CohomCalg is software written by Benjamin Jurke and Thorsten Rahn (in collaboration with Ralph Blumenhagen and Helmut Roschy) for computing the cohomology vectors of torus invariant divisors on a (normal) toric variety (see https://github.com/BenjaminJurke/cohomCalg for more information).
CohomCalg is an efficient and careful implementation. One limitation is that the number of rays in the fan and the number of generators of the Stanley-Reisner ideal of the fan must both be no larger than 64.
Here is a sample usage of this package in Macaulay2. Let's compute the cohomology of some divisors on a smooth Fano toric variety.
i1 : needsPackage "NormalToricVarieties" o1 = NormalToricVarieties o1 : Package |
i2 : X = smoothFanoToricVariety(3,15) o2 = X o2 : NormalToricVariety |
i3 : rays X o3 = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {0, -1, -1}, {0, -1, 0}, {-1, 0, 0}, {-1, 1, 0}} o3 : List |
i4 : max X o4 = {{0, 1, 2}, {0, 1, 3}, {0, 2, 4}, {0, 3, 4}, {1, 2, 6}, {1, 3, 6}, {2, 4, 5}, {2, 5, 6}, {3, 4, 5}, {3, 5, 6}} o4 : List |
i5 : S = ring X o5 = S o5 : PolynomialRing |
i6 : SR = dual monomialIdeal X o6 = monomialIdeal (x x , x x , x x , x x , x x , x x ) 2 3 1 4 0 5 1 5 0 6 4 6 o6 : MonomialIdeal of S |
i7 : KX = toricDivisor X o7 = - X - X - X - X - X - X - X 0 1 2 3 4 5 6 o7 : ToricDivisor on X |
i8 : assert isVeryAmple (-KX) |
i9 : cohoms1 = for i from 0 to 6 list X_i => cohomCalg X_i cohomCalg v0.32 (compiled for Linux/Unix x86-64 / 64 bit) author: Benjamin Jurke (mail@benjaminjurke.com) Based on the algorithm detailed in arXiv:1003.5217 Usage and generation of intermediate monomial files deactivated. Starting computation of secondary sequences... 0.00% completed (1 sec remaining)... Computation of secondary cohomologies and contributions complete. Computing target cohomology 1 of 1 (0.0% done)... 7 5 1 0 -1 0 1 1 0 -1 1 0 1 -1 1 -1 0 1 1 0 0 0 1 0 1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 -1 1 0 1 -1 -1 1 -2 1 1 0 0 0 1 0 1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 1 -1 -1 1 -1 1 -1 0 1 1 0 0 0 1 0 -1 1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 1 -1 -1 1 -1 -1 1 -2 1 1 0 0 0 1 0 -1 1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 1 1 1 1 -1 -1 -1 -1 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 2 1 0 -1 -1 -2 1 -1 -1 -1 -1 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 -1 -1 -2 1 -1 -1 -1 -1 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 1 1 1 1 -1 1 1 -1 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 2 1 0 -1 -1 -2 1 -1 1 1 -1 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 -1 -1 -2 1 -1 1 1 -1 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 2 1 0 -1 -1 -2 1 -1 -1 -1 -1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 2 1 0 -1 -1 -2 1 -1 1 1 -1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -2 1 0 -1 -1 -1 1 -1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -2 1 0 -1 -1 -1 1 -1 -1 -1 -3 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 -1 -1 -1 1 -1 1 1 1 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -2 1 0 -1 -1 -1 1 -1 1 1 1 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 1 1 0 1 -1 1 1 1 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 -1 -1 -1 1 -1 -1 -1 -3 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -2 1 0 -1 -1 -1 1 -1 -1 -1 -3 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 1 1 0 1 -1 -1 -1 -3 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 1 -1 0 1 -1 -1 1 0 1 1 0 0 0 1 0 -1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 1 -1 0 1 -1 1 -1 -2 1 1 0 0 0 1 0 -1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 -1 1 -1 1 -1 -1 1 0 1 1 0 0 0 1 0 1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 -1 1 -1 1 -1 1 -1 -2 1 1 0 0 0 1 0 1 -1 -1 1 0 1 0 0 1 0 0 1 0 Computation of the target cohomology group dimensions complete. All done. Program run successfully completed. cohomCalg v0.32 (compiled for Linux/Unix x86-64 / 64 bit) author: Benjamin Jurke (mail@benjaminjurke.com) Based on the algorithm detailed in arXiv:1003.5217 Usage and generation of intermediate monomial files deactivated. Starting computation of secondary sequences... 98.44% completed (0 secs remaining)... Computation of secondary cohomologies and contributions complete. Computing target cohomology 1 of 1 (0.0% done)... 7 5 1 0 -1 0 0 1 0 -1 1 1 1 -1 1 -1 0 1 1 0 0 0 1 0 1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 -1 1 1 1 -1 -1 1 -2 1 1 0 0 0 1 0 1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 -1 -2 1 -1 1 -1 0 1 1 0 0 0 1 0 -1 1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 -1 -2 1 -1 -1 1 -2 1 1 0 0 0 1 0 -1 1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 1 2 1 -1 -1 -1 -1 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -3 1 -1 -1 -1 -1 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 -1 -3 1 -1 -1 -1 -1 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 1 2 1 -1 1 1 -1 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -3 1 -1 1 1 -1 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 -1 -3 1 -1 1 1 -1 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -3 1 -1 -1 -1 -1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -3 1 -1 1 1 -1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 0 1 -1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 0 1 -1 -1 -1 -3 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 -1 -1 0 1 -1 1 1 1 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 0 1 -1 1 1 1 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 1 -1 1 -1 1 1 1 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 -1 -1 0 1 -1 -1 -1 -3 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 0 1 -1 -1 -1 -3 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 1 -1 1 -1 -1 -1 -3 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 -1 1 1 -1 -1 1 0 1 1 0 0 0 1 0 -1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 -1 1 1 -1 1 -1 -2 1 1 0 0 0 1 0 -1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 1 -2 1 -1 -1 1 0 1 1 0 0 0 1 0 1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 1 -2 1 -1 1 -1 -2 1 1 0 0 0 1 0 1 -1 -1 1 0 1 0 0 1 0 0 1 0 Computation of the target cohomology group dimensions complete. All done. Program run successfully completed. cohomCalg v0.32 (compiled for Linux/Unix x86-64 / 64 bit) author: Benjamin Jurke (mail@benjaminjurke.com) Based on the algorithm detailed in arXiv:1003.5217 Usage and generation of intermediate monomial files deactivated. Starting computation of secondary sequences... 98.44% completed (0 secs remaining)... Computation of secondary cohomologies and contributions complete. Computing target cohomology 1 of 1 (0.0% done)... 7 5 1 0 -1 0 0 1 0 -1 1 0 1 -1 1 -1 1 1 1 0 0 0 1 0 1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 -1 1 0 1 -1 -1 1 -3 1 1 0 0 0 1 0 1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 -1 -1 1 -1 1 -1 1 1 1 0 0 0 1 0 -1 1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 -1 -1 1 -1 -1 1 -3 1 1 0 0 0 1 0 -1 1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 1 1 1 -1 -1 -1 0 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -2 1 -1 -1 -1 0 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 -1 -2 1 -1 -1 -1 0 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 1 1 1 -1 1 1 -2 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -2 1 -1 1 1 -2 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 -1 -2 1 -1 1 1 -2 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -2 1 -1 -1 -1 0 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -2 1 -1 1 1 -2 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 -1 1 -1 1 1 2 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 -1 1 -1 -1 -1 -4 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 -1 -1 -1 1 -1 1 1 2 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 -1 1 -1 1 1 2 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 1 0 1 -1 1 1 2 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 -1 -1 -1 1 -1 -1 -1 -4 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 -1 1 -1 -1 -1 -4 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 1 0 1 -1 -1 -1 -4 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 -1 0 1 -1 -1 1 1 1 1 0 0 0 1 0 -1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 -1 0 1 -1 1 -1 -3 1 1 0 0 0 1 0 -1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 1 -1 1 -1 -1 1 1 1 1 0 0 0 1 0 1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 1 -1 1 -1 1 -1 -3 1 1 0 0 0 1 0 1 -1 -1 1 0 1 0 0 1 0 0 1 0 Computation of the target cohomology group dimensions complete. All done. Program run successfully completed. cohomCalg v0.32 (compiled for Linux/Unix x86-64 / 64 bit) author: Benjamin Jurke (mail@benjaminjurke.com) Based on the algorithm detailed in arXiv:1003.5217 Usage and generation of intermediate monomial files deactivated. Starting computation of secondary sequences... 