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CoefficientArrays

FilledSmallSquare CoefficientArrays[polys, vars] gives the arrays of coefficients of the variables vars in the polynomials polys.

FilledSmallSquare CoefficientArrays gives a list containing SparseArray objects, which can be converted to ordinary arrays using Normal.

FilledSmallSquare If CoefficientArrays[polys, vars] gives , , , ... , then polys can be reconstructed as + . vars + . vars . vars + ... .

FilledSmallSquare Any element of polys of the form lhs == rhs is taken to correspond to the polynomial lhs - rhs.

FilledSmallSquare CoefficientArrays[polys, , , ... ] takes all expressions in polys that match any of the to be variables.

FilledSmallSquare CoefficientArrays[polys] is equivalent to CoefficientArrays[polys, Variables[polys]].

FilledSmallSquare The length of the list CoefficientArrays[polys, vars] is one more than the total degree of polys.

FilledSmallSquare The are sparse arrays with ranks i + 1.

FilledSmallSquare The first element has the same length as the list polys.

FilledSmallSquare If polys is a single polynomial rather than a list, is also not a list.

FilledSmallSquare For linear equations, the solution to Thread[polys==0] is given by LinearSolve[, -].

FilledSmallSquare For nonlinear equations, the are not unique. CoefficientArrays by default assigns non-zero coefficients only to monomials where the variables appear in the same order as vars.

FilledSmallSquare CoefficientArrays[polys, vars, Symmetric->True] makes all the symmetric in all their indices. The resulting arrays will generally be less sparse.

FilledSmallSquare See Section 3.7.12.

FilledSmallSquare See also: CoefficientList, SparseArray, Solve.

FilledSmallSquare New in Version 5.0.

Further Examples