[SOLVED] Identify powers in an algebraic expression for a Buckingham Pi calculation in MatLab

Identify powers in an algebraic expression for a Buckingham Pi calculation in MatLab

This is a continuation of an earlier question I asked here.

If I create a symbolic expression in MatLab

syms L M T
F = M*L/T^2

I want to identify the powers of each dimension M, L, or T. In this case, the answer should be

for M, 1
for L, 1
for T, -2

There is a relatively easy way to do this if the expression F were a polynomial in MatLab employing the coeffs function. However, my expression is clearly not a polynomial as far as MatLab is concerned.

In the end, I will be working with at least two parameters so I will put them in a cell array since I anticipate cellfun will be useful.

V = L/T
param = {F,V};

The final output should be a table where the rows correspond to each dimension, L M and T and the columns are for each parameter F and V.

Solution

syms L M T
F = M*L/T^2

[C,T] = coeffs(expand(log(F),'IgnoreAnalyticConstraints',true))
[exp(T).' C.']

It returns the table: