Singular Manual: skewmat

| #### 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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