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_bertini__Parameter__Homotopy.out
-- -*- M2-comint -*- hash: 2393720217502712319 i1 : R=CC[u1,u2,u3,x,y]; i2 : f1=u1*(y-1)+u2*(y-2)+u3*(y-3); --parameters are u1, u2, and u3 i3 : f2=(x-11)*(x-12)*(x-13)-u1; i4 : paramValues0={1,0,0}; i5 : paramValues1={0,1+2*ii,0}; i6 : bPH=bertiniParameterHomotopy( {f1,f2}, {u1,u2,u3},{paramValues0 ,paramValues1 }) o6 = {{{11.3376-.56228*ii, 1}, {11.3376+.56228*ii, 1}, {13.3247, 1}}, {{11, ------------------------------------------------------------------------ 2}, {12, 2}, {13, 2}}} o6 : List i7 : bPH_0--the solutions to the system with parameters set equal to paramValues0 o7 = {{11.3376-.56228*ii, 1}, {11.3376+.56228*ii, 1}, {13.3247, 1}} o7 : List i8 : R=CC[x,y,z,u1,u2] o8 = R o8 : PolynomialRing i9 : f1=x^2+y^2-z^2 2 2 2 o9 = x + y - z o9 : R i10 : f2=u1*x+u2*y o10 = x*u1 + y*u2 o10 : R i11 : finalParameters0={0,1} o11 = {0, 1} o11 : List i12 : finalParameters1={1,0} o12 = {1, 0} o12 : List i13 : bPH=bertiniParameterHomotopy( {f1,f2}, {u1,u2},{finalParameters0 ,finalParameters1 },HomVariableGroup=>{x,y,z}) o13 = {{{1, 1.04634e-17-1.01448e-17*ii, -1}, {1, 1.32111e-17+6.418e-20*ii, ----------------------------------------------------------------------- 1}}, {{9.97833e-19+1.09185e-18*ii, 1, 1}, {-5.41884e-16+1.41201e-16*ii, ----------------------------------------------------------------------- 1, -1}}} o13 : List i14 : bPH_0--The two solutions for finalParameters0 o14 = {{1, 1.04634e-17-1.01448e-17*ii, -1}, {1, 1.32111e-17+6.418e-20*ii, 1}} o14 : List i15 : finParamValues={{1},{2}} o15 = {{1}, {2}} o15 : List i16 : bPH1=bertiniParameterHomotopy( {"x^2-u1"}, {u1},finParamValues,AffVariableGroup=>{x}) o16 = {{{-1}, {1}}, {{-1.41421}, {1.41421}}} o16 : List i17 : bPH2=bertiniParameterHomotopy( {"x^2-u1"}, {u1},finParamValues,AffVariableGroup=>{x},OutputStyle=>"OutSolutions") o17 = {{{-1}, {1}}, {{-1.41421}, {1.41421}}} o17 : List i18 : class bPH1_0_0 o18 = Point o18 : Type i19 : class bPH2_0_0 o19 = List o19 : Type i20 : dir1 := temporaryFileName(); -- build a directory to store temporary data i21 : makeDirectory dir1; i22 : bPH5=bertiniParameterHomotopy( {"x^2-u1"}, {u1},{{1},{2}},AffVariableGroup=>{x},OutputStyle=>"OutNone",TopDirectory=>dir1) i23 : B0=importSolutionsFile(dir1,NameSolutionsFile=>"ph_jade_0") o23 = {{-1}, {1}} o23 : List i24 : B1=importSolutionsFile(dir1,NameSolutionsFile=>"ph_jade_1") o24 = {{-1.41421}, {1.41421}} o24 : List i25 :