1 | LIB "tst.lib"; tst_init(); |
---|
2 | // Two transversal cusps in (k^3,0): |
---|
3 | ring r2 =0,(x,y,z),ds; |
---|
4 | ideal i =z2-1y3+x3y,xz,-1xy2+x4,x3z; |
---|
5 | resolution rs=mres(i,0); // computes a minimal resolution |
---|
6 | rs; // the standard representation of complexes |
---|
7 | list resi=rs; // convertion to a list |
---|
8 | print(resi[1]); // the 1st module is i minimized |
---|
9 | print(resi[2]); // the 1st syzygy module of i |
---|
10 | resi[3]; // the 2nd syzygy module of i |
---|
11 | ideal j=minor(resi[2],2); |
---|
12 | reduce(j,std(i)); // check whether j is contained in i |
---|
13 | size(reduce(i,std(j))); // check whether i is contained in j |
---|
14 | // size(<ideal>) counts the non-zero generators |
---|
15 | // --------------------------------------------- |
---|
16 | // The tangent developable of the rational normal curve in P^4: |
---|
17 | ring P = 0,(a,b,c,d,e),dp; |
---|
18 | ideal j= 3c2-4bd+ae, -2bcd+3ad2+3b2e-4ace, |
---|
19 | 8b2d2-9acd2-9b2ce+9ac2e+2abde-1a2e2; |
---|
20 | resolution rs=mres(j,0); |
---|
21 | rs; |
---|
22 | list L=rs; |
---|
23 | print(L[2]); |
---|
24 | // create an intmat with graded Betti numbers |
---|
25 | intmat B=betti(rs); |
---|
26 | // this gives a nice output of Betti numbers |
---|
27 | print(B,"betti"); |
---|
28 | // the user has access to all Betti numbers |
---|
29 | // the 2-nd column of B: |
---|
30 | B[1..4,2]; |
---|
31 | ring cyc5=32003,(a,b,c,d,e,h),dp; |
---|
32 | ideal i= |
---|
33 | a+b+c+d+e, |
---|
34 | ab+bc+cd+de+ea, |
---|
35 | abc+bcd+cde+dea+eab, |
---|
36 | abcd+bcde+cdea+deab+eabc, |
---|
37 | h5-abcde; |
---|
38 | resolution rs=lres(i,0); //computes the resolution according LaScala |
---|
39 | rs; //the shape of the minimal resolution |
---|
40 | print(betti(rs),"betti"); //shows the Betti-numbers of cyclic 5 |
---|
41 | dim(rs); //the homological dimension |
---|
42 | size(list(rs)); //gets the full (non-reduced) resolution |
---|
43 | minres(rs); //minimizes the resolution |
---|
44 | size(list(rs)); //gets the minimized resolution |
---|
45 | tst_status(1);$ |
---|