MATLAB: Possibly a bug in the ASSUME function (Symbolic Math Toolbox)

assumeassumptionssymbolic functionsSymbolic Math Toolbox

I am afraid I have bumped across a bug, or at least a confusing feature. It deals with imposing an assumption on a symbolic function. Consider the following code
clear all
syms theta1(t)
assume(theta1(t),'real')
theta1'                     % checking if conjugate transpose correctly reduces to transpose for a real function
assumptions                 % gives a list of all assumptions
The outputs are 
ans(t) =
 
theta1(t)
 
 
ans =
 
in(theta1(t), 'real')
Perfect. That is what we expect. But now consider a minor extension – we add one more symbolic function
clear all
syms theta1(t) 
syms theta2(t)
assume(theta1(t),'real')
assume(theta2(t),'real')
theta1'
theta2'
assumptions
The outputs are incorrect: 
ans(t) =
 
conj(theta1(t))
 
 
ans(t) =
 
theta2(t)
 
 
ans =
 
in(theta2(t), 'real')
It appears that upon imposing the second assumption, the first assumption is reset/removed.
Note that here the assumptions are imposed on two different/distinct objects; this is not the same case as the one with multiple assumptions mentioned in the manual.
But let's now check that the outcomes are correct if instead of symbolic functions we impose the assumptions on symbolic variables/expressions
clear all
syms theta1 
syms theta2
assume(theta1,'real')
assume(theta2,'real')
theta1'
theta2'
assumptions
The outputs are 
ans =
 
theta1
 
 
ans =
 
theta2
 
 
ans =
 
[in(theta1, 'real'), in(theta2, 'real')]
Correct. That is why I am tempted to conclude that the behaviour for functions exhibits a bug.

Best Answer

This is documented in the Tips section of assume() function: https://www.mathworks.com/help/releases/R2020b/symbolic/assume.html#bt07ws4-4
The toolbox does not support assumptions on symbolic functions. Make assumptions on symbolic variables and expressions instead.
Therefore, the results you are getting for second code can be considered undocumented behaviour.
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