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monodromy-experiment.m2
restart FF = CC_53 needsPackage "ReactionNetworks" needsPackage "NAGtools" CRN = reactionNetwork "A <--> 2B, A + C <--> D, B + E --> A + C, D --> B + E" stSpace = stoichiometricSubspace CRN F = matrix{steadyStateEquations(CRN,FF)} R = ring F n = numgens R pre0 = point{apply(n,i->random FF)} F0 = sub(F, apply(gens R,coordinates pre0,(x,x0)->x=>x0)) V = numericalIrreducibleDecomposition ideal F0 W = first V#3 c0 = sample W normals = sub(gens stSpace,FF) L = (vars R - matrix pre0) * normals setDefault(Software=>PHCPACK) stop = (n,L)->n>1 rMatrix = random(FF^(numgens R),FF^(numcols(F|L))) elapsedTime sols = solveViaMonodromy(sub(rMatrix,R) * transpose (F|L),c0,{pre0}, StoppingCriterion=>stop); end R' = FF[gens R] toR' = map(R',R, vars R' | random(FF^1,FF^(numgens coefficientRing R))) F' = toR' matrix{F} L = vars R' * sub(gens stSpace,FF) - random(FF^1,FF^(numgens stSpace)) I = ideal (F') isPrime I dec = decompose I sols = solveSystem polySystem transpose (F'|L_{1}) #sols
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