Singular Manual: codim

| #### D.6.20.1 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 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 Hilbert series iv1(t) of id1 and iv2(t) of id2. If codim(id1,id2) is finite, q(t)=(iv2(t)-iv1(t))/(1-t)^n is rational, and the codimension is the sum of the coefficients of q(t) (n = dimension of basering). Example:
    LIB "sing.lib";
    ring r  = 0,(x,y),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)
    ==> 23

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