0.00% completed (1 sec remaining)... Computation of secondary cohomologies and contributions complete. Computing target cohomology 1 of 1 (0.0% done)... 7 5 1 0 -1 0 0 1 0 -1 1 0 1 -1 1 -1 0 1 1 0 0 0 1 0 1 -1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 -1 1 0 1 -1 -1 1 -2 1 1 0 0 0 1 0 1 -1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 -1 -1 1 -1 1 -1 0 1 1 0 0 0 1 0 -1 1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 -1 -1 1 -1 -1 1 -2 1 1 0 0 0 1 0 -1 1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 1 1 1 -1 -1 -1 -1 1 1 0 0 0 1 0 -1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -2 1 -1 -1 -1 -1 1 1 0 0 0 1 0 -1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 -1 -2 1 -1 -1 -1 -1 1 1 0 0 0 1 0 -1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 1 1 1 -1 1 1 -1 1 1 0 0 0 1 0 -1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -2 1 -1 1 1 -1 1 1 0 0 0 1 0 -1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 -1 -2 1 -1 1 1 -1 1 1 0 0 0 1 0 -1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -2 1 -1 -1 -1 -1 1 1 0 0 0 1 0 1 1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -2 1 -1 1 1 -1 1 1 0 0 0 1 0 1 1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 -1 1 -1 1 1 1 1 1 0 0 0 1 0 1 1 2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 -1 1 -1 -1 -1 -3 1 1 0 0 0 1 0 1 1 2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 -1 -1 -1 1 -1 1 1 1 1 1 0 0 0 1 0 -1 -1 -3 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 -1 1 -1 1 1 1 1 1 0 0 0 1 0 -1 -1 -3 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 1 0 1 -1 1 1 1 1 1 0 0 0 1 0 -1 -1 -3 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 -1 -1 -1 1 -1 -1 -1 -3 1 1 0 0 0 1 0 -1 -1 -3 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 -1 1 -1 -1 -1 -3 1 1 0 0 0 1 0 -1 -1 -3 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 1 0 1 -1 -1 -1 -3 1 1 0 0 0 1 0 -1 -1 -3 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 -1 0 1 -1 -1 1 0 1 1 0 0 0 1 0 -1 1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 -1 0 1 -1 1 -1 -2 1 1 0 0 0 1 0 -1 1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 1 -1 1 -1 -1 1 0 1 1 0 0 0 1 0 1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 1 -1 1 -1 1 -1 -2 1 1 0 0 0 1 0 1 -1 -2 1 0 1 0 0 1 0 0 1 0 Computation of the target cohomology group dimensions complete. All done. Program run successfully completed. cohomCalg v0.32 (compiled for Linux/Unix x86-64 / 64 bit) author: Benjamin Jurke (mail@benjaminjurke.com) Based on the algorithm detailed in arXiv:1003.5217 Usage and generation of intermediate monomial files deactivated. Starting computation of secondary sequences... 0.00% completed (1 sec remaining)... Computation of secondary cohomologies and contributions complete. Computing target cohomology 1 of 1 (0.0% done)... 7 5 1 0 -1 0 1 1 0 -1 1 1 1 -1 1 -1 -1 1 1 0 0 0 1 0 1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 -1 1 1 1 -1 -1 1 -1 1 1 0 0 0 1 0 1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 1 -1 -2 1 -1 1 -1 -1 1 1 0 0 0 1 0 -1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 1 -1 -2 1 -1 -1 1 -1 1 1 0 0 0 1 0 -1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 1 1 2 1 -1 -1 -1 -2 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 2 1 0 -1 -1 -3 1 -1 -1 -1 -2 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 -1 -1 -3 1 -1 -1 -1 -2 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 1 1 2 1 -1 1 1 0 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 2 1 0 -1 -1 -3 1 -1 1 1 0 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 -1 -1 -3 1 -1 1 1 0 1 1 0 0 0 1 0 -1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 2 1 0 -1 -1 -3 1 -1 -1 -1 -2 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 2 1 0 -1 -1 -3 1 -1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -2 1 0 -1 -1 0 1 -1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -2 1 0 -1 -1 0 1 -1 -1 -1 -2 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 -1 -1 0 1 -1 1 1 0 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -2 1 0 -1 -1 0 1 -1 1 1 0 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 1 1 -1 1 -1 1 1 0 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 -1 -1 0 1 -1 -1 -1 -2 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -2 1 0 -1 -1 0 1 -1 -1 -1 -2 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 1 1 0 1 1 -1 1 -1 -1 -1 -2 1 1 0 0 0 1 0 -1 -1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 1 -1 1 1 -1 -1 1 -1 1 1 0 0 0 1 0 -1 1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 1 -1 1 1 -1 1 -1 -1 1 1 0 0 0 1 0 -1 1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 -1 1 -2 1 -1 -1 1 -1 1 1 0 0 0 1 0 1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -3 1 0 -1 1 -2 1 -1 1 -1 -1 1 1 0 0 0 1 0 1 -1 0 1 0 1 0 0 1 0 0 1 0 Computation of the target cohomology group dimensions complete. All done. Program run successfully completed. cohomCalg v0.32 (compiled for Linux/Unix x86-64 / 64 bit) author: Benjamin Jurke (mail@benjaminjurke.com) Based on the algorithm detailed in arXiv:1003.5217 Usage and generation of intermediate monomial files deactivated. Starting computation of secondary sequences... 0.00% completed (1 sec remaining)... Computation of secondary cohomologies and contributions complete. Computing target cohomology 1 of 1 (0.0% done)... 7 5 1 0 -1 0 0 1 0 -1 1 -1 1 -1 1 -1 1 1 1 0 0 0 1 0 1 -1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 -1 1 -1 1 -1 -1 1 -3 1 1 0 0 0 1 0 1 -1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 -1 0 1 -1 1 -1 1 1 1 0 0 0 1 0 -1 1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 -1 0 1 -1 -1 1 -3 1 1 0 0 0 1 0 -1 1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 1 0 1 -1 -1 -1 0 1 1 0 0 0 1 0 -1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -1 1 -1 -1 -1 0 1 1 0 0 0 1 0 -1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 -1 -1 1 -1 -1 -1 0 1 1 0 0 0 1 0 -1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 1 0 1 -1 1 1 -2 1 1 0 0 0 1 0 -1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -1 1 -1 1 1 -2 1 1 0 0 0 1 0 -1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 -1 -1 1 -1 1 1 -2 1 1 0 0 0 1 0 -1 -1 0 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -1 1 -1 -1 -1 0 1 1 0 0 0 1 0 1 1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 1 1 0 -1 -1 -1 1 -1 1 1 -2 1 1 0 0 0 1 0 1 1 -1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 -2 1 -1 1 1 2 1 1 0 0 0 1 0 1 1 2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 -2 1 -1 -1 -1 -4 1 1 0 0 0 1 0 1 1 2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 -1 -1 -2 1 -1 1 1 2 1 1 0 0 0 1 0 -1 -1 -3 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 -2 1 -1 1 1 2 1 1 0 0 0 1 0 -1 -1 -3 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 1 1 1 -1 1 1 2 1 1 0 0 0 1 0 -1 -1 -3 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 -1 -1 -2 1 -1 -1 -1 -4 1 1 0 0 0 1 0 -1 -1 -3 1 0 1 0 0 1 0 0 1 0 7 5 1 0 1 0 -1 1 0 -1 -1 -2 1 -1 -1 -1 -4 1 1 0 0 0 1 0 -1 -1 -3 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 0 1 0 1 1 1 1 -1 -1 -1 -4 1 1 0 0 0 1 0 -1 -1 -3 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 -1 -1 1 -1 -1 1 1 1 1 0 0 0 1 0 -1 1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 1 -1 -1 1 -1 1 -1 -3 1 1 0 0 0 1 0 -1 1 1 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 1 0 1 -1 -1 1 1 1 1 0 0 0 1 0 1 -1 -2 1 0 1 0 0 1 0 0 1 0 7 5 1 0 -1 0 -2 1 0 -1 1 0 1 -1 1 -1 -3 1 1 0 0 0 1 0 1 -1 -2 1 0 1 0 0 1 0 0 1 0 Computation of the target cohomology group dimensions complete. All done. Program run successfully completed. o9 = {X => {2, 0, 0, 0}, X => {1, 0, 0, 0}, X => {2, 0, 0, 0}, X => {2, 0, 0, 0}, X => {1, 0, 0, 0}, X => {1, 0, 0, 0}, X 0 1 2 3 4 5 6 ---------------------------------------------------------------------------------------------------------------------------- => {1, 0, 0, 0}} o9 : List |
i10 : cohoms2 = for i from 0 to 6 list X_i => ( for j from 0 to dim X list rank HH^j(X, OO_X(toSequence degree X_i)) ) o10 = {X => {2, 0, 0, 0}, X => {1, 0, 0, 0}, X => {2, 0, 0, 0}, X => {2, 0, 0, 0}, X => {1, 0, 0, 0}, X => {1, 0, 0, 0}, X 0 1 2 3 4 5 6 --------------------------------------------------------------------------------------------------------------------------- => {1, 0, 0, 0}} o10 : List |
i11 : assert(cohoms1 === cohoms2) |
For efficiency reasons, it is better, if this works for your use, to call CohomCalg by batching together several cohomology requests.
