MATLAB: Get coeffs of exponents

differential equationsmatrix

How can I get the coeffs of exponents?

for example:

A=-1*exp(t*w*-1i)/2 + exp(t*w*1i)/2 – exp(t*w*2i)/2 + exp(t*w*-2i)/2

I want to get: [-0.5, 0.5, -0.5, 0.5]

Best Answer

Hi,

You can use syms and coeffs.

Example:

syms t w i
A=-1*exp(t*w*-1i)/2 + exp(t*w*1i)/2 - exp(t*w*2i)/2 + exp(t*w*-2i)/2
coeffs(A)

Hope it helps.

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MATLAB: Complex polynomials

symbolic toolbox (MuPAD)

syms t w
expr=exp(1i*t*w*2)*exp(1i*t*w*3);
result = evalin(symengine,['simplify(' , char(expr),',exp)']);

MATLAB: Cant Solve ODE with dsolve

So you have a linear first-order differential equation looking something like this:

Then I'd suggest that special cases are combinations of A1 B1 and w equals zero. If I run your code without the numerical values of A1 B1 phi and w I get:

TSol = dsolve(diff(T) == (A1*exp(1i*(w*t+phi))+A1)*(B1*exp(1i*w*t)-T),cond)
TSol =
10*exp(-(A1*exp(phi*1i)*1i)/w)*exp(- A1*t + (A1*exp(phi*1i)*exp(t*w*1i)*1i)/w) + exp(- A1*t + (A1*exp(phi*1i)*exp(t*w*1i)*1i)/w)*int(A1*B1*exp(A1*u + u*w*1i - (A1*exp(phi*1i)*exp(u*w*1i)*1i)/w)*(exp(phi*1i + u*w*1i) + 1), u, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)
>> pretty(TSol)
                               t
                               /
   /   A1 #3 1i \             |           /             A1 #3 exp(#1) 1i \
exp| - -------- | #2 10 + #2  |  A1 B1 exp| A1 u + #1 - ---------------- | (exp(phi 1i + #1) + 1) du
   \       w    /            /            \                     w        /
                               0
where
   #1 == u w 1i
            /          A1 #3 exp(t w 1i) 1i \
   #2 == exp| - A1 t + -------------------- |
            \                    w          /
   #3 == exp(phi 1i)

It is a long expression, but it containe nothing extraordinarily complicated, but if for example w is zero this falls appart. You should be able to convert this into a regular m-function in a couple of minutes. It seems to fit the ode rather nicely.

HTH

Best Answer

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MATLAB: Complex polynomials

MATLAB: Cant Solve ODE with dsolve

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