BUILT-IN MATHEMATICA SYMBOL

# 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.

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

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