Assumption on another symbolic Variable affecting a previous assumption

Question

Christian Luciano Maendle 2024-4-4，10:25

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https://ww2.mathworks.cn/matlabcentral/answers/2102826-assumption-on-another-symbolic-variable-affecting-a-previous-assumption

评论： Christian Luciano Maendle 2024-4-5，10:26

Why is the assumption I made being changed by the next assumption I do on another variable ?

The assumpitons on Phi_geod and Phi_dot_geod are being changed by the assumptions on the variables lambda_geod and lambda_dot_geod.

Code:

syms Phi_geod(t) lambda_geod(t)

syms Phi_dot_geod(t) lambda_dot_geod(t)

assumptions(Phi_geod)

ans = Empty sym: 1-by-0

assume(Phi_geod(t),"real");

assumptions(Phi_geod)

ans =

assume(lambda_geod(t),"real");

assumptions(Phi_geod)

ans =

assume(Phi_dot_geod(t),"real");

assume(lambda_dot_geod(t),"real");

assumptions(Phi_geod)

ans =

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Answer 1

Dyuman Joshi 2024-4-4，11:13

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https://ww2.mathworks.cn/matlabcentral/answers/2102826-assumption-on-another-symbolic-variable-affecting-a-previous-assumption#answer_1436456

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Because assume over-writes assumptions.

From the Tips section in the documentation page -

"assume removes any assumptions previously set on the symbolic variables. To retain previous assumptions while adding an assumption, use assumeAlso."

As mentioned in the note above, you need to use assumeAlso, after using assume() the first time.

syms Phi_geod(t) lambda_geod(t)

syms Phi_dot_geod(t) lambda_dot_geod(t)

assumptions(Phi_geod)

ans = Empty sym: 1-by-0

assume(Phi_geod(t),"real");

assumptions(Phi_geod)

ans =

assumeAlso(lambda_geod(t),"real");

assumptions(Phi_geod)

ans =

assumeAlso(Phi_dot_geod(t),"real");

assumeAlso(lambda_dot_geod(t),"real");

ans =

assumptions(Phi_geod)

ans =

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Paul 2024-4-4，16:39

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Hi Dyuman,

I think that's a misreading of the Tip wrt to the "symbolic variables" the tip is referencing. In that context, the symbolic variables are referencing the variables in the input to the assume command.

For example:

syms x y

class(x), class(y)

ans = 'sym'

assumptions

ans = Empty sym: 1-by-0

assume(x,'positive')

assumptions

ans =

assume(y,'integer'); % doesn't change assumption on x

assumptions

ans =

assume(x,'real'); % removes previous assumption on x, doesn't change assumption on y

assumptions

ans =

However, assume() seems to work differently when the inputs are symfun, rather than sym

syms x(t) y(t)

class(x)

ans = 'symfun'

class(y)

ans = 'symfun'

assumptions % all assumptions cleared on x and y after call to syms

ans = Empty sym: 1-by-0

assume(x(t),'positive')

assumptions

ans =

Here, adding an assumption on y(t), which I assume is treated as a symbolic expression by assume, does remove assumptions on x. i don't understand why that is the case.

assume(y(t),'integer'); % does change assumption on x?

assumptions

ans =

Paul 2024-4-4，17:26

编辑：Paul 2024-4-4，19:24

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I was wondering about exactly this, i.e., how y(t) is treated by assume(). I said "[y(t)] is treated as a symbolic expression", because I saw that symfun is not listed as an allowable input to assume, but y(t) is, or appears to be, an expression

syms y(t)
isSymType(y(t),'expression')
ans = logical
   1

This works

assume(y(t),'positive')

z(t) = 2*y(t);assumptions

ans =

isAlways(z(t)>0)

ans = logical

1

which suggests that y(t) is being treated as an expression.

But this throws an error

try
    assume(y,'real')
catch ME
    ME.message
end
ans = 'Assumptions on symbolic functions not supported. Make assumptions on symbolic variables and expressions instead.'

presumably because the class of y ( not y(t) ) is a symfun.

I suspect that your other observation about the interaction between the independent variable in the expression y(t) is really at the heart of this situation.

Based on the evidence, when the doc says: "assume removes any assumptions previously set on the symbolic variables."

perhaps it should say: "assume removes any assumptions previously set on the symbolic variables and removes assumptions previously set on any expressions that contain the symbolic variables"

Dyuman Joshi 2024-4-5，8:16

编辑：Dyuman Joshi 2024-4-5，8:17

在 MATLAB Online 中打开

Yes, the class of y is symfun and the class of y(t) is not symfun.

And yes, the statement should be more precise as you have stated.

syms y(t)

class(y)

ans = 'symfun'

class(y(t))

ans = 'sym'

try

assume(y(t),'real')

catch ME

ME.message

end

assumptions

ans =

try

assume(y,'real')

catch ME

ME.message

end

ans = 'Assumptions on symbolic functions not supported. Make assumptions on symbolic variables and expressions instead.'

y(t) = t^2;

%returns the function definition

y

y(t) =

%returns the expression

y(t)

ans =

Christian Luciano Maendle 2024-4-5，10:26

Thank you very much! This constructive discussion has made it very clear to me. Thank you for your help! :)

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