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D.5.9.1 codim
Procedure from library sing.lib (see sing_lib).
- Usage:
- codim(id1,id2); id1,id2 ideal or module, both must be standard bases
- Return:
- int, which is:
1. the codimension of id2 in id1, i.e. the vectorspace dimension of
id1/id2 if id2 is contained in id1 and if this number is finite
2. -1 if the dimension of id1/id2 is infinite
3. -2 if id2 is not contained in id1,
- Compute:
- consider the two hilberseries iv1(t) and iv2(t), then, in case 1.,
q(t)=(iv2(t)-iv1(t))/(1-t)^n must be rational, and the result is the
sum of the coefficients of q(t) (n dimension of basering)
Example:
| LIB "sing.lib";
ring r = 0,(x,y,z),dp;
ideal j = y6,x4;
ideal m = x,y;
attrib(m,"isSB",1); //let Singular know that ideals are a standard basis
attrib(j,"isSB",1);
codim(m,j); // should be 23 (Milnor number -1 of y7-x5)
==> -1
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