i1 : verifyAllAssertionsOfThePaper() /// --run the following commands in Macaulay 2 setRandomSeed("verify all") isPrime 10001, isPrime 10003, isPrime 10007 -- smallest prime >10^4 kk:=ZZ/10007 S:=kk[x_0..x_3] -- experiment on page 7 hV:=hVector 20|reverse hVector 10 time tally apply(10^4,c->testSplitting(S,hV,20)) -- used 431.164 seconds -- output --Tally{false => 6132} -- true => 3868 --------------------------------------------------- -- section 2 univariate polynomial statistic -- --------------------------------------------------- q:=symbol q Q:=QQ[q] numOfIrreducible(6,Q) numOfSquareFree(6,Q) polynomialsWithFactor(6,3,Q) q=symbol q Q=RR[q,MonomialOrder=>Lex,Inverses=>true]; probOfFactor(30,20,10007) probOfFactor(30,20,Q,1) probOfFactor(15,1,Q,1) probOfFactor(15,1) --------------------------------- -- section 4 main theorem -- --------------------------------- #createCandidates 100 == #createCandidates 5 -- corollar 4.3 L:=createCandidates 5 (Lgood,Lbad):=checkCandidates(L,S) (#Lgood,#Lbad)==(93,9) -- main theorem G=getGraph Lgood LgoodhVs=unique apply(Lgood,c->c_0_1) #LgoodhVs --graphvizFile("bidominanceGraph.dot","H",G,0) --in a shell, execute: dot -Tpdf bidominanceGraph.dot -o bidominanceGraph.pdf netList Lbad -- remark 4.6 finiteFibers=apply( select(Lgood,b->b_1_0==0) ,b->(b_0_0,b_0_1,b_3)) netList finiteFibers ---------------- -- section 1 -- ----------------- -- graphvizFile("bidominanceGraph.dot","H",G,0) -- in a shell, execute: dot -Tpdf bidominanceGraph.dot -o bidominanceGraph.pdf -- question: 34? hVector 34, hVector 21 hV55=hVector 35|reverse hVector 20 (dimFormula hV55,3*34)==(99,102) checkCandidates({(34,hV55)},S) hVector 36, hVector 34 hV70=hVector 35|reverse hVector 35 checkCandidates({(36,hV70)},S) hV68=hVector 34|reverse hVector 34 checkCandidates({(34,hV68)},S) /// |