i12 : needsPackage "ReflexivePolytopesDB" o12 = ReflexivePolytopesDB o12 : Package |
i13 : topes = kreuzerSkarke(21, Limit => 20); using offline data file: ks21-n100.txt |
i14 : A = matrix topes_10 o14 = | 1 0 0 -1 2 0 0 -3 -2 1 | | 0 1 0 1 -1 1 0 1 0 -1 | | 0 0 1 1 -1 -1 0 4 2 -2 | | 0 0 0 0 0 0 1 -1 -1 1 | 4 10 o14 : Matrix ZZ <--- ZZ |
i15 : P = convexHull A o15 = P o15 : Polyhedron |
i16 : X = normalToricVariety P o16 = X o16 : NormalToricVariety |
i17 : SR = dual monomialIdeal X o17 = monomialIdeal (x x , x x x , x x , x x x , x x x , x x x x , x x x , x x x , x x x x , x x x , x x x , x x x x , x x x x , 1 2 0 1 3 0 4 0 2 6 0 3 6 1 3 5 6 1 3 7 1 4 7 0 3 5 7 2 4 8 2 6 8 3 5 6 8 4 5 6 8 --------------------------------------------------------------------------------------------------------------------------- x x x , x x x x , x x x x , x x x x , x x x , x x x , x x , x x x , x x x , x x x , x x x ) 4 7 8 2 5 7 8 3 5 7 8 3 6 7 8 0 1 9 2 4 9 5 9 0 6 9 2 6 9 1 7 9 4 7 9 o17 : MonomialIdeal of QQ[x ..x ] 0 9 |
i18 : D2 = subsets(for i from 0 to #rays X - 1 list (-X_i), 2) o18 = {{- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - 0 1 0 2 1 2 0 3 1 3 2 3 0 4 1 4 2 --------------------------------------------------------------------------------------------------------------------------- X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , 4 3 4 0 5 1 5 2 5 3 5 4 5 0 6 1 6 2 --------------------------------------------------------------------------------------------------------------------------- - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- 6 3 6 4 6 5 6 0 7 1 7 2 7 3 7 4 7 --------------------------------------------------------------------------------------------------------------------------- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, 5 7 6 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 --------------------------------------------------------------------------------------------------------------------------- {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - 7 8 0 9 1 9 2 9 3 9 4 9 5 9 6 9 7 --------------------------------------------------------------------------------------------------------------------------- X }, {- X , - X }} 9 8 9 o18 : List |
i19 : D2 = D2/sum/degree o19 = {{0, 1, -2, -2, 4, 0}, {0, 1, -1, 1, 0, -2}, {2, 2, 3, 1, -4, -6}, {-1, 0, -4, -2, 5, 3}, {1, 1, 0, -2, 1, -1}, {1, 1, 1, --------------------------------------------------------------------------------------------------------------------------- 1, -3, -3}, {-2, 0, -3, -1, 4, 2}, {0, 1, 1, -1, 0, -2}, {0, 1, 2, 2, -4, -4}, {-1, 0, -1, -1, 1, 1}, {-1, -1, -3, -1, 4, --------------------------------------------------------------------------------------------------------------------------- 2}, {1, 0, 1, -1, 0, -2}, {1, 0, 2, 2, -4, -4}, {0, -1, -1, -1, 1, 1}, {-1, -1, 0, 0, 0, 0}, {-1, 0, -4, -1, 4, 2}, {1, 1, --------------------------------------------------------------------------------------------------------------------------- 0, -1, 0, -2}, {1, 1, 1, 2, -4, -4}, {0, 0, -2, -1, 1, 1}, {-1, 0, -1, 0, 0, 0}, {0, -1, -1, 0, 0, 0}, {-1, 0, -3, -2, 4, --------------------------------------------------------------------------------------------------------------------------- 2}, {1, 1, 1, -2, 0, -2}, {1, 1, 2, 1, -4, -4}, {0, 0, -1, -2, 1, 1}, {-1, 0, 0, -1, 0, 0}, {0, -1, 0, -1, 0, 0}, {0, 0, --------------------------------------------------------------------------------------------------------------------------- -1, -1, 0, 0}, {-1, 0, -3, -1, 3, 2}, {1, 1, 1, -1, -1, -2}, {1, 1, 2, 2, -5, -4}, {0, 0, -1, -1, 0, 1}, {-1, 0, 0, 0, -1, --------------------------------------------------------------------------------------------------------------------------- 0}, {0, -1, 0, 0, -1, 0}, {0, 0, -1, 0, -1, 0}, {0, 0, 0, -1, -1, 0}, {-1, 0, -3, -1, 4, 1}, {1, 1, 1, -1, 0, -3}, {1, 1, --------------------------------------------------------------------------------------------------------------------------- 2, 2, -4, -5}, {0, 0, -1, -1, 1, 0}, {-1, 0, 0, 0, 0, -1}, {0, -1, 0, 0, 0, -1}, {0, 0, -1, 0, 0, -1}, {0, 0, 0, -1, 0, --------------------------------------------------------------------------------------------------------------------------- -1}, {0, 0, 0, 0, -1, -1}} o19 : List |
i20 : elapsedTime hvecs = cohomCalg(X, D2) cohomCalg v0.32 (compiled for Linux/Unix x86-64 / 64 bit) author: Benjamin Jurke (mail@benjaminjurke.com) Based on the algorithm detailed in arXiv:1003.5217 Usage and generation of intermediate monomial files deactivated. Starting computation of secondary sequences... 0.00% completed (1 sec remaining)... 56.25% completed (0 secs remaining)... WARNING: The Serre dualization reduction was unable to uniquely resolve 86 of the original 90 ambiguous monoms. Computation of secondary cohomologies and contributions complete. Computing target cohomology 1 of 45 (0.0% done)... 10 6 1 0 0 0 8 8 1 8 8 0 8 24 1 0 8 8 8 -32 1 0 6 4 0 -14 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 5 1 0 1 2 0 -11 1 2 3 2 4 0 10 6 1 8 8 0 8 0 1 0 0 0 8 8 1 -8 -8 -8 -8 8 1 0 -2 4 0 -2 1 0 0 8 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -5 1 0 1 2 0 -5 1 2 3 2 4 0 10 6 1 0 8 0 8 8 1 0 0 0 8 24 1 0 8 8 8 -32 1 -2 -2 4 0 -14 1 0 0 -8 -8 0 1 0 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 -11 1 1 3 2 4 0 10 6 1 0 8 0 8 0 1 0 0 0 8 16 1 0 -8 -8 -8 16 1 -2 -2 4 0 -6 1 0 0 8 8 0 1 0 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 -7 1 1 3 2 4 0 10 6 1 0 0 8 8 8 1 8 8 8 8 24 1 0 0 0 8 -32 1 0 2 -4 0 -14 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 5 1 0 1 2 0 10 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 -8 -8 -8 -8 -24 1 0 0 0 8 -24 1 0 -2 4 0 4 1 8 8 0 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 5 1 0 1 2 0 6 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 -8 -8 -8 -8 -24 1 0 0 0 8 -24 1 0 2 -4 0 -6 1 8 8 0 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 5 1 0 1 2 0 6 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 8 8 8 1 8 0 0 8 -16 1 0 6 4 0 0 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -5 1 0 1 2 0 4 1 2 1 2 4 0 10 6 1 8 8 8 8 0 1 0 0 8 8 8 1 -8 0 0 -8 8 1 0 -6 -4 0 -2 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -5 1 0 1 2 0 4 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 8 8 8 1 8 0 0 8 -16 1 0 -6 -4 0 -2 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -5 1 0 1 2 0 4 1 2 1 2 4 0 10 6 1 8 8 8 8 0 1 8 0 8 8 0 1 0 0 0 8 -16 1 -6 -6 -4 0 -6 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -2 1 1 1 2 0 2 1 3 1 2 4 0 10 6 1 8 8 8 8 -8 1 8 0 8 8 -8 1 0 0 0 -8 0 1 -6 -6 -4 0 2 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -2 1 1 1 2 0 -2 1 3 1 2 4 0 10 6 1 8 8 8 8 -8 1 -8 0 -8 -8 0 1 0 0 0 8 -8 1 -6 -6 -4 0 2 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -2 1 1 1 2 0 -2 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 8 0 8 8 -8 1 0 0 0 8 -8 1 -6 -6 -4 0 2 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -2 1 1 1 2 0 -2 1 3 1 2 4 0 10 6 1 8 8 8 8 8 1 8 0 8 8 24 1 0 0 0 -8 24 1 -6 -6 -4 0 -14 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 10 1 3 1 2 4 0 10 6 1 8 8 8 8 8 1 -8 0 -8 -8 -32 1 0 0 0 8 -32 1 -6 -6 -4 0 -14 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 10 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 -16 1 8 0 8 8 24 1 0 0 0 8 -32 1 -6 -6 -4 0 -14 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 10 1 3 1 2 4 0 10 6 1 8 8 8 8 8 1 8 0 8 8 24 1 0 0 0 8 -32 1 -6 -6 -4 0 -14 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 10 1 3 1 2 4 0 10 6 1 8 8 8 8 0 1 -8 0 -8 -8 -24 1 0 0 0 8 -24 1 6 6 4 0 4 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 8 0 8 8 16 1 0 0 0 8 -24 1 6 6 4 0 4 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 8 8 8 8 0 1 -8 0 -8 -8 -24 1 0 0 0 -8 16 1 -6 -6 -4 0 -6 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 8 0 8 8 16 1 0 0 0 -8 16 1 -6 -6 -4 0 -6 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 8 8 8 8 0 1 8 0 8 8 16 1 0 0 0 -8 16 1 -6 -6 -4 0 -6 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 -8 0 -8 -8 -24 1 0 0 0 8 -24 