D.2.5.9 triagmatrix

Procedure from library random.lib (see random_lib).

Usage:

triagmatrix(n,m,o[,u,pe,pp,b]); n,m,o,u,pe,pp,b integers

Return:

nxm lower triagonal matrix, diagonal entries equal to 1, about p percent of lower diagonal entries are 0, the remaining are random polynomials of degree d, u<=d<=o, with pp percent of the terms being 0, the remaining have random coefficients in the interval [1,b] [default: (pe,u,pp,b) = (0,50,75,100)]

Example:

LIB "random.lib";
ring r = 0,(a,b,c,d),dp;
// sparse triagonal matrix of sparse polys of degree <=2:
print(triagmatrix(3,4,2));"";
→ 1,                                 0,0,0,
→ 52ac+54cd+14c,                     1,0,0,
→ 17a2+19b2+45ac+94bc+50b+87c+54d+21,0,1,0 
→ 
// dense triagonal matrix of sparse linear forms:
print(triagmatrix(3,3,1,1,0,55,9));
→ 1,       0,    0,
→ 7a+8d,   1,    0,
→ 9b+7c+4d,7b+9d,1