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D.3.1.10 skewmat
Procedure from library matrix.lib (see matrix_lib).
- Usage:
- skewmat(n[,id]); n integer, id ideal
- Return:
- skew-symmetric nxn matrix, with entries from id
(default: id=maxideal(1))
skewmat(n); creates the generic skew-symmetric matrix
- Note:
- if id has less than n*(n-1)/2 elements, the matrix is
filled with 0's,
Example:
| | LIB "matrix.lib";
ring R=0,x(1..5),lp;
print(skewmat(4)); // the generic skew-symmetric matrix
==> 0, x(1), x(2),x(3),
==> -x(1),0, x(4),x(5),
==> -x(2),-x(4),0, 0,
==> -x(3),-x(5),0, 0
ring R1 = 0,(a,b,c),dp;
matrix A=skewmat(4,maxideal(1)^2);
print(A);
==> 0, a2, ab, ac,
==> -a2,0, b2, bc,
==> -ab,-b2,0, c2,
==> -ac,-bc,-c2,0
int n=3;
ideal i = ideal(randommat(1,n*(n-1) div 2,maxideal(1),9));
print(skewmat(n,i)); // skew matrix of generic linear forms
==> 0, 4a+b-8c, -a+6b+c,
==> -4a-b+8c,0, -8a+2b-9c,
==> a-6b-c, 8a-2b+9c,0
kill R1;
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