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

## Synopsis

• Function: cohomCalg
• Usage:
H = cohomCalg X
• Inputs:
• X, ,
• Optional inputs:
• Silent (missing documentation) => , default value null, Not used in this particular method
• Outputs:
• H, ,
• Consequences:
• The mutable hash table is stashed into X.cache#CohomCalg. If it doesn't exist yet, it is created.

## 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

• cohomCalg -- compute cohomology vectors using the CohomCalg software