Coefficients of polynomial
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Syntax
C = coeffs(p)
C = coeffs(p,var)
C = coeffs(p,vars)
[C,T] =coeffs(___)
___ = coeffs(___,'All')
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. The coefficients are ordered from the lowest degree to the highest degree.
syms xc = coeffs(16*x^2 + 19*x + 11)
Reverse the ordering of coefficients by using fliplr.
c = fliplr(c)
c =[ 16, 19, 11]
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 ycx = 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 ycxy = 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. When two outputs are provided, the coefficients are ordered from the highest degree to the lowest degree.
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'. The returned coefficients are ordered from the highest degree to the lowest degree.
Find all coefficients of 3x2.
syms xc = 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
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p — Polynomial
symbolic expression | symbolic function
Polynomial, specified as a symbolic expression or function.
var — Polynomial variable
symbolic variable
Polynomial variable, specified as a symbolic variable.
vars — Polynomial variables
vector of symbolic variables
Polynomial variables, specified as a vector of symbolic variables.
Output Arguments
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C — Coefficients of polynomial
symbolic number | symbolic variable | symbolic expression | symbolic vector | symbolic matrix | symbolic multidimensional array
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.
T — Terms of polynomial
symbolic number | symbolic variable | symbolic expression | symbolic vector | symbolic matrix | symbolic multidimensional array
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.
Version History
Introduced before R2006a
See Also
poly2sym | sym2poly
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