Using solve command for unknown vectors

Hello, I believe the problem I have is rather simple but I am new to MATLAB and I did not manage to find a solution. I think the situation can be described with the following simple example:

If I want to find the vectors whose Euclidean norm is 4, I would write :

V = sym('V', [3, 1], 'real')
solve(sqrt(dot(V, V)) == sym(4), V, 'real', true)

But I get weird results where V1 is 4 or -4 and V2 = V3 = 0... In the real problem I have, the only result I get is "unable to find a solution", and I thought there might be a link with this, as I am trying to solve a system depending on three vectors, and that it quite obviously doesn't work as I would expect...

Thank you for your help.

Regards,

Sacha Levy

[Torsten]

You have one equation and three unknowns - thus there are infinitely many solutions (given by the sphere around 0 with radius 4).

Best wishes

Torsten.

Answer 1

[Walter Roberson]

See https://www.mathworks.com/matlabcentral/answers/356969-solving-absolute-value-inequality about cases in which solve returns a definite number when the solution is multiple numbers.

See https://www.mathworks.com/matlabcentral/answers/318722-please-let-me-have-a-help-with-the-solve-command for a problem that can show up when solving for multiple variables and expecting a struct of solutions to be returned. I did not test to see if they have resolved that one yet.

Answer 2

[Sacha Levy]

Hello, I know there are inifinitely many solutions... The problem is: why does solve only return one random solution? I would expect to give the whole set of solutions... So I there is something I should or shouldn't do to get it to work the way I expect... At some point I had a closer result to what I expect, but I had been trying for a while and written in a form that was not convenient at all. Could you please tell me what should I do to normally solve this kind of problem?

Thanks for you help

Sacha Levy

Answer 3

[Sacha Levy]

So it seems like in the situation I described, the problem simply comes from the fact 'ReturnConditions' must be set to true...

Thank you!