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bertiniParameterHomotopy.tst.m2
needsPackage "Bertini" myPoints={ { point{{11, 1}}, point{{13, 1}}, point{{12, 1}} }, { point{{11, 2}}, point{{13, 2}}, point{{12, 2}} }} R=CC[u1,u2,u3,x,y] f1=u1*(y-1)+u2*(y-2)+u3*(y-3) f2=(x-11)*(x-12)*(x-13) bPH=bertiniParameterHomotopy( {f1,f2},--list of polynomials that have zero dimensional solutions {u1,u2,u3},--your parameters { {1,0,0}, {0,1,0} })---list of {list of numbers}) apply(bPH/first,{1,2},(P,yValue)->assert(abs((matrix P)_(0,1)-yValue)<1e-6 )) ------ R=CC[x,u1] f1=x^2-u1 finalParameters0={1} finalParameters1={2} bPH=bertiniParameterHomotopy( {f1}, {u1},{finalParameters0 ,finalParameters1 },AffVariableGroup=>{x}) --TODO: need new assertions -- assert(1===#radicalList({ (((bPH_0_0)#Coordinates)_0)^2,1}) ) -- assert(2===#radicalList({ (((bPH_1_0)#Coordinates)_0)^2,1}) ) R=CC[x,y,u1] f1=x^2-u1*y^2 finalParameters0={1} finalParameters1={2} bPH3=bertiniParameterHomotopy( {f1}, {u1},{finalParameters0 ,finalParameters1 },HomVariableGroup=>{x,y}) assert(#bPH3==2) assert(#bPH3_0==2) assert(#bPH3_1==2) ---- ------ R=CC[x,u1] f1=x^2-u1 finalParameters0={1} finalParameters1={2} bPH4=bertiniParameterHomotopy( {f1}, {u1},{finalParameters0 ,finalParameters1 },AffVariableGroup=>{x},OutputStyle=>"OutSolutions") assert(class bPH4===List) --TODO: need new assertions -- assert(1===#radicalList({ (((bPH4_0_0))_0)^2,1}) ) -- assert(2===#radicalList({ (((bPH4_1_0))_0)^2,1}) ) -- R=CC[x,u1] f1=x^2-u1 finalParameters0={1} finalParameters1={2} dir1 := temporaryFileName(); -- build a directory to store temporary data makeDirectory dir1; bPH5=bertiniParameterHomotopy( {f1}, {u1},{finalParameters0 ,finalParameters1 },AffVariableGroup=>{x},OutputStyle=>"OutNone",TopDirectory=>dir1) B0=importSolutionsFile(dir1,NameSolutionsFile=>"ph_jade_0") B1=importSolutionsFile(dir1,NameSolutionsFile=>"ph_jade_1") --TODO: need new assertions -- assert(1===#radicalList({ (B0_0_0)^2,1}) ) -- assert(1===#radicalList({ (B1_0_0)^2,2}) )