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makeBSlice.tst.m2
needsPackage "Bertini" --When we have a multiprojective variety we can different types of slices. --To make a slice we need to specify the type of slice we want followed by variable groups. sliceType={1,1} variableGroups={{x0,x1},{y0,y1,y2}} xySlice=makeB'Slice(sliceType,variableGroups,B'NumberCoefficients=>{{2,3},{5,7,11}}) --Our slice consists of two sections. --The ith section is in the variables variableGroups_(sliceType_i) assert(xySlice#B'SectionString_0==="(2)*(x0)+(3)*(x1)") assert(xySlice#B'SectionString_1==="(5)*(y0)+(7)*(y1)+(11)*(y2)") ----We can use slices to determine multidegrees. f1="x0*y0+x1*y0+x2*y2" f2="x0*y0^2+x1*y1*y2+x2*y0*y2" variableGroups={{x0,x1,x2},{y0,y1,y2}} xxSlice=makeB'Slice({2,0},variableGroups) makeB'InputFile(storeBM2Files, HomVariableGroup=>variableGroups, B'Polynomials=>{f1,f2}|xxSlice#ListB'Sections) runBertini(storeBM2Files) xxDegree=#importSolutionsFile(storeBM2Files) assert(xxDegree==2) xySlice=makeB'Slice({1,1},variableGroups,ContainsMultiProjectivePoint=>{{1,2,3},{4,5,6}},B'Homogenization=>{hx,hy},B'NumberCoefficients=>{{20,21,22},{30,31,32}}) assert(xySlice#B'SectionString_0==="(20)*(x0-(hx)*(1))+(21)*(x1-(hx)*(2))+(22)*(x2-(hx)*(3))") assert(xySlice#B'SectionString_1==="(30)*(y0-(hy)*(4))+(31)*(y1-(hy)*(5))+(32)*(y2-(hy)*(6))") ---Commented out below "makeB'InputFile(storeBM2Files, HomVariableGroup=>variableGroups, B'Polynomials=>{f1,f2}|xySlice#ListB'Sections) runBertini(storeBM2Files) xyDegree=#importSolutionsFile(storeBM2Files) makeB'InputFile(storeBM2Files, HomVariableGroup=>variableGroups, B'Polynomials=>{f1,f2}|yySlice#ListB'Sections) runBertini(storeBM2Files) yyDegree=#importSolutionsFile(storeBM2Files)"
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