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coeffs

Coefficients of polynomial

Syntax

Description

example

C = coeffs(p) returns coefficients of the polynomial p with respect to all variables determined in p by symvar.

example

C = coeffs(p,var) returns coefficients of the polynomial p with respect to the variable var.

example

C = coeffs(p,vars) returns coefficients of the multivariate polynomial p with respect to the variables vars.

example

[C,T] = coeffs(___) returns the coefficient C and the corresponding terms T of the polynomial p.

___ = coeffs(___,'All') returns all coefficients, including coefficients that are 0. For example, coeffs(2*x^2,'All') returns [ 2, 0, 0] instead of 2.

Examples

Coefficients of Univariate Polynomial

Find the coefficients of this univariate polynomial.

syms x
c = coeffs(16*x^2 + 19*x + 11)
c =
[ 11, 19, 16]

Coefficients of Multivariate Polynomial with Respect to Particular Variable

Find the coefficients of this polynomial with respect to variable x and variable y.

syms x y
cx = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, x)
cy = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, y)
cx =
[ 4*y^3, 3*y^2, 2*y, 1]
 
cy =
[ x^3, 2*x^2, 3*x, 4]

Coefficients of Multivariate Polynomial with Respect to Two Variables

Find the coefficients of this polynomial with respect to both variables x and y.

syms x y
cxy = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [x,y])
cyx = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [y,x])
cxy =
[ 4, 3, 2, 1]
 
cyx =
[ 1, 2, 3, 4]

Coefficients and Corresponding Terms of Univariate Polynomial

Find the coefficients and the corresponding terms of this univariate polynomial.

syms x
[c,t] = coeffs(16*x^2 + 19*x + 11)
c =
[ 16, 19, 11]
 
t =
[ x^2, x, 1]

Coefficients and Corresponding Terms of Multivariate Polynomial

Find the coefficients and the corresponding terms of this polynomial with respect to variable x and variable y.

syms x y
[cx,tx] = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, x)
[cy,ty] = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, y)
cx =
[ 1, 2*y, 3*y^2, 4*y^3]
 
tx =
[ x^3, x^2, x, 1]
 
cy =
[ 4, 3*x, 2*x^2, x^3]
 
ty =
[ y^3, y^2, y, 1]

Find the coefficients of this polynomial with respect to both variables x and y.

syms x y
[cxy, txy] = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [x,y])
[cyx, tyx] = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [y,x])
cxy =
[ 1, 2, 3, 4]
 
txy =
[ x^3, x^2*y, x*y^2, y^3]
 
cyx =
[ 4, 3, 2, 1]
 
tyx =
[ y^3, x*y^2, x^2*y, x^3]

All Coefficients of Polynomial

Find all coefficients of a polynomial, including coefficients that are 0, by specifying the option 'All'.

Find all coefficients of 3x2.

syms x
c = coeffs(3*x^2, 'All')
c =
[ 3, 0, 0]

If you find coefficients with respect to multiple variables and specify 'All', then coeffs returns coefficients for all combinations of the variables.

Find all coefficients and corresponding terms of ax2 + by.

syms a b y
[cxy, txy] = coeffs(a*x^2 + b*y, [y x], 'All')
cxy =
[ 0, 0, b]
[ a, 0, 0]
txy =
[ x^2*y, x*y, y]
[   x^2,   x, 1]

Input Arguments

collapse all

Polynomial, specified as a symbolic expression or function.

Polynomial variable, specified as a symbolic variable.

Polynomial variables, specified as a vector of symbolic variables.

Output Arguments

collapse all

Coefficients of polynomial, returned as a symbolic number, variable, expression, vector, matrix, or multidimensional array. If there is only one coefficient and one corresponding term, then C is returned as a scalar.

Terms of polynomial, returned as a symbolic number, variable, expression, vector, matrix, or multidimensional array. If there is only one coefficient and one corresponding term, then T is returned as a scalar.

See Also

Introduced before R2006a

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