# How to extract powers of a symbolic polynomial?

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Alina Rossi-Conaway on 18 Mar 2021
Commented: Walter Roberson on 19 Jul 2021
I'm working with a symbolic polynomial
y = 0.96*z^3500 + 0.04*z^0
I can extract the coefficients easily with
coeffs(y)
but I cannot figure out a way to pull off the corresponding powers of z into a vector. I've tried doing some wonky stuff with logs, but nothing so far. Am I SOL?
Thank you!!

Steven Lord on 22 Mar 2021
syms z
y = 0.96*z^3500 + 0.04*z^0
y =
[coefficients, powers] = coeffs(y)
coefficients =
powers =
syms y positive
exponents = simplify(subs(log(powers)./log(z), z, y))
exponents =
Walter Roberson on 19 Jul 2021
Different formulation for finding the exponents.
syms z
y = 0.96*z^randi(9999) + 0.04*z^randi(9999)
y =
[coefficients, powers] = coeffs(y)
coefficients =
powers =
exponents = mapSymType(powers, 'power', @(Z) children(Z,2));
if powers(end) == 1; exponents(end) = 0; end
exponents
exponents =
This particular code relies on an enhancement to children() that was made a small number of releases ago. A workaround is possible for older releases.

Shubham Rawat on 22 Mar 2021
Hi Alina,
You may first find coefficients of all variables like this:
coef = sym2poly(y);
Then you can find all the index of all the non zero elements and -1 as indexing start from 1 in MATLAB:
polyPowers = find(coef) - 1;
Hope this Helps!
Davy Figaro on 19 Jul 2021
This is good, but because symbolic polynomial powers are presented in descending order, you need to double flip to get the polyPowers to line up to the original polynomial:
polyPowers = flip(find(flip(coef))) - 1;