Collect coefficients
Collect the coefficients of a symbolic expression.
syms x coeffs = collect((exp(x) + x)*(x + 2))
coeffs = x^2 + (exp(x) + 2)*x + 2*exp(x)
Because you did not specify the variable, collect
uses
the default variable defined by symvar
. For this
expression, the default variable is x
.
symvar((exp(x) + x)*(x + 2), 1)
ans = x
Collect coefficients of a particular variable
by specifying the variable as the second argument to collect
.
Collect coefficients of an expression in powers of x
,
and then in powers of y
.
syms x y coeffs_x = collect(x^2*y + y*x - x^2 - 2*x, x) coeffs_y = collect(x^2*y + y*x - x^2 - 2*x, y)
coeffs_x = (y - 1)*x^2 + (y - 2)*x coeffs_y = (x^2 + x)*y - x^2 - 2*x
Collect coefficients in powers of both x
and y
by
specifying the second argument as a vector of variables.
syms a b coeffs_xy = collect(a^2*x*y + a*b*x^2 + a*x*y + x^2, [x y])
coeffs_xy = (a*b + 1)*x^2 + (a^2 + a)*x*y
i
and pi
Collect coefficients of an expression in terms
of i
, and then in terms of pi
.
syms x y coeffs_i = collect(2*x*i - 3*i*y, i) coeffs_pi = collect(x*pi*(pi - y) + x*(pi + i) + 3*pi*y, pi)
coeffs_i = (2*x - 3*y)*1i coeffs_pi = x*pi^2 + (x + 3*y - x*y)*pi + x*1i
Collect coefficients of expressions and functions by specifying the second argument as an expression or function. Collect coefficients of multiple expressions or functions by using vector input.
Expand sin(x + 3*y)
and collect coefficients
of cos(y)
, and then of both sin(x)
and sin(y)
.
syms x y f = expand(sin(x + 3*y)); coeffs_cosy = collect(f, cos(y))
coeffs_cosy = 4*sin(x)*cos(y)^3 + 4*cos(x)*sin(y)*cos(y)^2 + (-3*sin(x))*cos(y) - cos(x)*sin(y)
coeffs_sinxsiny = collect(f, [sin(x) sin(y)])
coeffs_sinxsiny = (4*cos(y)^3 - 3*cos(y))*sin(x) + (4*cos(x)*cos(y)^2 - cos(x))*sin(y)
Collect coefficients of the symbolic function y(x)
in
a symbolic expression.
syms y(x) f = y^2*x + y*x^2 + y*sin(x) + x*y; coeffs_y = collect(f, y)
coeffs_y(x) = x*y(x)^2 + (x + sin(x) + x^2)*y(x)
Call collect
on a matrix. collect
acts
element-wise on the matrix.
syms x y collect([(x + 1)*(y + 1), x^2 + x*(x -y); 2*x*y - x, x*y + x/y], x)
ans = [ (y + 1)*x + y + 1, 2*x^2 - y*x] [ (2*y - 1)*x, (y + 1/y)*x]
Collect coefficients of calls to a particular function by specifying the function name as the second argument. Collect coefficients of function calls with respect to multiple functions by specifying the multiple functions as a cell array of character vectors.
Collect coefficients of calls to the sin
function
in F
, where F
contains multiple
calls to different functions.
syms a b c d e f x F = a*sin(2*x) + b*sin(2*x) + c*cos(x) + d*cos(x) + e*sin(3*x) +f*sin(3*x); collect(F, 'sin')
ans = (a + b)*sin(2*x) + (e + f)*sin(3*x) + c*cos(x) + d*cos(x)
Collect coefficients of calls to both the sin
and cos
functions
in F
.
collect(F, {'sin' 'cos'})
ans = (c + d)*cos(x) + (a + b)*sin(2*x) + (e + f)*sin(3*x)
combine
| expand
| factor
| horner
| numden
| rewrite
| simplify
| simplifyFraction
| symvar