The keys of this hash table are the divisor classes (degrees) whose cohomology vector has already been computed. The value of the hash table for this key is a list of two things: the cohomology vector, and a list representing the denominators which appear for this degree.
i1 : needsPackage "ReflexivePolytopesDB" o1 = ReflexivePolytopesDB o1 : Package |
i2 : topes = kreuzerSkarke(5, Limit => 20); using offline data file: ks5-n50.txt |
i3 : A = matrix topes_15 o3 = | 1 1 0 1 -1 -2 1 | | 0 2 0 0 -4 0 6 | | 0 0 1 0 2 -1 -4 | | 0 0 0 2 -2 0 0 | 4 7 o3 : Matrix ZZ <--- ZZ |
i4 : P = convexHull A o4 = P o4 : Polyhedron |
i5 : X = normalToricVariety P o5 = X o5 : NormalToricVariety |
i6 : H = cohomCalg X o6 = MutableHashTable{} o6 : MutableHashTable |
Notice that the hash table H is empty, as we haven't tried computing any cohomology vectors yet.
i7 : cohomCalg(X, {-4, 10, -9}) 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 6 1 0 0 4 -4 0 1 2 0 4 -2 -20 1 -2 -4 -4 -2 -64 1 1 0 0 0 0 1 0 1 0 0 29 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 0 4 4 0 1 -2 0 -4 -2 -26 1 2 -4 4 -2 -58 1 1 0 0 0 0 1 0 1 0 0 29 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 -4 -4 -4 0 1 -2 2 4 2 20 1 2 -2 -4 2 64 1 1 0 0 0 0 1 0 1 0 0 -32 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 -4 -4 -4 0 1 -2 -2 -4 -2 -24 1 2 2 4 -2 -64 1 1 0 0 0 0 1 0 1 0 0 -32 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 4 4 4 0 1 -2 -2 -4 -2 -26 1 2 2 4 -2 -58 1 1 0 0 0 0 1 0 1 0 0 -30 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 -4 -4 -4 0 1 2 2 4 2 22 1 -2 -2 -4 2 62 1 1 0 0 0 0 1 0 1 0 0 -32 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 -4 -4 -4 0 1 -2 -2 -4 -2 20 1 2 2 4 -2 52 1 1 0 0 0 0 1 0 1 0 0 26 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 -4 -4 -4 0 1 -2 2 4 2 -24 1 2 -2 -4 2 -52 1 1 0 0 0 0 1 0 1 0 0 26 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 -4 -4 -4 0 1 2 -2 -4 -2 22 1 -2 2 4 -2 50 1 1 0 0 0 0 1 0 1 0 0 26 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 0 4 4 0 1 -2 0 -4 -2 18 1 2 -4 4 -2 58 1 1 0 0 0 0 1 0 1 0 0 -29 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 0 -4 -4 0 1 -2 0 -4 -2 20 1 2 -4 4 -2 52 1 1 0 0 0 0 1 0 1 0 0 -27 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 -4 4 -4 0 1 -2 2 -4 2 -26 1 2 -2 4 2 -54 1 1 0 0 0 0 1 0 1 0 0 28 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 0 -4 4 0 1 -2 0 4 -2 20 1 2 -4 -4 -2 60 1 1 0 0 0 0 1 0 1 0 0 -31 1 0 0 1 0 0 1 0 1 0 2 0 7 6 1 0 0 4 -4 0 1 2 0 4 -2 24 1 -2 -4 -4 -2 52 1 1 0 0 0 0 1 0 1 0 0 -29 1 0 0 1 0 0 1 0 1 0 2 0 Computation of the target cohomology group dimensions complete. All done. Program run successfully completed. o7 = {0, 0, 0, 12960, 0} o7 : List |
i8 : for i from 0 to dim X list rank HH^i(X, OO_X(-4, 10, -9)) o8 = {0, 0, 0, 12960, 0} o8 : List |
i9 : peek cohomCalg X o9 = MutableHashTable{{-4, 10, -9} => {{0, 0, 0, 12960, 0}, {{3, 1x0*x1*x2*x6}, {3, 1x0*x1*x2*x3*x6}, {3, 1x0*x1*x2*x4*x6}}}} |