D.2.5.1 genericid

Procedure from library random.lib (see random_lib).

Usage:

genericid(id,[,p,b]); id ideal/module, k,p,b integers

Return:

system of generators of id which are generic, sparse, triagonal linear combinations of given generators with coefficients in [1,b] and sparseness p percent, bigger p being sparser (default: p=75, b=30000)

Note:

For performance reasons try small bound b in characteristic 0

Example:

LIB "random.lib";
ring r=0,(t,x,y,z),ds;
ideal i= x3+y4,z4+yx,t+x+y+z;
genericid(i,0,10);
→ _[1]=3t+3x+3y+3z+2xy+x3+y4+2z4
→ _[2]=4t+4x+4y+4z+xy+z4
→ _[3]=t+x+y+z
module m=[x,0,0,0],[0,y2,0,0],[0,0,z3,0],[0,0,0,t4];
print(genericid(m));
→ x,      0,      0, 0,
→ 17904y2,y2,     0, 0,
→ 0,      24170z3,z3,0,
→ 0,      0,      0, t4