1 | LIB "tst.lib"; |
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2 | tst_init(); |
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3 | |
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4 | LIB "sheafcoh.lib"; |
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5 | |
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6 | // Kohomologie der Strukturgarbe von P^5: |
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7 | //---------------------------------------- |
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8 | ring r=0,x(1..6),dp; |
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9 | module M=0; |
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10 | def A=sheafCoh(M,-10,5); |
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11 | A=sheafCoh(M,-10,5,"sres"); |
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12 | def B=sheafCohBGG(M,-10,5); |
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13 | displayCohom(A,-10,5,5); |
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14 | displayCohom(B,-10,5,5); |
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15 | // Kohomologie der getwisteten Strukturgarbe von P^5: |
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16 | //---------------------------------------------------- |
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17 | attrib(M,"isHomog",intvec(-2)); |
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18 | A=sheafCoh(M,-10,3); |
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19 | A=sheafCoh(M,-10,3,"sres"); |
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20 | B=sheafCohBGG(M,-10,3); |
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21 | // Kohomologie direkter Summen getwisteter Strukturgarben von P^5: |
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22 | //---------------------------------------------------------------- |
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23 | matrix MM[3][1]; |
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24 | M=MM; |
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25 | attrib(M,"isHomog",intvec(-1,0,2)); |
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26 | A=sheafCoh(M,-9,5); |
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27 | A=sheafCoh(M,-9,4,"sres"); |
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28 | B=sheafCohBGG(M,-8,3); |
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29 | // Kohomologie von O(-2)+O(-1)+(O/x(1))(1) = O_5(-2)+o_5(-1)+O_4(1): |
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30 | //------------------------------------------------------------------- |
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31 | MM=0,x(1),0; |
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32 | M=MM; |
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33 | attrib(M,"isHomog",intvec(-2,1,-1)); |
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34 | A=sheafCoh(M,-8,4); |
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35 | A=sheafCoh(M,-8,4,"sres"); |
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36 | B=sheafCohBGG(M,-8,3); |
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37 | kill r; |
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38 | |
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39 | // Kohomologie der Idealgarbe der Veronese Flaeche in $\P^3$: |
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40 | //------------------------------------------------------------ |
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41 | ring S = 32003, x(0..4), dp; |
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42 | module MI=maxideal(1); |
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43 | attrib(MI,"isHomog",intvec(-1)); |
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44 | resolution kos = nres(MI,0); |
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45 | print(betti(kos),"betti"); |
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46 | matrix alpha0 = random(32002,10,3); |
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47 | module pres = module(alpha0)+kos[3]; |
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48 | attrib(pres,"isHomog",intvec(1,1,1,1,1,1,1,1,1,1)); |
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49 | resolution fcokernel = mres(pres,0); |
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50 | print(betti(fcokernel),"betti"); |
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51 | module dir = transpose(pres); |
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52 | attrib(dir,"isHomog",intvec(-1,-1,-1,-2,-2,-2, |
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53 | -2,-2,-2,-2,-2,-2,-2)); |
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54 | resolution fdir = mres(dir,2); |
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55 | print(betti(fdir),"betti"); |
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56 | ideal I = groebner(flatten(fdir[2])); |
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57 | resolution FI = mres(I,0); |
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58 | print(betti(FI),"betti"); |
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59 | module F=FI[2]; |
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60 | A=sheafCoh(F,-4,4); |
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61 | A=sheafCoh(F,-4,4,"sres"); |
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62 | B=sheafCohBGG(F,-4,2); |
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63 | |
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64 | dimH(3,F,-4); |
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65 | dimH(1,F,1); |
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66 | |
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67 | A=sheafCoh(F,-1,1); |
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68 | kill S; |
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69 | |
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70 | // -------------------------------------------------- |
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71 | // Test of truncate: |
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72 | ring R=0,(x,y,z),dp; |
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73 | module M=x2,y3,z4; |
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74 | homog(M); |
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75 | // compute presentation matrix for truncated module (R/<x2,y3,z4>)_(>=2) |
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76 | module M2=truncate(M,2); |
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77 | print(M2); |
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78 | dimGradedPart(M2,1); |
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79 | dimGradedPart(M,1); |
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80 | dimGradedPart(M2,2); |
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81 | // this should coincide with: |
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82 | dimGradedPart(M,2); |
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83 | dimGradedPart(M,3); |
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84 | // shift grading by -1: |
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85 | intvec v=-1; |
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86 | attrib(M,"isHomog",v); |
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87 | M2=truncate(M,2); |
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88 | print(M2); |
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89 | dimGradedPart(M2,2); |
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90 | |
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91 | tst_status(1);$ |
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92 | |
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