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CohomCalg :: cohomCalg(NormalToricVariety)

cohomCalg(NormalToricVariety) -- locally stashed cohomology vectors from CohomCalg

Synopsis

Description

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})

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}}}}

See also