1 -6 -6 -4 0 -6 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 8 8 8 8 0 1 -8 0 -8 -8 -24 1 0 0 0 8 -24 1 -6 -6 -4 0 -6 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 8 0 8 8 16 1 0 0 0 8 -24 1 -6 -6 -4 0 -6 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 -8 0 -8 -8 -8 1 0 0 0 -8 -8 1 6 6 4 0 4 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 2 1 1 1 2 0 0 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 -8 -8 8 1 -8 0 0 -8 -24 1 0 6 4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 0 1 2 0 -6 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 -8 -8 0 1 -8 0 0 -8 -16 1 0 -6 -4 0 -2 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 0 1 2 0 -2 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 8 8 -8 1 -8 0 0 -8 -16 1 0 6 4 0 0 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 0 1 2 0 -2 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 -8 -8 0 1 -8 0 0 -8 -16 1 0 6 4 0 0 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 0 1 2 0 -2 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 8 1 0 0 -8 -8 32 1 -8 0 0 -8 -40 1 0 -6 -4 0 14 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 -14 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 8 1 0 0 -8 -8 32 1 8 0 0 8 32 1 0 6 4 0 -16 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 -14 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 8 1 0 0 -8 -8 32 1 -8 0 0 -8 -40 1 0 6 4 0 -16 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 -14 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 8 8 -32 1 -8 0 0 -8 -32 1 0 -6 -4 0 6 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 -10 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 -8 -8 24 1 -8 0 0 -8 -32 1 0 -6 -4 0 6 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 -10 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 -8 -8 -8 -8 -8 1 0 0 0 -8 -8 1 0 2 -4 0 -6 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 0 1 2 0 0 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 -8 -8 -8 -8 -8 1 0 0 0 8 0 1 0 -2 4 0 4 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 0 1 2 0 0 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 -8 -8 -8 -8 -8 1 0 0 0 -8 -8 1 0 -2 4 0 4 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 0 1 2 0 0 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 -8 -8 -8 -8 -8 1 0 0 0 -8 -8 1 0 -2 4 0 4 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 0 1 2 0 0 1 2 1 2 4 0 10 6 1 0 0 -8 -8 8 1 -8 -8 -8 -8 24 1 0 0 0 8 24 1 0 -2 4 0 -12 1 8 8 0 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 0 1 2 0 -12 1 2 1 2 4 0 10 6 1 0 0 -8 -8 0 1 -8 -8 -8 -8 16 1 0 0 0 8 16 1 0 2 -4 0 2 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 0 1 2 0 -8 1 2 1 2 4 0 10 6 1 0 0 8 8 -8 1 -8 -8 -8 -8 16 1 0 0 0 -8 -24 1 0 2 -4 0 2 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 0 1 2 0 -8 1 2 1 2 4 0 10 6 1 0 0 -8 -8 0 1 -8 -8 -8 -8 16 1 0 0 0 -8 -24 1 0 2 -4 0 2 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 0 1 2 0 -8 1 2 1 2 4 0 10 6 1 0 0 -8 -8 0 1 -8 -8 -8 -8 16 1 0 0 0 8 16 1 0 -2 4 0 -4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 0 1 2 0 -8 1 2 1 2 4 0 10 6 1 -8 0 -8 -8 8 1 -8 -8 -8 -8 32 1 8 0 0 8 32 1 -2 -2 4 0 -16 1 8 8 0 8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 1 1 2 0 -14 1 3 1 2 4 0 10 6 1 8 0 8 8 -16 1 -8 -8 -8 -8 32 1 -8 0 0 -8 -40 1 -2 -2 4 0 -16 1 8 8 0 8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 1 1 2 0 -14 1 3 1 2 4 0 10 6 1 -8 0 -8 -8 8 1 -8 -8 -8 -8 32 1 -8 0 0 -8 -40 1 -2 -2 4 0 -16 1 8 8 0 8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 1 1 2 0 -14 1 3 1 2 4 0 10 6 1 -8 0 -8 -8 0 1 8 8 8 8 -32 1 8 0 0 8 24 1 -2 -2 4 0 -8 1 -8 -8 0 -8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 1 1 2 0 -10 1 3 1 2 4 0 10 6 1 -8 0 -8 -8 0 1 -8 -8 -8 -8 24 1 8 0 0 8 24 1 -2 -2 4 0 -8 1 -8 -8 0 -8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 1 1 2 0 -10 1 3 1 2 4 0 10 6 1 0 -8 0 -8 -8 1 0 0 0 -8 -8 1 0 -8 -8 -8 -8 1 -2 -2 4 0 -6 1 0 0 -8 -8 0 1 0 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 2 1 1 1 2 0 -1 1 1 3 2 4 0 10 6 1 -8 -8 0 -8 0 1 0 0 0 -8 8 1 -8 -8 -8 -8 -24 1 0 -2 4 0 6 1 0 0 8 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 0 1 2 0 5 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 -8 1 0 0 0 8 -8 1 -8 -8 -8 -8 -16 1 0 -2 4 0 -2 1 0 0 -8 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 0 1 2 0 1 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 -8 1 0 0 0 -8 0 1 -8 -8 -8 -8 -16 1 0 -2 4 0 -2 1 0 0 -8 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 0 1 2 0 1 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 8 1 0 0 0 -8 32 1 8 8 8 8 32 1 0 2 -4 0 -16 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 13 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 8 1 0 0 0 8 -40 1 -8 -8 -8 -8 -40 1 0 2 -4 0 -16 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 13 1 2 3 2 4 0 10 6 1 8 8 0 8 -16 1 0 0 0 -8 32 1 -8 -8 -8 -8 -40 1 0 2 -4 0 -16 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 13 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 8 1 0 0 0 -8 32 1 -8 -8 -8 -8 -40 1 0 2 -4 0 -16 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 13 1 2 3 2 4 0 10 6 1 8 8 0 8 -8 1 0 0 0 8 -32 1 -8 -8 -8 -8 -32 1 0 -2 4 0 6 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 0 1 0 0 0 8 -32 1 -8 -8 -8 -8 -32 1 0 -2 4 0 6 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 0 1 0 0 0 8 -32 1 8 8 8 8 24 1 0 2 -4 0 -8 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 8 8 0 8 -8 1 0 0 0 8 -32 1 -8 -8 -8 -8 -32 1 0 2 -4 0 -8 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 0 1 0 0 0 8 -32 1 -8 -8 -8 -8 -32 1 0 2 -4 0 -8 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 7 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 0 0 0 -8 -8 1 -8 -8 0 -8 -8 1 0 8 8 8 0 1 0 6 4 0 -6 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 0 1 2 0 -1 1 2 3 2 4 0 10 6 1 0 0 0 8 0 1 -8 -8 0 -8 -8 1 0 -8 -8 -8 -8 1 0 6 4 0 -6 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 0 1 2 0 -1 1 2 3 2 4 0 10 6 1 0 0 0 -8 -8 1 -8 -8 0 -8 -8 1 0 -8 -8 -8 -8 1 0 6 4 0 -6 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 0 1 2 0 -1 1 2 3 2 4 0 10 6 1 0 0 0 -8 8 1 -8 -8 0 -8 24 1 0 8 8 8 24 1 0 -6 -4 0 -12 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 0 0 0 8 -16 1 -8 -8 0 -8 24 1 0 -8 -8 -8 -32 1 0 -6 -4 0 -12 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 8 8 0 8 -24 1 0 -8 -8 -8 -24 1 0 6 4 0 2 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 0 1 2 0 7 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 -8 -8 0 -8 16 1 0 -8 -8 -8 -24 1 0 6 4 0 2 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 0 1 2 0 7 1 2 3 2 4 0 10 6 1 0 0 0 -8 0 1 8 8 0 8 -24 1 0 8 8 8 16 1 0 -6 -4 0 -4 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 0 1 2 0 7 1 2 3 2 4 0 10 6 1 0 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1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 1 1 2 0 9 1 1 3 2 4 0 10 6 1 0 0 0 -8 -8 1 0 8 0 8 -32 1 8 8 8 8 24 1 -6 -6 -4 0 -6 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 1 1 2 0 9 1 1 3 2 4 0 10 6 1 0 0 0 -8 -8 1 0 -8 0 -8 24 1 -8 -8 -8 -8 -32 1 -6 -6 -4 0 -6 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 1 1 2 0 9 1 1 3 2 4 0 Computation of the target cohomology group dimensions complete. All done. Program run successfully completed. -- 3.25786 seconds elapsed o20 = {{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, --------------------------------------------------------------------------------------------------------------------------- 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, --------------------------------------------------------------------------------------------------------------------------- 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, --------------------------------------------------------------------------------------------------------------------------- 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, --------------------------------------------------------------------------------------------------------------------------- 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, --------------------------------------------------------------------------------------------------------------------------- {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, --------------------------------------------------------------------------------------------------------------------------- 0, 0, 0, 0}, {0, 0, 0, 0, 0}} o20 : List |
