CoefficientArrays

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

Details and OptionsDetails and Options

  • 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 . »
  • Any element of polys of the form is taken to correspond to the polynomial . »
  • CoefficientArrays[polys, {form1, form2, ...}] 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 .
  • 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[m1, -m0].
  • For nonlinear equations, the are not unique. CoefficientArrays by default assigns nonzero 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.
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