how to express operators in symbolic algebra

Question

Fritz Sonnichsen 2023-12-17

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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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Answer 1

Walter Roberson 2023-12-17

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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.

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Answer 2

Torsten 2023-12-17

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编辑：Torsten 2023-12-17

在 MATLAB Online 中打开

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.

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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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Answer 3

Paul 2023-12-17

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编辑：Paul 2023-12-17

在 MATLAB Online 中打开

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 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 2023-12-22

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

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