ComputeSparsePolyBasis.txt

read "multires03.txt":
with(Groebner):
with(ArrayTools):
with(CodeGeneration):
read "LargestInvrtbleSubMat.txt": 

EstimatePolytopes := proc (listOfEqns ::list, vars ::list, hiddenVar) 
 	local p,q:
	print("Trying to find the polytopes of the equations..."):
    	p,q := `toric/polytope`(listOfEqns,vars);
	p,q:
end:

BasisBySprseResultant := proc (listOfEqns ::list, vars ::list, hiddenVar) 
local spBasis, coeffMatrix, degreeHidVar, AllCs, M11, M12, M21, M22, Cs, newMonomialBasis1, newCoeffMatrix, largestSize, temp2s, oCoeffMatrix, oMonomialBasis, newCoeffMatrix1:
description "Calculate a sparse resultant of the given list of polynomials in given list of variables"; 
    print("Computing the sparse resultant...", listOfEqns):
	coeffMatrix, spBasis := spresultant(listOfEqns, vars):
	coeffMatrix := convert(coeffMatrix, Matrix):

	print(cat("Trying to optimize the size of monomial basis. Original size is \n \n", Size(spBasis)[2])):    	
	M11, M12, M21, M22, newCoeffMatrix1, newMonomialBasis1, largestSize, temp2s, oCoeffMatrix, oMonomialBasis := ReorderCoeffMatrix(coeffMatrix, hiddenVar, spBasis, degreeHidVar):
	
	newCoeffMatrix := newCoeffMatrix1:
	
	print("We need the largest degree of a polynomial in the hidden variable.");
	degreeHidVar := max(map( f -> degree(f,hiddenVar), newCoeffMatrix1));	
	AllCs:= map(i -> coeff(newCoeffMatrix, hiddenVar^i), [seq(1..degreeHidVar)]):
	Cs := [coeff(newCoeffMatrix * hiddenVar, hiddenVar), op(AllCs)]:
	Cs := convert(Cs, Matrix):

    M11, M12, M21, M22, Cs, LinearAlgebra[Transpose](convert(newMonomialBasis1,Matrix)), degreeHidVar, newCoeffMatrix, largestSize, temp2s, oCoeffMatrix, oMonomialBasis, coeffMatrix :
	
end:

MatlabCodeCreator := proc(CoeffMatrices, varName, fileName)
description "Take in the coeffmatrices estimate the eigenvalues and eigenvectors for these CS matrices";

	# Once we have the coefficient matrices, we need to create a MATLAB code that will work with these matrices. 
	Matlab(CoeffMatrices, output=fileName, resultname=varName);

end:
BasisByGbBasis := proc (listOfEqns ::list, vars :: list) 
local gbBasis, ringBasis:
description "Calculate a basis using groebner bases"; 
	
	gbBasis := Basis(listOfEqns, tdeg(seq(vars))):
	ringBasis := NormalSet(gbBasis, tdeg(seq(vars))):
	ringBasis[1]:
end: