How can I define general properties of symbolic functions?

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Jaime Abad Arredondo
评论： Jaime Abad Arredondo 2021-3-29
I'm trying to work with undefined symbolic functions, but I want to take advantage of some of its properties. For instance, I know that my functions fulfill:
As such I tried the following:
syms x y xx yy f(x)
assume(f(x)*f(y)==f(x+y))
Z=f(x)*f(y);
K=f(yy)*f(xx);
simplify(Z)
simplify(K)
While Z returns f(x+y) (the set identity as expected), it doesn't work on K as I don't know how to set the assumption on generic variables. I would very much like to avoid setting the assumption on every pair of arguments of my model, any clue on how to do this?

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Ananya Tewari
Ananya Tewari 2021-3-24
I understand that you want to set assumptions on generic variables. Currently it is not supported by MATLAB. A workaround if you do not wish to set assumption on every pair of argument, you can try using function handle to create a generic assume statement.
% creating function handle for assume statement
funAssume = @(a,b) assumeAlso(f(a)*f(b)==f(a+b)) % using assumeAlso to keep multiple assumptions
% calling funAssume() with any symbolic variable
funAssume(xx,yy)
K=f(yy)*f(xx);
simplify(K)
  1 个评论
Jaime Abad Arredondo
Jaime Abad Arredondo 2021-3-29
In the end I created a new class with objects that operated as I wanted. Much more laborious, but worked as intended. I accept the answer as it's a nice work-around. Still have to loop through every single variable combination calling the funAssume though...

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