Singular

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;