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makeMembershipFile.tst.m2
loadPackage("Bertini",Reload=>true) ---Given a set of sample solutions or a solutions file AND a witness data file (this is created after performing a Bertini positive dimensional run) we can do a component membership test. --A component membership test is tracktype 3. makeB'InputFile(storeBM2Files, BertiniInputConfiguration=>{{TrackType,1}}, AffVariableGroup=>{x,y,z}, B'Polynomials=>{"z*((x+y+z)^3-1)","z*(y^2-3+z)"} ) ---By running Bertini we will create a witness_data file. runBertini(storeBM2Files) assert(7==#importMainDataFile(storeBM2Files)) --We create solutions file. makeSampleSolutionsFile(storeBM2Files,2,SpecifyComponent=>{1,0},NameSolutionsFile=>"our_test_solutions") --Now we do a membership test which creates an incidenceMatrix file. assert(fileExists(storeBM2Files|"/our_test_solutions")) makeMembershipFile(storeBM2Files, NameSolutionsFile=>"our_test_solutions") --Import the information of the membership test we need to import the incidence matrix. theIM= importIncidenceMatrix(storeBM2Files) assert(2==#theIM) assert({(2,0)}==theIM_0) assert((2,0)==theIM_0_0) --Our incidence matrix is flattened to a list. --The number of elements in theIM is equal to the number of points in the solutions file. --Each element of theIM is a list of sequences of 2 elements (codim,component Number). --Note that we follow the Bertini convention and switch from (dimension,component number) indexing to (codimension,component number) indexing. makeMembershipFile(storeBM2Files, TestSolutions=>{{1,2,0},{3,2,1}}) newIM= importIncidenceMatrix(storeBM2Files) assert(newIM_0=={(1,0)}) -- says that the 0th point of TestSolutions is in component (1,0) meaning in codimension 1 the 0th component. assert(newIM_1=={}) -- says that the other point of TestSolutions is in no components. ---------It is possible for a TestSolution to be in more than one point. makeB'InputFile(storeBM2Files, BertiniInputConfiguration=>{{TrackType,1}}, AffVariableGroup=>{x,y,z}, B'Polynomials=>{"x*y"} ) ---By running Bertini we will create a witness_data file. runBertini(storeBM2Files) ourTestSolutions={{0,0,1},{0,1,1},{1,0,1},{1,1,1}} makeMembershipFile(storeBM2Files, TestSolutions=>ourTestSolutions) anotherIM=importIncidenceMatrix(storeBM2Files) assert(2==#anotherIM_0)--Says ourTestSolutions_0 is in two components assert(1==#anotherIM_1)--Says ourTestSolutions_1 is in one component assert(1==#anotherIM_2)--Says ourTestSolutions_2 is in one component assert(0==#anotherIM_3)--Says ourTestSolutions_3 is in no components.
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