i21 : peek cohomCalg X o21 = MutableHashTable{{-1, -1, -3, -1, 4, 2} => {{0, 0, 0, 0, 0}, {}} } {-1, -1, 0, 0, 0, 0} => {{0, 0, 0, 0, 0}, {}} {-1, 0, -1, -1, 1, 1} => {{0, 0, 0, 0, 0}, {}} {-1, 0, -1, 0, 0, 0} => {{0, 0, 0, 0, 0}, {}} {-1, 0, -3, -1, 3, 2} => {{0, 0, 0, 0, 0}, {}} {-1, 0, -3, -1, 4, 1} => {{0, 0, 0, 0, 0}, {}} {-1, 0, -3, -2, 4, 2} => {{0, 0, 0, 0, 0}, {}} {-1, 0, -4, -1, 4, 2} => {{0, 0, 0, 0, 0}, {}} {-1, 0, -4, -2, 5, 3} => {{0, 0, 0, 0, 0}, {}} {-1, 0, 0, -1, 0, 0} => {{0, 0, 0, 0, 0}, {}} {-1, 0, 0, 0, -1, 0} => {{0, 0, 0, 0, 0}, {}} {-1, 0, 0, 0, 0, -1} => {{0, 0, 0, 0, 0}, {}} {-2, 0, -3, -1, 4, 2} => {{0, 1, 0, 0, 0}, {{1, 1x0*x4}}} {0, -1, -1, -1, 1, 1} => {{0, 0, 0, 0, 0}, {}} {0, -1, -1, 0, 0, 0} => {{0, 0, 0, 0, 0}, {}} {0, -1, 0, -1, 0, 0} => {{0, 0, 0, 0, 0}, {}} {0, -1, 0, 0, -1, 0} => {{0, 0, 0, 0, 0}, {}} {0, -1, 0, 0, 0, -1} => {{0, 1, 0, 0, 0}, {{1, 1x5*x9}}} {0, 0, -1, -1, 0, 0} => {{0, 0, 0, 0, 0}, {}} {0, 0, -1, -1, 0, 1} => {{0, 0, 0, 0, 0}, {}} {0, 0, -1, -1, 1, 0} => {{0, 0, 0, 0, 0}, {}} {0, 0, -1, -2, 1, 1} => {{0, 0, 0, 0, 0}, {}} {0, 0, -1, 0, -1, 0} => {{0, 0, 0, 0, 0}, {}} {0, 0, -1, 0, 0, -1} => {{0, 0, 0, 0, 0}, {}} {0, 0, -2, -1, 1, 1} => {{0, 0, 0, 0, 0}, {}} {0, 0, 0, -1, -1, 0} => {{0, 0, 0, 0, 0}, {}} {0, 0, 0, -1, 0, -1} => {{0, 0, 0, 0, 0}, {}} {0, 0, 0, 0, -1, -1} => {{0, 0, 0, 0, 0}, {}} {0, 1, -1, 1, 0, -2} => {{0, 0, 0, 0, 0}, {}} {0, 1, -2, -2, 4, 0} => {{0, 0, 0, 0, 0}, {}} {0, 1, 1, -1, 0, -2} => {{0, 0, 0, 0, 0}, {}} {0, 1, 2, 2, -4, -4} => {{0, 0, 0, 0, 0}, {}} {1, 0, 1, -1, 0, -2} => {{0, 0, 0, 0, 0}, {}} {1, 0, 2, 2, -4, -4} => {{0, 0, 0, 0, 0}, {}} {1, 1, 0, -1, 0, -2} => {{0, 0, 0, 0, 0}, {}} {1, 1, 0, -2, 1, -1} => {{0, 0, 0, 0, 0}, {}} {1, 1, 1, -1, -1, -2} => {{0, 0, 0, 0, 0}, {}} {1, 1, 1, -1, 0, -3} => {{0, 0, 0, 0, 0}, {}} {1, 1, 1, -2, 0, -2} => {{0, 0, 0, 0, 0}, {}} {1, 1, 1, 1, -3, -3} => {{0, 0, 0, 0, 0}, {}} {1, 1, 1, 2, -4, -4} => {{0, 0, 0, 0, 0}, {}} {1, 1, 2, 1, -4, -4} => {{0, 0, 0, 0, 0}, {}} {1, 1, 2, 2, -4, -5} => {{0, 0, 0, 0, 0}, {}} {1, 1, 2, 2, -5, -4} => {{0, 0, 0, 0, 0}, {}} {2, 2, 3, 1, -4, -6} => {{0, 1, 0, 0, 0}, {{1, 1x1*x2}}} |
i22 : degree(X_3 + X_7 + X_8) o22 = {0, 0, 1, 2, 0, -1} o22 : List |
i23 : elapsedTime cohomvec1 = cohomCalg(X_3 + X_7 + X_8) cohomCalg v0.32 (compiled for Linux/Unix x86-64 / 64 bit) author: Benjamin Jurke (mail@benjaminjurke.com) Based on the algorithm detailed in arXiv:1003.5217 Usage and generation of intermediate monomial files deactivated. Starting computation of secondary sequences... 0.00% completed (1 sec remaining)... 81.25% completed (0 secs remaining)... WARNING: The Serre dualization reduction was unable to uniquely resolve 86 of the original 90 ambiguous monoms. Computation of secondary cohomologies and contributions complete. Computing target cohomology 1 of 1 (0.0% done)... 10 6 1 0 0 0 8 0 1 8 8 0 8 24 1 0 8 8 8 -32 1 0 6 4 0 -16 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 6 1 0 1 2 0 -9 1 2 3 2 4 0 10 6 1 8 8 0 8 -8 1 0 0 0 8 8 1 -8 -8 -8 -8 8 1 0 -2 4 0 -4 1 0 0 8 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 0 1 2 0 -3 1 2 3 2 4 0 10 6 1 0 8 0 8 0 1 0 0 0 8 24 1 0 8 8 8 -32 1 -2 -2 4 0 -16 1 0 0 -8 -8 0 1 0 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 -9 1 1 3 2 4 0 10 6 1 0 8 0 8 -8 1 0 0 0 8 16 1 0 -8 -8 -8 16 1 -2 -2 4 0 -8 1 0 0 8 8 0 1 0 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 -5 1 1 3 2 4 0 10 6 1 0 0 8 8 0 1 8 8 8 8 24 1 0 0 0 8 -32 1 0 2 -4 0 -16 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 6 1 0 1 2 0 8 1 2 1 2 4 0 10 6 1 0 0 8 8 -8 1 -8 -8 -8 -8 -24 1 0 0 0 8 -24 1 0 -2 4 0 6 1 8 8 0 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 6 1 0 1 2 0 4 1 2 1 2 4 0 10 6 1 0 0 8 8 -8 1 -8 -8 -8 -8 -24 1 0 0 0 8 -24 1 0 2 -4 0 -8 1 8 8 0 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 6 1 0 1 2 0 4 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 8 8 8 1 8 0 0 8 -16 1 0 6 4 0 2 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 0 1 2 0 2 1 2 1 2 4 0 10 6 1 8 8 8 8 -8 1 0 0 8 8 8 1 -8 0 0 -8 8 1 0 -6 -4 0 -4 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 0 1 2 0 2 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 8 8 8 1 8 0 0 8 -16 1 0 -6 -4 0 -4 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 0 1 2 0 2 1 2 1 2 4 0 10 6 1 8 8 8 8 -8 1 8 0 8 8 0 1 0 0 0 8 -16 1 -6 -6 -4 0 -8 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 1 1 2 0 0 1 3 1 2 4 0 10 6 1 8 8 8 8 -16 1 8 0 8 8 -8 1 0 0 0 -8 0 1 -6 -6 -4 0 0 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 1 1 2 0 -4 1 3 1 2 4 0 10 6 1 8 8 8 8 -16 1 -8 0 -8 -8 0 1 0 0 0 8 -8 1 -6 -6 -4 0 0 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 1 1 2 0 -4 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 8 1 8 0 8 8 -8 1 0 0 0 8 -8 1 -6 -6 -4 0 0 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 1 1 2 0 -4 1 3 1 2 4 0 10 6 1 8 8 8 8 0 1 8 0 8 8 24 1 0 0 0 -8 24 1 -6 -6 -4 0 -16 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 8 1 3 1 2 4 0 10 6 1 8 8 8 8 0 1 -8 0 -8 -8 -32 1 0 0 0 8 -32 1 -6 -6 -4 0 -16 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 8 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 8 0 8 8 24 1 0 0 0 8 -32 1 -6 -6 -4 0 -16 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 8 1 3 1 2 4 0 10 6 1 8 8 8 8 0 1 8 0 8 8 24 1 0 0 0 8 -32 1 -6 -6 -4 0 -16 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 8 1 3 1 2 4 0 10 6 1 8 8 8 8 -8 1 -8 0 -8 -8 -24 1 0 0 0 8 -24 1 6 6 4 0 6 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 4 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 8 0 8 8 16 1 0 0 0 8 -24 1 6 6 4 0 6 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 4 1 3 1 2 4 0 10 6 1 8 8 8 8 -8 1 -8 0 -8 -8 -24 1 0 0 0 -8 16 1 -6 -6 -4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 4 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 8 0 8 8 16 1 0 0 0 -8 16 1 -6 -6 -4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 4 1 3 1 2 4 0 10 6 1 8 8 8 8 -8 1 8 0 8 8 16 1 0 0 0 -8 16 1 -6 -6 -4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 4 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 -8 0 -8 -8 -24 1 0 0 0 8 -24 1 -6 -6 -4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 4 1 3 1 2 4 0 10 6 1 8 8 8 8 -8 1 -8 0 -8 -8 -24 1 0 0 0 8 -24 1 -6 -6 -4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 4 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 8 0 8 8 16 1 0 0 0 8 -24 1 -6 -6 -4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 4 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 -16 1 -8 0 -8 -8 -8 1 0 0 0 -8 -8 1 6 6 4 0 2 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 1 1 2 0 2 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 -8 -8 8 1 -8 0 0 -8 -24 1 0 6 4 0 -10 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 -4 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -16 1 0 0 -8 -8 0 1 -8 0 0 -8 -16 1 0 -6 -4 0 0 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 0 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -16 1 0 0 8 8 -8 1 -8 0 0 -8 -16 1 0 6 4 0 -2 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 0 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -16 1 0 0 -8 -8 0 1 -8 0 0 -8 -16 1 0 6 4 0 -2 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 0 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 -8 -8 32 1 -8 0 0 -8 -40 1 0 -6 -4 0 16 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -12 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 -8 -8 32 1 8 0 0 8 32 1 0 6 4 0 -18 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -12 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 -8 -8 32 1 -8 0 0 -8 -40 1 0 6 4 0 -18 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -12 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 8 8 -32 1 -8 0 0 -8 -32 1 0 -6 -4 0 8 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -8 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 -8 -8 24 1 -8 0 0 -8 -32 1 0 -6 -4 0 8 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -8 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -16 1 -8 -8 -8 -8 -8 1 0 0 0 -8 -8 1 0 2 -4 0 -4 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 2 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -16 1 -8 -8 -8 -8 -8 1 0 0 0 8 0 1 0 -2 4 0 2 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 2 1 2 1 2 4 0 10 6 1 0 0 8 8 8 1 -8 -8 -8 -8 -8 1 0 0 0 -8 -8 1 0 -2 4 0 2 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 2 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -16 1 -8 -8 -8 -8 -8 1 0 0 0 -8 -8 1 0 -2 4 0 2 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 2 1 2 1 2 4 0 10 6 1 0 0 -8 -8 0 1 -8 -8 -8 -8 24 1 0 0 0 8 24 1 0 -2 4 0 -14 1 8 8 0 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -10 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 -8 -8 -8 -8 16 1 0 0 0 8 16 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -6 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 -8 -8 -8 -8 16 1 0 0 0 -8 -24 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -6 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 -8 -8 -8 -8 16 1 0 0 0 -8 -24 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -6 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 -8 -8 -8 -8 16 1 0 0 0 8 16 1 0 -2 4 0 -6 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -6 1 2 1 2 4 0 10 6 1 -8 0 -8 -8 0 1 -8 -8 -8 -8 32 1 8 0 0 8 32 1 -2 -2 4 0 -18 1 8 8 0 8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 -12 1 3 1 2 4 0 10 6 1 8 0 8 8 -8 1 -8 -8 -8 -8 32 1 -8 0 0 -8 -40 1 -2 -2 4 0 -18 1 8 8 0 8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 -12 1 3 1 2 4 0 10 6 1 -8 0 -8 -8 0 1 -8 -8 -8 -8 32 1 -8 0 0 -8 -40 1 -2 -2 4 0 -18 1 8 8 0 8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 -12 1 3 1 2 4 0 10 6 1 -8 0 -8 -8 -8 1 8 8 8 8 -32 1 8 0 0 8 24 1 -2 -2 4 0 -10 1 -8 -8 0 -8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 -8 1 3 1 2 4 0 10 6 1 -8 0 -8 -8 -8 1 -8 -8 -8 -8 24 1 8 0 0 8 24 1 -2 -2 4 0 -10 1 -8 -8 0 -8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 -8 1 3 1 2 4 0 10 6 1 0 -8 0 -8 -16 1 0 0 0 -8 -8 1 0 -8 -8 -8 -8 1 -2 -2 4 0 -4 1 0 0 -8 -8 0 1 0 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 1 1 2 0 -3 1 1 3 2 4 0 10 6 1 -8 -8 0 -8 -8 1 0 0 0 -8 8 1 -8 -8 -8 -8 -24 1 0 -2 4 0 8 1 0 0 8 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 3 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 -16 1 0 0 0 8 -8 1 -8 -8 -8 -8 -16 1 0 -2 4 0 0 1 0 0 -8 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 -1 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 -16 1 0 0 0 -8 0 1 -8 -8 -8 -8 -16 1 0 -2 4 0 0 1 0 0 -8 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 -1 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 0 1 0 0 0 -8 32 1 8 8 8 8 32 1 0 2 -4 0 -18 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 0 1 0 0 0 8 -40 1 -8 -8 -8 -8 -40 1 0 2 -4 0 -18 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 8 8 0 8 -8 1 0 0 0 -8 32 1 -8 -8 -8 -8 -40 1 0 2 -4 0 -18 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 0 1 0 0 0 -8 32 1 -8 -8 -8 -8 -40 1 0 2 -4 0 -18 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 8 8 0 8 0 1 0 0 0 8 -32 1 -8 -8 -8 -8 -32 1 0 -2 4 0 8 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 7 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 -8 1 0 0 0 8 -32 1 -8 -8 -8 -8 -32 1 0 -2 4 0 8 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 7 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 -8 1 0 0 0 8 -32 1 8 8 8 8 24 1 0 2 -4 0 -10 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 7 1 2 3 2 4 0 10 6 1 8 8 0 8 0 1 0 0 0 8 -32 1 -8 -8 -8 -8 -32 1 0 2 -4 0 -10 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 7 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 -8 1 0 0 0 8 -32 1 -8 -8 -8 -8 -32 1 0 2 -4 0 -10 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 7 1 2 3 2 4 0 10 6 1 0 0 0 -8 -16 1 -8 -8 0 -8 -8 1 0 8 8 8 0 1 0 6 4 0 -4 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -3 1 2 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8 0 1 8 8 8 8 -24 1 0 0 0 8 16 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -6 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 8 8 8 8 -24 1 0 0 0 8 16 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -6 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 -8 -8 -8 -8 16 1 0 0 0 8 16 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -6 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 8 8 8 8 -24 1 0 0 0 -8 -24 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -6 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 8 8 8 8 -24 1 0 0 0 -8 -24 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -6 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 8 8 8 8 -24 1 0 0 0 8 16 1 0 -2 4 0 -6 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -6 1 2 1 2 4 0 10 6 1 -8 0 -8 -8 0 1 8 8 8 8 -40 1 8 0 0 8 32 1 -2 -2 4 0 -18 1 8 8 0 8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 -12 1 3 1 2 4 0 10 6 1 8 0 8 8 -8 1 -8 -8 -8 -8 32 1 8 0 0 8 32 1 -2 -2 4 0 -18 1 8 8 0 8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 -12 1 3 1 2 4 0 10 6 1 0 8 0 8 8 1 0 0 0 8 0 1 0 -8 -8 -8 -8 1 -2 -2 4 0 -4 1 0 0 -8 -8 0 1 0 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 1 1 2 0 -3 1 1 3 2 4 0 10 6 1 0 -8 0 -8 -16 1 0 0 0 8 0 1 0 -8 -8 -8 -8 1 -2 -2 4 0 -4 1 0 0 -8 -8 0 1 0 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 1 1 2 0 -3 1 1 3 2 4 0 10 6 1 0 8 0 8 8 1 0 0 0 -8 -8 1 0 -8 -8 -8 -8 1 -2 -2 4 0 -4 1 0 0 -8 -8 0 1 0 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 1 1 2 0 -3 1 1 3 2 4 0 10 6 1 8 8 0 8 0 1 0 0 0 8 -16 1 -8 -8 -8 -8 -24 1 0 -2 4 0 8 1 0 0 8 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 3 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 -8 1 0 0 0 8 -16 1 -8 -8 -8 -8 -24 1 0 -2 4 0 8 1 0 0 8 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 3 1 2 3 2 4 0 10 6 1 8 8 0 8 0 1 0 0 0 -8 8 1 -8 -8 -8 -8 -24 1 0 -2 4 0 8 1 0 0 8 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 3 1 2 3 2 4 0 10 6 1 8 8 0 8 8 1 0 0 0 8 -8 1 -8 -8 -8 -8 -16 1 0 -2 4 0 0 1 0 0 -8 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 -1 1 2 3 2 4 0 10 6 1 8 8 0 8 8 1 0 0 0 -8 0 1 -8 -8 -8 -8 -16 1 0 -2 4 0 0 1 0 0 -8 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 -1 1 2 3 2 4 0 10 6 1 8 8 0 8 -8 1 0 0 0 8 -40 1 8 8 8 8 32 1 0 2 -4 0 -18 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 0 1 0 0 0 8 -40 1 8 8 8 8 32 1 0 2 -4 0 -18 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 8 8 0 8 -8 1 0 0 0 -8 32 1 8 8 8 8 32 1 0 2 -4 0 -18 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 8 8 0 8 -8 1 0 0 0 8 -40 1 -8 -8 -8 -8 -40 1 0 2 -4 0 -18 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 8 8 0 8 0 1 0 0 0 8 -32 1 8 8 8 8 24 1 0 -2 4 0 8 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 7 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 -8 1 0 0 0 8 -32 1 8 8 8 8 24 1 0 -2 4 0 8 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 7 1 2 3 2 4 0 10 6 1 8 8 0 8 0 1 0 0 0 8 -32 1 8 8 8 8 24 1 0 2 -4 0 -10 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 7 1 2 3 2 4 0 10 6 1 0 0 0 8 8 1 8 8 0 8 0 1 0 8 8 8 0 1 0 6 4 0 -4 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -3 1 2 3 2 4 0 10 6 1 0 0 0 -8 -16 1 8 8 0 8 0 1 0 8 8 8 0 1 0 6 4 0 -4 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -3 1 2 3 2 4 0 10 6 1 0 0 0 8 8 1 -8 -8 0 -8 -8 1 0 8 8 8 0 1 0 6 4 0 -4 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -3 1 2 3 2 4 0 10 6 1 0 0 0 8 8 1 8 8 0 8 0 1 0 -8 -8 -8 -8 1 0 6 4 0 -4 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -3 1 2 3 2 4 0 10 6 1 0 0 0 -8 -16 1 8 8 0 8 0 1 0 -8 -8 -8 -8 1 0 6 4 0 -4 