# matlab - MuPAD: How to determine just the existence of solutions to a set of linear inequalities?

Using MuPAD, I want to find out if *at least one solution* exists for a set of of linear inequalities. For example, the following system of linear inequalities:

which I solve in MuPAD by:

```
solve({x+z>2*y,z>y,2*z>2*x,x>0,y>0,z>0},{x,y,z}
```

and MuPAD returns the set of solutions, in some type of notation:

However, I do not care about the exact form of the solution set, i.e., whether it is finite, or infinite, I just care if there is at least one viable solution.

I would like to call MuPAD from Matlab, ask if a solution set exists to the inequalities, and then get back a "yes" or "no" answer. I could test for the empty set being returned, but I do not know how to test if a symbolic variable represents the empty set.

## Alan-

2019-11-13

Here's an example using MuPAD's

`solve`

and`sym/isempty`

called from Matlab:The first case returns true,

`1`

, indicating that there is at least one solution. The second returns false,`0`

, as there is no solution.If you want to do this within MuPAD, you can use the

`is`

function:However, the first case will return

`UNKNOWN`

, which is rather difficult to deal with. You may want to use something like the following instead:which assumes that only an empty solution, Ø, will have a

`length`

of one. (The MuPAD code is two characters,`{}`

, but it displays as one, Ø, has a length of one, and means empty/zero.) There are probably other ways.