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 |