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -3 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 8 8 0 8 -32 1 0 -8 -8 -8 -32 1 0 6 4 0 12 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 -8 -8 0 -8 24 1 0 -8 -8 -8 -32 1 0 6 4 0 12 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 8 8 0 8 -32 1 0 8 8 8 24 1 0 -6 -4 0 -14 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 0 0 0 -8 0 1 8 8 0 8 -32 1 0 8 8 8 24 1 0 -6 -4 0 -14 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 -8 -8 0 -8 24 1 0 8 8 8 24 1 0 -6 -4 0 -14 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 8 8 0 8 -32 1 0 -8 -8 -8 -32 1 0 -6 -4 0 -14 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 0 0 0 8 0 1 8 8 0 8 -24 1 0 8 8 8 16 1 0 -6 -4 0 -6 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 5 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 0 8 0 8 -40 1 -8 -8 -8 -8 -40 1 6 6 4 0 16 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 11 1 1 3 2 4 0 10 6 1 0 0 0 8 -8 1 0 8 0 8 -40 1 8 8 8 8 32 1 -6 -6 -4 0 -18 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 11 1 1 3 2 4 0 10 6 1 0 0 0 8 -8 1 0 -8 0 -8 32 1 -8 -8 -8 -8 -40 1 -6 -6 -4 0 -18 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 11 1 1 3 2 4 0 10 6 1 0 0 0 8 0 1 0 8 0 8 -32 1 8 8 8 8 24 1 6 6 4 0 8 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 7 1 1 3 2 4 0 10 6 1 0 0 0 -8 -8 1 0 8 0 8 -32 1 8 8 8 8 24 1 -6 -6 -4 0 -10 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 7 1 1 3 2 4 0 10 6 1 0 0 0 -8 -8 1 0 -8 0 -8 24 1 -8 -8 -8 -8 -32 1 -6 -6 -4 0 -10 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 7 1 1 3 2 4 0 Computation of the target cohomology group dimensions complete. All done. Program run successfully completed. -- 0.380137 seconds elapsed o23 = {1, 0, 0, 0, 0} o23 : List |
i24 : elapsedTime cohomvec2 = for j from 0 to dim X list rank HH^j(X, OO_X(0,0,1,2,0,-1)) -- 8.47246 seconds elapsed o24 = {1, 0, 0, 0, 0} o24 : List |
i25 : assert(cohomvec1 == cohomvec2) |
i26 : degree(X_3 + X_7 - X_8) o26 = {0, 0, 1, 2, -2, -1} o26 : List |
i27 : elapsedTime cohomvec1 = cohomCalg(X_3 + X_7 - X_8) cohomCalg v0.32 (compiled for Linux/Unix x86-64 / 64 bit) author: Benjamin Jurke (mail@benjaminjurke.com) Based on the algorithm detailed in arXiv:1003.5217 Usage and generation of intermediate monomial files deactivated. Starting computation of secondary sequences... 0.00% completed (1 sec remaining)... 81.25% completed (0 secs remaining)... WARNING: The Serre dualization reduction was unable to uniquely resolve 86 of the original 90 ambiguous monoms. Computation of secondary cohomologies and contributions complete. Computing target cohomology 1 of 1 (0.0% done)... 10 6 1 0 0 0 8 0 1 8 8 0 8 24 1 0 8 8 8 -32 1 0 6 4 0 -16 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 6 1 0 1 2 0 -11 1 2 3 2 4 0 10 6 1 8 8 0 8 -8 1 0 0 0 8 8 1 -8 -8 -8 -8 8 1 0 -2 4 0 -4 1 0 0 8 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 0 1 2 0 -5 1 2 3 2 4 0 10 6 1 0 8 0 8 0 1 0 0 0 8 24 1 0 8 8 8 -32 1 -2 -2 4 0 -16 1 0 0 -8 -8 0 1 0 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 -11 1 1 3 2 4 0 10 6 1 0 8 0 8 -8 1 0 0 0 8 16 1 0 -8 -8 -8 16 1 -2 -2 4 0 -8 1 0 0 8 8 0 1 0 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 -7 1 1 3 2 4 0 10 6 1 0 0 8 8 0 1 8 8 8 8 24 1 0 0 0 8 -32 1 0 2 -4 0 -16 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 6 1 0 1 2 0 10 1 2 1 2 4 0 10 6 1 0 0 8 8 -8 1 -8 -8 -8 -8 -24 1 0 0 0 8 -24 1 0 -2 4 0 6 1 8 8 0 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 6 1 0 1 2 0 6 1 2 1 2 4 0 10 6 1 0 0 8 8 -8 1 -8 -8 -8 -8 -24 1 0 0 0 8 -24 1 0 2 -4 0 -8 1 8 8 0 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 6 1 0 1 2 0 6 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 8 8 8 1 8 0 0 8 -16 1 0 6 4 0 2 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 0 1 2 0 4 1 2 1 2 4 0 10 6 1 8 8 8 8 -8 1 0 0 8 8 8 1 -8 0 0 -8 8 1 0 -6 -4 0 -4 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 0 1 2 0 4 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 8 8 8 1 8 0 0 8 -16 1 0 -6 -4 0 -4 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -6 1 0 1 2 0 4 1 2 1 2 4 0 10 6 1 8 8 8 8 -8 1 8 0 8 8 0 1 0 0 0 8 -16 1 -6 -6 -4 0 -8 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 1 1 2 0 2 1 3 1 2 4 0 10 6 1 8 8 8 8 -16 1 8 0 8 8 -8 1 0 0 0 -8 0 1 -6 -6 -4 0 0 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 1 1 2 0 -2 1 3 1 2 4 0 10 6 1 8 8 8 8 -16 1 -8 0 -8 -8 0 1 0 0 0 8 -8 1 -6 -6 -4 0 0 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 1 1 2 0 -2 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 8 1 8 0 8 8 -8 1 0 0 0 8 -8 1 -6 -6 -4 0 0 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -3 1 1 1 2 0 -2 1 3 1 2 4 0 10 6 1 8 8 8 8 0 1 8 0 8 8 24 1 0 0 0 -8 24 1 -6 -6 -4 0 -16 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 10 1 3 1 2 4 0 10 6 1 8 8 8 8 0 1 -8 0 -8 -8 -32 1 0 0 0 8 -32 1 -6 -6 -4 0 -16 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 10 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 8 0 8 8 24 1 0 0 0 8 -32 1 -6 -6 -4 0 -16 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 10 1 3 1 2 4 0 10 6 1 8 8 8 8 0 1 8 0 8 8 24 1 0 0 0 8 -32 1 -6 -6 -4 0 -16 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 10 1 3 1 2 4 0 10 6 1 8 8 8 8 -8 1 -8 0 -8 -8 -24 1 0 0 0 8 -24 1 6 6 4 0 6 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 8 0 8 8 16 1 0 0 0 8 -24 1 6 6 4 0 6 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 8 8 8 8 -8 1 -8 0 -8 -8 -24 1 0 0 0 -8 16 1 -6 -6 -4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 8 0 8 8 16 1 0 0 0 -8 16 1 -6 -6 -4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 8 8 8 8 -8 1 8 0 8 8 16 1 0 0 0 -8 16 1 -6 -6 -4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 -8 0 -8 -8 -24 1 0 0 0 8 -24 1 -6 -6 -4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 8 8 8 8 -8 1 -8 0 -8 -8 -24 1 0 0 0 8 -24 1 -6 -6 -4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 8 0 8 8 16 1 0 0 0 8 -24 1 -6 -6 -4 0 -8 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -7 1 1 1 2 0 6 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 -16 1 -8 0 -8 -8 -8 1 0 0 0 -8 -8 1 6 6 4 0 2 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 3 1 1 1 2 0 0 1 3 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 -8 -8 8 1 -8 0 0 -8 -24 1 0 6 4 0 -10 1 0 -8 0 8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 -6 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -16 1 0 0 -8 -8 0 1 -8 0 0 -8 -16 1 0 -6 -4 0 0 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 -2 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -16 1 0 0 8 8 -8 1 -8 0 0 -8 -16 1 0 6 4 0 -2 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 -2 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -16 1 0 0 -8 -8 0 1 -8 0 0 -8 -16 1 0 6 4 0 -2 1 0 8 0 -8 0 1 4 0 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 -2 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 -8 -8 32 1 -8 0 0 -8 -40 1 0 -6 -4 0 16 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -14 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 -8 -8 32 1 8 0 0 8 32 1 0 6 4 0 -18 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -14 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 -8 -8 32 1 -8 0 0 -8 -40 1 0 6 4 0 -18 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -14 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 8 8 -32 1 -8 0 0 -8 -32 1 0 -6 -4 0 8 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -10 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 -8 -8 24 1 -8 0 0 -8 -32 1 0 -6 -4 0 8 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 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0 1 2 0 -14 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 0 1 0 0 8 8 -40 1 -8 0 0 -8 -40 1 0 -6 -4 0 16 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -14 1 2 1 2 4 0 10 6 1 8 8 8 8 -8 1 0 0 -8 -8 32 1 -8 0 0 -8 -40 1 0 -6 -4 0 16 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -14 1 2 1 2 4 0 10 6 1 8 8 8 8 -8 1 0 0 -8 -8 32 1 8 0 0 8 32 1 0 6 4 