Simplify symbolic functions: remove terms

Hi I want to simplify a symbolic function in this way:

this is my function:

a*b+dx*dy+dx^2*dy+a*dx+a+dy*dz+dt*da

I want that Matlab:

1. Remove the terms in which there is a product between dx*dy, dy*dx, dt*da, dx^2*dy etc.
2. Make two function: In the first there are all terms that are multiplied by dx, dy, dt and in the other, the other terms.

Thanks!

[bio lim]

I think your best bet is to check simplify

Answer 1

[Hildo]

Do you want to remove a specific variable

You can use

new_equation = subs(equation,var,0);
new_equation2 = simplify(equation); % Maybe is not necessary simplify in this case

Of all the cross multiplication between variables?

Answer 2

[Walter Roberson]

Note: for this purpose I exclude all squared terms such as dx^2, guessing that your rule was that multiplying two or more derivatives together was going to give a result too small to matter.

syms a b dx dy dz dt da
r = a*b+dx*dy+dx^2*dy+a*dx+a+dy*dz+dt*da;

[A,B] = coeffs(r,[dx,dy,dz,da,dt], 'all');
[tf, idx] = ismember([dx,dy,dz,da,dt],B);
just_constants = cellfun(@(C) isempty(symvar(C)), num2cell(B));

first_term = sum(A(idx(tf)) .* B(idx(tf)));
second_term = sum(A(just_constants) .* B(just_constants));

[Francesco Mela]

Thanks for the answer.

You're right, my purpose is to multiplying two derivatives together. However I have also a case in which there are dx^2*dy etc. How I can modify the code?

Thanks!

[Walter Roberson]

The code already removes dx^2*dy which you had specifically requested to be removed. What was not completely clear though was whether dx^N by itself should be removed, with N greater than 1? Is the rule that the term should be removed if the total order of derivatives is more than 1, or is the rule that the term should be removed only if there are multiple derivative variables involved?

[Francesco Mela]

Both things: the term should be removed if the total order of derivatives is more than 1 and if if there are multiple derivative variables involved. I want to remove both dx^2 both dx*dy both dx*dy^2, but not a*dx, x*dy ....

Another thing: the code works if I replace this

[A,B] = coeffs(r,[dx,dy,dz,da,dt], 'all');

with this

[A,B] = coeffs(r,[dx,dy,dz,da,dt]);

[Walter Roberson]

I did test the code with the expression you gave.

My expression originally involved some positional computations, but in mentally reviewing, I think that you are correct that the 'all' is not actually necessary, but it should not hurt.