more elements, then only the first rows*cols elements are used. If the right-hand side is a matrix expression the matrix on the left-hand side gets the same size as the right-hand side, otherwise the size is determined by the left-hand side. If the size is omitted a 1x1 matrix is created.

Default:

0 (1 x 1 matrix)

Example:

int ro = 3; ring r = 32003,(x,y,z),dp; poly f=xyz; poly g=z*f; ideal i=f,g,g^2; matrix m[ro][3] = x3y4, 0, i, f ; // a 3 x 3 matrix m; ==> m[1,1]=x3y4 ==> m[1,2]=0 ==> m[1,3]=xyz ==> m[2,1]=xyz2 ==> m[2,2]=x2y2z4 ==> m[2,3]=xyz ==> m[3,1]=0 ==> m[3,2]=0 ==> m[3,3]=0 print(m); ==> x3y4,0, xyz, ==> xyz2,x2y2z4,xyz, ==> 0, 0, 0 matrix A; // the 1 x 1 zero matrix matrix B[2][2] = m[1..2, 2..3]; //defines a submatrix print(B); ==> 0, xyz, ==> x2y2z4,xyz matrix C=m; // defines C as a 3 x 3 matrix equal to m print(C); ==> x3y4,0, xyz, ==> xyz2,x2y2z4,xyz, ==> 0, 0, 0