|
 |
 |
 |
 |
 |
 |
 |
 |
 |
D.3.1.12 symmat
Procedure from library matrix.lib (see matrix_lib).
- Usage:
symmat(n[,id]); n integer, id ideal
- Return:
symmetric nxn matrix, with entries from id (default: id=maxideal(1))
- Note:
if id has less than n*(n+1)/2 elements, the matrix is filled with 0’s, symmat(n); creates the generic symmetric matrix
Example:
LIB "matrix.lib"; ring R=0,x(1..10),lp; print(symmat(4)); // the generic symmetric matrix → x(1),x(2),x(3),x(4), → x(2),x(5),x(6),x(7), → x(3),x(6),x(8),x(9), → x(4),x(7),x(9),x(10) ring R1 = 0,(a,b,c),dp; matrix A=symmat(4,maxideal(1)^3); print(A); → a3, a2b,a2c,ab2, → a2b,abc,ac2,b3, → a2c,ac2,b2c,bc2, → ab2,b3, bc2,c3 int n=3; ideal i = ideal(randommat(1,n*(n+1) div 2,maxideal(1),9)); print(symmat(n,i)); // symmetric matrix of generic linear forms → 4a-8b-2c,-a+b-4c, -8a-9b+c, → -a+b-4c, a-9b+9c, 6a-5b+9c, → -8a-9b+c,6a-5b+9c,2a+8c kill R1; |