operations on simple sparse polynomial zonotopes

[lucaferranti]

This PR adds the operations on SSPZ described in Niklas presentation. Currently I added those into the same file of SSPZ, but maybe we want to move those in the corresponding files in concrete_operations?

TODO

• linear combination in future PR
• quadratic map in future PR
• convex hull in future PR
• tests

[schillic]

Looks good after moving the binary methods to the respective files 👍

[lucaferranti]

Looks good after moving the binary methods to the respective files 👍

among the functions implemented here, it seems only cartesian_product and minkowski_sum have a corresponding file in ConcreteOperations, should I create a new file for linear_map or leave it under SimpleSparsePolynomialZonotope.jl ?

[schillic]

linear_map is not binary and hence we keep it in the same file.

[lucaferranti]

moved the files. Out of curiosity, does LazySets rely on promotion mechanisms or how should it handles things like e.g.

minkowski_sum(::SimpleSparsePolynomialZonotope, ::Star)

[schillic]

moved the files. Out of curiosity, does LazySets rely on promotion mechanisms or how should it handles things like e.g.

minkowski_sum(::SimpleSparsePolynomialZonotope, ::Star)

That would require adding a specific method and is out of scope for now.

[lucaferranti]

btw currently the following fails

linear_map(I, S)

where S is SSPZ, the reason for this is that I is UniformScaling and it's not a subtype of AbstractMatrix, that's arguably a pretty boring linear map to apply. Is it worth to change the signature for that?

[schillic]

Is it worth to change the signature for that?

I do not think so.