bertiniImageMonodromyCollect -- Uses monodromy to find more solutions to a parameterized system of polynomial equations.

i1 : f="x^3+x*y^2+y+y^3+x-2";     h="a1*x+a2*y-1";

i3 : writeStartFile(storeBM2Files,{{1,0}},NameStartFile=>"startSave");

i4 : writeParameterFile(storeBM2Files,{1,0},NameParameterFile=>"start_parameters");

i5 : makeB'InputFile(storeBM2Files,
         B'Configs=>{{PARAMETERHOMOTOPY,2},{MPTYPE,2}},AffVariableGroup=>{x,y},ParameterGroup=>{a1,a2}, B'Polynomials=>{f,h}    )

<<<<<<< HEAD
o5 = /var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-7067-0/0/input
=======
o5 = /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-22983-0/0/input
>>>>>>> origin/master

o5 : File

i6 : bertiniImageMonodromyCollect(storeBM2Files,
         NameStartFile=>"startSave",
         StorageFolder=>"StoreFiles",
         AffVariableGroup=>{x,y},
         NumberOfLoops=>10,NumSolBound=>3,
         MonodromyStartParameters=>{1,0}        )
Starting monodromy loop number: 1.
Current fiber size: 1
Starting monodromy loop number: 2.
Current fiber size: 2
Starting monodromy loop number: 3.
Current fiber size: 2
Starting monodromy loop number: 4.
Current fiber size: 2
Starting monodromy loop number: 5.
Current fiber size: 3
Number of loops: 5.
NumSolBound has been reached.

o6 = {{1, 0}, {1, -.5+.866025*ii}, {1, -.5-.866025*ii}}

o6 : List

i7 : f="x^3+x*y^2+y+y^3+x-2";     h="a1*x+a2*y-1";

i9 : makeB'InputFile(storeBM2Files,
         B'Configs=>{{PARAMETERHOMOTOPY,2},{MPTYPE,2}},AffVariableGroup=>{x,y},ParameterGroup=>{a1,a2}, B'Polynomials=>{f,h}    )

<<<<<<< HEAD
o9 = /var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-7067-0/0/input
=======
o9 = /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-22983-0/0/input
>>>>>>> origin/master

o9 : File

i10 : bertiniImageMonodromyCollect(storeBM2Files,
          AffVariableGroup=>{x,y},
          StorageFolder=>"StoreFiles",
          MonodromyStartPoints=>{{1,0}},
          NumberOfLoops=>10,NumSolBound=>3)
Starting monodromy loop number: 1.
Current fiber size: 2
Starting monodromy loop number: 2.
Current fiber size: 3
Number of loops: 2.
NumSolBound has been reached.

o10 = {{1, 0}, {1, -.5+.866025*ii}, {1, -.5-.866025*ii}}

o10 : List

i11 : f="x^3+x*y^2+y+y^3+x-2";     h="a1*x+a2*y-1";

i13 : makeB'InputFile(storeBM2Files,
          B'Configs=>{{PARAMETERHOMOTOPY,2},{MPTYPE,2}},AffVariableGroup=>{x,y},ParameterGroup=>{a1,a2}, B'Polynomials=>{f,h}    )

<<<<<<< HEAD
o13 = /var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-7067-0/0/input
=======
o13 = /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-22983-0/0/input
>>>>>>> origin/master

o13 : File

i14 : s1=bertiniImageMonodromyCollect(storeBM2Files,
          AffVariableGroup=>{x,y},
          MonodromyStartPoints=>{{1,0}},
          MonodromyStartParameters=>{1,0},
          NumberOfLoops=>10,NumSolBound=>3,
          MonodromyStartParameters=>{1,0},
          ImageCoordinates=>({x}))
Starting monodromy loop number: 1.
Current fiber size: 1
Starting monodromy loop number: 2.
Current fiber size: 1
Starting monodromy loop number: 3.
Current fiber size: 1
Starting monodromy loop number: 4.
Current fiber size: 1
Starting monodromy loop number: 5.
Current fiber size: 1
Starting monodromy loop number: 6.
Current fiber size: 1
Starting monodromy loop number: 7.
Current fiber size: 1
Starting monodromy loop number: 8.
Current fiber size: 1
Starting monodromy loop number: 9.
Current fiber size: 1
Starting monodromy loop number: 10.
Current fiber size: 1
NumberOfLoops has been reached.

o14 = {{1, 0}}

o14 : List

i15 : #s1==1

o15 = true

i16 : s2=bertiniImageMonodromyCollect(storeBM2Files,
          MonodromyStartPoints=>{{1,0}},
          MonodromyStartParameters=>{1,0},
          NumberOfLoops=>10,NumSolBound=>3,
          MonodromyStartParameters=>{1,0},
          AffVariableGroup=>{x,y},
          ImageCoordinates=>{"x^3+x*y^2+y+y^3+x-2"})
Starting monodromy loop number: 1.
Current fiber size: 1
Starting monodromy loop number: 2.
Current fiber size: 1
Starting monodromy loop number: 3.
Current fiber size: 1
Starting monodromy loop number: 4.
Current fiber size: 1
Starting monodromy loop number: 5.
Current fiber size: 1
Starting monodromy loop number: 6.
Current fiber size: 1
Starting monodromy loop number: 7.
Current fiber size: 1
Starting monodromy loop number: 8.
Current fiber size: 1
Starting monodromy loop number: 9.
Current fiber size: 1
Starting monodromy loop number: 10.
Current fiber size: 1
NumberOfLoops has been reached.

o16 = {{1, 0}}

o16 : List

i17 : #s2==1

o17 = true