The strongec package requires one first to load the LinearAlgebra package. Also, a global variable SAMPLE must be set by hand.restart;with(LinearAlgebra):I have to tell Maple where the library containing the strongec package is.libname := "/Users/chris/UserMapleLib/EC.mla", libname;with(strongec);We set the global variable SAMPLE to one. We will not be taking advantage of Kawamata-Viehweg vanishing, just Kodaira vanishing to start.SAMPLE := 1;Let's take a look at a particular example, the toric variety L^{253} characterized by the following fan.L253fan := [[0,-1],[3,4],[1,2],[-1,-1]];We also load in a strong exceptional collection of line bundles in the format (a_1, a_2, ..., a_n) = O(\sum_i a_i D_i). In this case there are four rays in the fan and so four distinct divisors D_i.L253EC := [[0,0,0,0],[1,0,0,0],[1,1,0,0],[2,0,0,0],[2,1,0,0],[2,2,0,0],[3,1,0,0]];The most important program in the collection is matrixconvert, which calls all the others in its running. The program requires both the fan and the exceptional collection. It also requires two dummy variables, M0 and M2 below, which after running each will contain an array of numbers.M0 contains the dimension of the zeroth cohomology of the pairwise differences of line bundles. M2 contains the dimension of the second cohomology. If M2 is not zero, then the collection is not strongly exceptional and a warning message will be generated. If M0 is not upper diagonal, the collection is not strongly exceptional and a warning message will also be generated. M0 and M2 are computed directly. matrixconvert attempts to verify that the dimension of the first cohomology vanishes using Kodaira vanishing or successively stronger versions of Kawamata-Viehweg vanishing as SAMPLE is increased from one. Given a fan of length L, Kawamata-Viehweg is tested by sampling L^SAMPLE points in a hypercube of length one -- these points correspond to the "boundary divisor". A "not-convex" or "semi-convex" warning means a failure to find any boundary divisor that would lead to a vanishing of H^1. Increasing SAMPLE can often eliminate these warnings.The function matrixconvert returns the sum M0+M2. matrixconvert(L253EC, M0, M2, L253fan);SAMPLE := 2;matrixconvert(L253EC, M0, M2, L253fan);Setting X := Matrix(M0) produces a data form that is a matrix rather than a nested list [[..],[..],..,[..]].MatrixInverse(Matrix(M0));The function H0num takes a fan for a surface V and a divisor D as arguments and computes the dimension of H^0(V, O(D))H0num(L253fan, [0,1,0,3]);Given a divisor D, the function sectiongen attempts to establish if any divisor D-E where E = \sum_i d_i D_i and 0 \leq d_i \leq 1has a strictly convex \Psi_{D-E} function. From Fulton we know that if \Psi_{D-E} is strictly convex, then D-E is ample. We need an ampleness condition on D-E to apply Kawamata-Viehweg. Not all possible d_i are sampled, just L^SAMPLE evenly distributed points. The functionreturns 0 for semi-convex, 1 for strictly convex, -1 otherwise. If SAMPLE = 1, then just D itself is tested.SAMPLE := 1;sectiongen(L253fan, [-1,-1,1,1]);SAMPLE := 3;sectiongen(L253fan, [-1,-1,1,1]);