coeffs

Coefficients of the polynomial.

Library

EngeeDSP

Syntax

Function call

C, T = coeffs(p) — returns coefficients and corresponding terms of a polynomial p with respect to all variables.

C, T = coeffs(p, var) — returns coefficients and corresponding terms of a polynomial p with respect to all variables var.

C, T = coeffs(p, vars) — returns coefficients and corresponding terms p with respect to all variables vars.

C, T = coeffs(_, "All") — returns all coefficients, including coefficients that are equal to 0. For example, coeffs(2*x^2, "All") returns [ 2, 0, 0] rather than 2.

Arguments

Input arguments

# p — the polynomial

+ symbolic expression | symbolic function

Details

A polynomial defined as a symbolic expression or function.

# var is a variable of the polynomial

+ character variable

Details

A polynomial variable specified as a symbolic variable.

# vars is a vector of variables of the polynomial

+ vector of symbolic variables

Details

Variables of the polynomial, defined as a vector of symbolic variables.

Output arguments

# C — coefficients of the polynomial

Details

The coefficients of a polynomial returned as a symbolic number, variable, expression, vector, matrix, or N-dimensional array. If there is only one coefficient and one corresponding term, then C it is returned as a scalar.

# T — terms of the polynomial

Details

The terms of a polynomial returned as a character number, variable, expression, vector, matrix, or N-dimensional array. If there is only one coefficient and one corresponding term, then T it is returned as a scalar.

Examples

Coefficients of a one-dimensional polynomial

Details

Let’s find the coefficients of the one-dimensional polynomial. The coefficients are ordered from the smallest degree to the largest.

import EngeeDSP.Functions: coeffs
using DynamicPolynomials
@polyvar x
out = coeffs(16*x^2 + 19*x + 11)[1]

3-element Vector{Int64}:
 11
 19
 16

Coefficients of a multidimensional polynomial for a specific variable

Details

Let’s find the coefficients of the polynomial in the variable x:

import EngeeDSP.Functions: coeffs
using DynamicPolynomials
@polyvar x y
out1 = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, x)[1]

4-element Vector{Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}, Int64}}:
 1
 2y
 3y²
 4y³

and by variable y:

out2 = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, y)[1]

4-element Vector{Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}, Int64}}:
 4
 3x
 2x²
 x³

Coefficients of a multidimensional polynomial in two variables

Details

Let’s find the coefficients of the polynomial with respect to both variables x and y.

import EngeeDSP.Functions: coeffs
using DynamicPolynomials
@polyvar x y
out = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, [x, y])[1]

4-element Vector{Int64}:
 1
 2
 3
 4

Coefficients and corresponding terms of a one-dimensional polynomial

Details

Let’s find the coefficients and the corresponding terms of the one-dimensional polynomial. When there are two outputs, the coefficients are ordered from the largest to the smallest.

import EngeeDSP.Functions: coeffs
using DynamicPolynomials
@polyvar x y

out1,out2 = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, x)
println(out1)
println(out2)
out1,out2 = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, y)
println(out1)
println(out2)

Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}, Int64}[1, 2y, 3y², 4y³]
Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}, Int64}[x³, x², x, 1]
Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}, Int64}[4, 3x, 2x², x³]
Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}, Int64}[y³, y², y, 1]

All coefficients of the polynomial

Details

Let’s find all coefficients of the polynomial, including coefficients equal to 0 by specifying the option "All". The coefficients returned are ordered from the largest to the smallest.

Let’s find all the coefficients .

import EngeeDSP.Functions: coeffs
using DynamicPolynomials
@polyvar x
out = coeffs(3*x^2, "All")[1]

3-element Vector{Int64}:
 3
 0
 0