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D.2.7.1 genericid
Procedure from library random.lib (see random_lib).
- Usage:
- genericid(id[,p,b]); id ideal/module, 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
sparsety 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
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