how to express operators in symbolic algebra

I want to express an operator, P, which is simply the differential operator. I cannot find how to do this--one failed attempt is shown--any help appreciated

Fritz

==============================================

clear all
syms x
syms P(q), q(x)
q(x)=x^2
P(q) = diff(q(x),1) +5
return

Answer 1

[Walter Roberson]

MATLAB does not support creating operators: it only supports creating functions and expressions.

For example, P^3 to represent third derivative is not supported by MATLAB.

Answer 2

[Torsten]

Maybe like this

syms x
syms P(x) q(x)
q(x) = x^2
P(x) = diff(q(x),1) + 5

?

You can't define P as a function of a dependent variable (q).

You could define PP(x) = P(q(x)), if you want.

[Fritz Sonnichsen]

P(q(x)) = diff(q(x),1) dosen't seem to work either. Maybe the simpler way to answer this question is:

How to I express and operator in matlab symbolic algebra? (The operator can be any assortment of things but in my case generally a differential plus a constant.

thanks

Fritz

Answer 3

[Paul]

I'm not sure how define a function of a function. But this seems to work, at least for this simple case:

syms x t
syms q(t) v(x) % v is our dummy function
P = diff(v,argnames(v),1) + 5  % "operator" P

P(x) = 

q(t) = t^2

q(t) = 

P(t)  % show what P(t) is

ans = 

subs(P(argnames(q)),v,q)  % subs the dummy function with the actual function

ans = 

Or, more generally w/o needing to know the symfun buried in P

subs(P(argnames(q)),symfun(findSymType(P,'symfun'),symvar(P)),q)  % subs the dummy function

ans = 

I'm not sure this is the best way.

It can probably be wrapped in cleaner functionality, like

operateon = @(P,q) subs(P(argnames(q)),symfun(findSymType(P,'symfun'),symvar(P)),q);  % subs the dummy function

operateon(P,q)

ans = 

Exending to other operations as defined in Matlab

operateon(2*P,q)

ans = 

operateon(P^3,q)

ans = 

[Fritz Sonnichsen]

OK-your attention to this is appreciated

-I am still working on the best way to do this but I think the comment here indicates that matlab-sym does not have a way to directly do operator algebras--I must use a function.

Of additional interest here---I note you are able to get graphic values (instead of messy text values) for your results. I was looking for an option to do this and cannot find one. Can you tell me how to turn this on?

thanks

Fritz

[Paul]

Use Live Script to see Symbolic Toolbox Results with mathematical formatting.

Here on Answers, the formatting is done automatically when running code with the Run button.

[Fritz Sonnichsen]

OK--I never would have guessed! Live Script is now working and makes things a lot easier to read as my equations accumulate a lot of clutter

thanks

fritz

[Paul]

If you need to export your symbolic equations out of Matlab to some other application, you may also be interested in: latex.

p.s. In the future, please be careful about creating a new answer that really should be a comment to an existing answer. I've made that mistake myself because the new answer box is just below and much bigger than the comment box for preceding answer.

[Fritz Sonnichsen]

thanks for the comment - I think I have this answer in the correct box now. -I used latex many years ago and probably should review it. Fritz

[Dyuman Joshi]

I've moved the responses to be continued under @Paul's answer.

Also, @Fritz Sonnichsen, if this answer solved your problem, please consider accepting the answer. The general idea is to accept the answer that is most fitting to the question asked.

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