how to express operators in symbolic algebra

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Fritz Sonnichsen
Fritz Sonnichsen 2023-12-17
评论： Dyuman Joshi 2023-12-22
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

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回答（3 个）

Walter Roberson
Walter Roberson 2023-12-17
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.
Torsten
Torsten 2023-12-17
编辑：Torsten 2023-12-17
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.
  1 个评论
Fritz Sonnichsen
Fritz Sonnichsen 2023-12-17
移动：Dyuman Joshi 2023-12-21
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

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Paul
Paul 2023-12-17
编辑：Paul 2023-12-17
Ran in:
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 = 
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Fritz Sonnichsen
Fritz Sonnichsen 2023-12-22
移动：Dyuman Joshi 2023-12-22
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
Dyuman Joshi 2023-12-22
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.
Accepting an answer indicates that your problem has been solved (which can be helpful to other people in future) and it awards the volunteer with reputation points for helping you.
You can accept only 1 answer for a question, but you can vote for as many answers as you want. Voting an answer also provides reputation points.

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