CoefficientArrays
 Usage
• CoefficientArrays[polys, vars] gives the arrays of coefficients of the variables vars in the polynomials polys.
Notes
• 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[polys0] 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. • New in Version 5. • Advanced Documentation.
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