MATLAB: Isolate Coefficients of Multivariate Linear Polynomial

coeffsMATLABmultivariatepolynomialsyms

Hi, I have a symbolic expression

eqn = r - 2*x +7/4

I would like to isolate the coefficients of the variables (x, r and y (y's coefficient is 0)). How do I do that? I've tried using coeffs but that only lets me specify one variable. It would also be ok if I got two vectors back:

[ -2 , 1 , 7/4]
[x , r , 1]

even if they don't include y. Thanks!

Best Answer

If you know that you have only linear terms and only x, r, and y, you could use diff to get the coefficients:

 syms x r y
 eqn = r - 2*x +7/4;
 [diff(eqn, x), diff(eqn, r), diff(eqn, y)]

This gives:

 ans =
 [ -2, 1, 0]

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MATLAB: How to get the degree of a polynomial defined symbolically in MATLAB

As of release R2014a, there is no MATLAB function in the Symbolic Math Toolbox that can get the degree of a polynomial defined symbolically.

As a workaround you can use the MuPAD function "degree". To call the MuPAD engine from within MATLAB in order to use "degree", use the "feval" function as follows:

>> syms x y z
>> P = x^4 + 3*x^2*y^2 - z^3 + y + 1;
>> feval(symengine, 'degree', P)
ans =
4

To get the degree of "P" with respect to a specific variable, use the following:

>> syms x y z
>> P = x^4 + 3*x^2*y^2 - z^3 + y + 1;
>> feval(symengine, 'degree', P, y)
ans =
2

MATLAB: Factorization With Symbolic Terms

simplify() can handle some cases. However it is not sophisticated so while it might find x^2+6*x+9 it will certainly not find x^2+6*x+11 = (x+3)^2+2

subs will also not dig out opportunities for substitution . subs(5*xx+5*yy,xx+yy,zz) will not notice the opportunity as it looks for exact node matches.

So generally you would proceed like

simplify(subs(TheExpression, y, z-x))

Best Answer

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MATLAB: How to get the degree of a polynomial defined symbolically in MATLAB

MATLAB: Factorization With Symbolic Terms

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