BUILT-IN MATHEMATICA SYMBOL

CoefficientArrays

gives the arrays of coefficients of the variables vars in the polynomials polys.

MORE INFORMATION

CoefficientArrays gives a list containing SparseArray objects, which can be converted to ordinary arrays using Normal.

If CoefficientArrays gives , then polys can be reconstructed as . »

Any element of polys of the form is taken to correspond to the polynomial . »

CoefficientArrays 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 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 is given by LinearSolve.

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.

Out[1]=

Out[2]=

Scope (4)

Linear polynomial:

List of linear polynomials:

Nonlinear polynomials:

Polynomial equations:

Options (1)

The default coefficient of a quadratic form corresponding to

is zero:

With

True, CoefficientArrays gives symmetric arrays:

Applications (1)

Convert linear equations to arrays suitable for LinearSolve:

Properties & Relations (3)

The polynomial can be reconstructed by using Dot (

):

The symmetric coefficient arrays correspond to vector derivatives at the origin:

CoefficientArrays gives a list of arrays of polynomial coefficients ordered by total degrees:

CoefficientList gives a tensor of the coefficients:

Use Coefficient to find the coefficient of

:

In

the position is

concatenated with a

s and b

s (

and

indicate the first and second variables):

In

the coefficient of

is the element at position

: