This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 CoefficientArrays CoefficientArrays[polys, vars] gives the arrays of coefficients of the variables vars in the polynomials polys. CoefficientArrays gives a list containing SparseArray objects, which can be converted to ordinary arrays using Normal. If CoefficientArrays[polys, vars] gives , , , ... , then polys can be reconstructed as + . vars + . vars . vars + ... . Any element of polys of the form lhs == rhs is taken to correspond to the polynomial lhs - rhs. CoefficientArrays[polys, , , ... ] takes all expressions in polys that match any of the to be variables. CoefficientArrays[polys] is equivalent to CoefficientArrays[polys, Variables[polys]]. The length of the list CoefficientArrays[polys, vars] is one more than the total degree of polys. The are sparse arrays with ranks i + 1. The first element has the same length as the list polys. If polys is a single polynomial rather than a list, is also not a list. For linear equations, the solution to Thread[polys==0] is given by LinearSolve[, -]. 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. CoefficientArrays[polys, vars, Symmetric->True] makes all the symmetric in all their indices. The resulting arrays will generally be less sparse. See Section 3.7.12. See also: CoefficientList, SparseArray, Solve. New in Version 5.0.