problem with coeffs command

I have a symbollic expression

5*w - 5*z - u*((603367941593515*x)/4503599627370496 - y/2) - v*(x/2 + (603367941593515*y)/4503599627370496) - 1/8

which I want to extract the coefficient of u from. But the coeff command gives an erroneous result:

ans =
 
5*w - 5*z - u*((603367941593515*x)/4503599627370496 - y/2) - v*(x/2 + (603367941593515*y)/4503599627370496) - 1/8
 
coeffs(ans,u)
 
ans =
 
[5*w - 5*z - v*(x/2 + (603367941593515*y)/4503599627370496) - 1/8, y/2 - (603367941593515*x)/4503599627370496]

The first 'ans' is a multilinear polynomial in x y z u v and w, so shouldn't this work as coeffs is for polynomials.

Answer 1

[Paul]

syms w z u y v x
5*w - 5*z - u*((603367941593515*x)/4503599627370496 - y/2) - v*(x/2 + (603367941593515*y)/4503599627370496) - 1/8

ans = 

coeffs(ans,u).'

ans = 

The second term in the result is the coefficient of u and the first term is everything else.

Is that not the expected result?

[Steven Lord]

Note that the convention used by coeffs (returning in ascending order of power when called with 1 output) is different than the convention used by some of the other polynomial functions in MATLAB like polyfit, which returns the coefficients in descending order of power.

p = [1 2 3]; % x^2+2*x+3
x = 1:10;
y = polyval(p, x);
polyfitCoefficients = polyfit(x, y, 2) % Quadratic term first

polyfitCoefficients = 1×3

1.0000 2.0000 3.0000

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syms z
polynomialSym = p(1)*z^2+p(2)*z+p(3)

polynomialSym = 

coeffsCoefficients1Output = coeffs(polynomialSym, z) % Constant term first

coeffsCoefficients1Output = 

But if you call coeffs with two outputs, it will return it in descending order of power like polyfit does.

[coeffsCoefficients2Output, powersOfZ] = coeffs(polynomialSym, z)

coeffsCoefficients2Output = 

powersOfZ = 

[Sam Chak]

Hi @Ali Kiral

The coeffs(ans, u) function essentially extracts the coefficients for the and terms. If you specify the output arguments clearly using [coefficients, terms], you will observe the results.

syms w z u y v x

expr = 5*w - 5*z - u*((603367941593515*x)/4503599627370496 - y/2) - v*(x/2 + (603367941593515*y)/4503599627370496) - 1/8

expr = 

[coefficients, terms] = coeffs(expr, u)

coefficients = 

terms = 

If you only want to retrieve the coefficient for the u term, then enter this:

coefficients(1)

ans = 

[Steven Lord]

The coeffs(ans, u) function essentially extracts the coefficients for the and terms.

That's true if called with two outputs. If not it returns them in the opposite order, and .

syms w z u y v x
expr = 5*w - 5*z - u*((603367941593515*x)/4503599627370496 - y/2) - v*(x/2 + (603367941593515*y)/4503599627370496) - 1/8;
oneOutput = coeffs(expr, u);
[twoOutputs, terms] = coeffs(expr, u);
isequal(oneOutput, twoOutputs) % false

ans = logical
   0

isequal(flip(oneOutput), twoOutputs) % true

ans = logical
   1

[Ali Kiral]

@Paul I didn't know this command also gives an output for the zeroth power of u. You're right.