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Bertini :: b'PHGaloisGroup

b'PHGaloisGroup -- Uses homotopy continuation to compute monodromy/Galois groups.

Synopsis

Description

Given a directory that has a Bertini input file that has ParameterHomotopy set to 2, a start file, for startparameters, this function uses parameter homotopies to perform a monodromy homotopy.

i1 : R=CC[x,T]

o1 = R

o1 : PolynomialRing
i2 : f=x^6+2*x^4+3*x^2+T

      6     4     2
o2 = x  + 2x  + 3x  + T

o2 : R
i3 : makeB'InputFile(storeBM2Files,AffVariableGroup=>{x,T},B'Polynomials=>{f,diff(x,f)})

o3 = /var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-74840-0/0/input

o3 : File
i4 : runBertini(storeBM2Files)
~/bertini
i5 : TCoordinates=importSolutionsFile(storeBM2Files)/last

o5 = {6.86018e-18+1.83757e-18*ii, 1.40741-.828173*ii, 1.40741+.828173*ii,
     ------------------------------------------------------------------------
     1.40741-.828173*ii, 1.40741+.828173*ii}

o5 : List
i6 : TBranchPoints=radicalList(TCoordinates)

o6 = {6.86018e-18+1.83757e-18*ii, 1.40741-.828173*ii, 1.40741+.828173*ii}

o6 : List
i7 : makeB'InputFile(storeBM2Files,B'Configs=>{{ParameterHomotopy,1}},AffVariableGroup=>{x},ParameterGroup=>{T},B'Polynomials=>{f})

o7 = /var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-74840-0/0/input

o7 : File
i8 : runBertini(storeBM2Files,PreparePH2=>true)
~/bertini
i9 : b'PHGaloisGroup(storeBM2Files,BranchPoints=>TBranchPoints)
~/bertini
~/bertini
~/bertini
~/bertini
~/bertini
(gg, [1, 2, 6, 4, 5, 3])
~/bertini
~/bertini
~/bertini
~/bertini
~/bertini
(gg, [1, 3, 2, 4, 6, 5])
~/bertini
~/bertini
~/bertini
~/bertini
~/bertini
(gg, [6, 2, 4, 3, 5, 1])
There were 0 loop failures.
/var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-74840-0/0/gggFile

o9 = [[1, 2, 6, 4, 5, 3], [1, 3, 2, 4, 6, 5], [6, 2, 4, 3, 5, 1]]

o9 : Array
i10 : b'PHGaloisGroup(storeBM2Files,BranchPoints=>TBranchPoints,LoopRadius=>.5)
~/bertini
~/bertini
~/bertini
~/bertini
~/bertini
(gg, [1, 2, 6, 4, 5, 3])
~/bertini
~/bertini
~/bertini
~/bertini
~/bertini
(gg, [1, 3, 2, 4, 6, 5])
~/bertini
~/bertini
~/bertini
~/bertini
~/bertini
(gg, [6, 2, 4, 3, 5, 1])
There were 0 loop failures.
/var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-74840-0/0/gggFile

o10 = [[1, 2, 6, 4, 5, 3], [1, 3, 2, 4, 6, 5], [6, 2, 4, 3, 5, 1]]

o10 : Array

Ways to use b'PHGaloisGroup :