Built-in Mathematica Symbol

CoefficientList

CoefficientList[poly, var]
gives a list of coefficients of powers of var in poly, starting with power 0.

CoefficientList[poly, {var₁, var₂, ...}]
gives an array of coefficients of the var_i.

The dimensions of the array returned by CoefficientList are determined by the values of the Exponent[poly, var_i].

Terms that do not contain positive integer powers of a particular variable are included in the first element of the list for that variable.

CoefficientList always returns a full rectangular array. Combinations of powers that do not appear in poly give zeros in the array.

Find the coefficients in a polynomial:

CoefficientList works even when the polynomial has not been expanded out:

Matrix of coefficients for a quadratic form:

Find the coefficients in a polynomial:

CoefficientList works even when the polynomial has not been expanded out:

Matrix of coefficients for a quadratic form:

Univariate polynomial coefficient lists:

Multivariate polynomial coefficient lists:

Coefficient list over the integers modulo 2:

Use Coefficient to get a coefficient at a specified power of the variable:

The list of coefficients can be obtained using Coefficient and Exponent:

FromDigits can reconstruct a univariate polynomial from the list of its coefficients:

Fold the operation for multivariate polynomials:

Polynomial multiplication is convolution as performed by ListConvolve:

For multivariate polynomials CoefficientList gives a tensor of the coefficients:

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

The coefficient of

:

In cl the coefficient of x^a y^b is the element at position a+1, b+1:

In ca the position is a+b+1 concatenated with a 1s & b 2s (1 & 2 indicate the first & second variables):