Expressions as Functions API

[ratnania]

Up to now, we were allowing expression (using the coordinates) to be passed directly in the weak formulation. We encountered two major problems with this approach

• sometimes an error is raised because we cannot check the linearity/bilinearity of a form.
• it may make the code very slow

This issue aims at allowing the definition of a Function, as a container, for two major uses;

• [ ] by providing its symbolic expression. example,

  F = Function((x,y), x**2+y**2)

  in which case, F will not appear as a free-variable, and its expression will be provided in TerminalExpr like in the valued Constant case.

• [ ] by providing its actual implementation, meaning, providing a Python code. In this case, the code must be pyccelized first to check that it can be used in our pipeline with psydac.

[yguclu]

Do we want a Function to be only scalar valued, or also vector and matrix valued?

[yguclu]

Given that we already have the classes ScalarFunction and VectorFunction, which must belong to a ScalarFunctionSpace or VectorFunctionSpace, I suggest that we use the name UserFunction for this class.

[ratnania]

I agree that we need to think about the API. We have different ways of doing it;

• Use ScalarFunction and VectorFunction and allow them to have an expression or implemented code,
• Rename ScalarFunction and VectorFunction to UndefinedScalarFunction and UndefinedVectorFunction, and use ScalarFunction and VectorFunction with expression/code, in addition to a new object MatrixFunction. The latter seems to be more appropriate, since the user (does not and) will not call UndefinedScalarFunction and UndefinedVectorFunction constructors, but use element_of.