1 | // Two transversal cusps in (k^3,0): |
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2 | ring r2 =0,(x,y,z),ds; |
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3 | ideal i =z2-1y3+x3y,xz,-1xy2+x4,x3z; |
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4 | list resi=mres(i,0); // computes a minimal resolution |
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5 | print(resi[1]); // the 1-st module is i minimized |
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6 | print(resi[2]); // the 1-st syzygy module of i |
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7 | resi[3]; // the 2-nd syzygy module of i |
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8 | ideal j=minor(resi[2],2); |
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9 | reduce(j,std(i)); // check whether j is contained in i |
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10 | size(reduce(i,std(j))); // check whether i is contained in j |
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11 | // size(<ideal>) counts the non-zero generators |
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12 | // --------------------------------------------- |
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13 | // The tangent developable of the rational normal curve in P^4: |
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14 | ring P = 0,(a,b,c,d,e),dp; |
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15 | ideal j= 3c2-4bd+ae, -2bcd+3ad2+3b2e-4ace, |
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16 | 8b2d2-9acd2-9b2ce+9ac2e+2abde-1a2e2; |
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17 | list L=mres(j,0); |
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18 | print(L[2]); |
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19 | // create an intmat with graded betti numbers |
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20 | intmat B=betti(L); |
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21 | // this gives a nice output of betti numbers |
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22 | print(B,"betti"); |
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23 | // the user has acess to all betti numbers |
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24 | // the 2-nd column of B: |
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25 | B[1..4,2]; |
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26 | LIB "tst.lib";tst_status(1);$ |
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