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GlicciPointsInP3 :: verifyAllAssertionsOfThePaper

verifyAllAssertionsOfThePaper -- print commands to verfy the assertions of the paper

Synopsis

Description

Prints the commands needed to verify the assertions made in our paper Twenty Points in P^3. Now (perhaps with copy and paste), you could run them.
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)
///