ToDo list

[HechtiDerLachs]

• implement the plausibility checks in the several constructors of the different structs.

• Reimplement printing with short and verbose printing depending on the io context.

• Implement a constructor for affine Schemes with an explicit list of variable names as argument.

• Check and eventually correct the following: The inner constructors do not have type parameters, yet. Do we need that?

• Make the Scheme Morphism struct extend the Map type from AA

• implement reduced( X::Scheme ) to pass from a given scheme to a reduced scheme. This should also return the associated projection.

• implement the primary decomposition of a given scheme together with its various inclusions.

• Implement the smoothness test

• Implement and debug the methods for the morphisms of affine schemes (translation from ring homomorphism to fractional representation and back).

• Implement glueings and CoveredScheme

[simonbrandhorst]

More to dos

• make the tests pass.
• do not force the construction of the ambient_ring of the parent when constructing the ambient_ring of a child.
• coordinate rings of affine schemes
• systematically write more tests until we have 100% coverage