0 -18 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -14 1 2 1 2 4 0 10 6 1 8 8 8 8 -8 1 0 0 -8 -8 32 1 -8 0 0 -8 -40 1 0 6 4 0 -18 1 0 -8 0 8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -14 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 8 8 -32 1 8 0 0 8 24 1 0 -6 -4 0 8 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -10 1 2 1 2 4 0 10 6 1 -8 -8 -8 -8 -8 1 0 0 -8 -8 24 1 8 0 0 8 24 1 0 -6 -4 0 8 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -10 1 2 1 2 4 0 10 6 1 8 8 8 8 0 1 0 0 8 8 -32 1 -8 0 0 -8 -32 1 0 -6 -4 0 8 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -10 1 2 1 2 4 0 10 6 1 8 8 8 8 0 1 0 0 -8 -8 24 1 -8 0 0 -8 -32 1 0 -6 -4 0 8 1 0 8 0 -8 0 1 -4 0 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 -10 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 -8 -8 -8 -8 0 1 0 0 0 8 8 1 0 2 -4 0 4 1 8 8 0 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -4 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 -8 -8 -8 -8 0 1 0 0 0 8 8 1 0 2 -4 0 4 1 8 8 0 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -4 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 -8 -8 -8 -8 0 1 0 0 0 -8 -16 1 0 2 -4 0 4 1 8 8 0 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -4 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 -8 -8 -8 -8 0 1 0 0 0 -8 -16 1 0 2 -4 0 4 1 8 8 0 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -4 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 -8 -8 -8 -8 0 1 0 0 0 8 8 1 0 -2 4 0 -6 1 8 8 0 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -4 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 -8 -8 -8 -8 0 1 0 0 0 8 8 1 0 -2 4 0 -6 1 8 8 0 8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -4 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 -8 -8 -8 -8 0 1 0 0 0 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0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 0 1 2 1 2 4 0 10 6 1 0 0 8 8 8 1 -8 -8 -8 -8 -8 1 0 0 0 -8 -8 1 0 2 -4 0 -4 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 0 1 2 1 2 4 0 10 6 1 0 0 8 8 8 1 -8 -8 -8 -8 -8 1 0 0 0 8 0 1 0 -2 4 0 2 1 -8 -8 0 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 0 1 2 1 2 4 0 10 6 1 0 0 8 8 -8 1 -8 -8 -8 -8 24 1 0 0 0 8 24 1 0 2 -4 0 12 1 8 8 0 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -12 1 2 1 2 4 0 10 6 1 0 0 -8 -8 0 1 -8 -8 -8 -8 24 1 0 0 0 8 24 1 0 2 -4 0 12 1 8 8 0 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -12 1 2 1 2 4 0 10 6 1 0 0 8 8 -8 1 -8 -8 -8 -8 24 1 0 0 0 -8 -32 1 0 2 -4 0 12 1 8 8 0 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -12 1 2 1 2 4 0 10 6 1 0 0 -8 -8 0 1 -8 -8 -8 -8 24 1 0 0 0 -8 -32 1 0 2 -4 0 12 1 8 8 0 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -12 1 2 1 2 4 0 10 6 1 0 0 -8 -8 0 1 8 8 8 8 -32 1 0 0 0 8 24 1 0 -2 4 0 -14 1 8 8 0 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -12 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 8 8 8 8 -24 1 0 0 0 8 16 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -8 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 8 8 8 8 -24 1 0 0 0 8 16 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -8 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 -8 -8 -8 -8 16 1 0 0 0 8 16 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -8 1 2 1 2 4 0 10 6 1 0 0 8 8 0 1 8 8 8 8 -24 1 0 0 0 -8 -24 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -8 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 8 8 8 8 -24 1 0 0 0 -8 -24 1 0 2 -4 0 4 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -8 1 2 1 2 4 0 10 6 1 0 0 -8 -8 -8 1 8 8 8 8 -24 1 0 0 0 8 16 1 0 -2 4 0 -6 1 -8 -8 0 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 -8 1 2 1 2 4 0 10 6 1 -8 0 -8 -8 0 1 8 8 8 8 -40 1 8 0 0 8 32 1 -2 -2 4 0 -18 1 8 8 0 8 0 1 -8 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 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8 -8 1 -8 -8 -8 -8 -16 1 0 -2 4 0 0 1 0 0 -8 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 1 1 2 3 2 4 0 10 6 1 8 8 0 8 8 1 0 0 0 -8 0 1 -8 -8 -8 -8 -16 1 0 -2 4 0 0 1 0 0 -8 -8 0 1 4 4 4 8 0 1 1 0 0 0 0 1 1 2 0 0 4 1 0 1 2 0 1 1 2 3 2 4 0 10 6 1 8 8 0 8 -8 1 0 0 0 8 -40 1 8 8 8 8 32 1 0 2 -4 0 -18 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 13 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 0 1 0 0 0 8 -40 1 8 8 8 8 32 1 0 2 -4 0 -18 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 13 1 2 3 2 4 0 10 6 1 8 8 0 8 -8 1 0 0 0 -8 32 1 8 8 8 8 32 1 0 2 -4 0 -18 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 13 1 2 3 2 4 0 10 6 1 8 8 0 8 -8 1 0 0 0 8 -40 1 -8 -8 -8 -8 -40 1 0 2 -4 0 -18 1 0 0 8 8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 13 1 2 3 2 4 0 10 6 1 8 8 0 8 0 1 0 0 0 8 -32 1 8 8 8 8 24 1 0 -2 4 0 8 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 -8 -8 0 -8 -8 1 0 0 0 8 -32 1 8 8 8 8 24 1 0 -2 4 0 8 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 8 8 0 8 0 1 0 0 0 8 -32 1 8 8 8 8 24 1 0 2 -4 0 -10 1 0 0 -8 -8 0 1 -4 -4 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 8 1 0 1 2 0 9 1 2 3 2 4 0 10 6 1 0 0 0 8 8 1 8 8 0 8 0 1 0 8 8 8 0 1 0 6 4 0 -4 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -1 1 2 3 2 4 0 10 6 1 0 0 0 -8 -16 1 8 8 0 8 0 1 0 8 8 8 0 1 0 6 4 0 -4 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -1 1 2 3 2 4 0 10 6 1 0 0 0 8 8 1 -8 -8 0 -8 -8 1 0 8 8 8 0 1 0 6 4 0 -4 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -1 1 2 3 2 4 0 10 6 1 0 0 0 8 8 1 8 8 0 8 0 1 0 -8 -8 -8 -8 1 0 6 4 0 -4 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -1 1 2 3 2 4 0 10 6 1 0 0 0 -8 -16 1 8 8 0 8 0 1 0 -8 -8 -8 -8 1 0 6 4 0 -4 1 -8 -16 -8 -8 0 1 4 8 4 8 0 1 1 0 0 0 0 1 1 2 0 0 -4 1 0 1 2 0 -1 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 8 8 0 8 -32 1 0 -8 -8 -8 -32 1 0 6 4 0 12 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 -8 -8 0 -8 24 1 0 -8 -8 -8 -32 1 0 6 4 0 12 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 8 8 0 8 -32 1 0 8 8 8 24 1 0 -6 -4 0 -14 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 0 0 0 -8 0 1 8 8 0 8 -32 1 0 8 8 8 24 1 0 -6 -4 0 -14 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 -8 -8 0 -8 24 1 0 8 8 8 24 1 0 -6 -4 0 -14 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 8 8 0 8 -32 1 0 -8 -8 -8 -32 1 0 -6 -4 0 -14 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 11 1 2 3 2 4 0 10 6 1 0 0 0 8 0 1 8 8 0 8 -24 1 0 8 8 8 16 1 0 -6 -4 0 -6 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -8 1 0 1 2 0 7 1 2 3 2 4 0 10 6 1 0 0 0 8 -8 1 0 8 0 8 -40 1 -8 -8 -8 -8 -40 1 6 6 4 0 16 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 13 1 1 3 2 4 0 10 6 1 0 0 0 8 -8 1 0 8 0 8 -40 1 8 8 8 8 32 1 -6 -6 -4 0 -18 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 13 1 1 3 2 4 0 10 6 1 0 0 0 8 -8 1 0 -8 0 -8 32 1 -8 -8 -8 -8 -40 1 -6 -6 -4 0 -18 1 8 16 8 8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 13 1 1 3 2 4 0 10 6 1 0 0 0 8 0 1 0 8 0 8 -32 1 8 8 8 8 24 1 6 6 4 0 8 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 9 1 1 3 2 4 0 10 6 1 0 0 0 -8 -8 1 0 8 0 8 -32 1 8 8 8 8 24 1 -6 -6 -4 0 -10 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 9 1 1 3 2 4 0 10 6 1 0 0 0 -8 -8 1 0 -8 0 -8 24 1 -8 -8 -8 -8 -32 1 -6 -6 -4 0 -10 1 -8 -16 -8 -8 0 1 -4 -8 -4 -8 0 1 1 0 0 0 0 1 1 2 0 0 -9 1 1 1 2 0 9 1 1 3 2 4 0 Computation of the target cohomology group dimensions complete. All done. Program run successfully completed. -- 0.378353 seconds elapsed o27 = {0, 0, 0, 0, 0} o27 : List |
i28 : elapsedTime cohomvec2 = elapsedTime for j from 0 to dim X list rank HH^j(X, OO_X(0,0,1,2,-2,-1)) -- 0.152519 seconds elapsed -- 0.152548 seconds elapsed o28 = {0, 0, 0, 0, 0} o28 : List |
i29 : assert(cohomvec1 == cohomvec2) |
cohomCalg computes cohomology vectors by calling CohomCalg. It also stashes it's results in the toric variety's cache table, so computations need not be performed twice.
This documentation describes version 0.8 of CohomCalg.
The source code from which this documentation is derived is in the file CohomCalg.m2. The auxiliary files accompanying it are in the directory CohomCalg/.