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CoefficientArrays

CoefficientArrays[polys, vars]
gives the arrays of coefficients of the variables vars in the polynomials polys.
  • If CoefficientArrays[polys, vars] gives {m0, m1, m2, ...}, then polys can be reconstructed as m0+m1.vars+m2.vars.vars+....  »
  • Any element of polys of the form lhsrhs is taken to correspond to the polynomial lhs-rhs.  »
  • CoefficientArrays[polys, {form1, form2, ...}] takes all expressions in polys that match any of the formi to be variables.
  • The length of the list CoefficientArrays[polys, vars] is one more than the total degree of polys.
  • The mi are sparse arrays with ranks i+1.
  • The first element m0 has the same length as the list polys.
  • If polys is a single polynomial rather than a list, m0 is also not a list.
  • For linear equations, the solution to Thread[polys0] is given by LinearSolve[m1, -m0].
  • For nonlinear equations, the mi 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 mi symmetric in all their indices. The resulting arrays will generally be less sparse.
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