Project: implement ZZ mod n in the engine for composite n

• Potential advisor/consultant(s): Mike Stillman
• Goal: Implement ZZ/n for composite n in the engine
• Current status: volunteers welcome!
• Skill level: beginner with some Macaulay2 experience, knowledge of C++ is necessary
• Mathematical experience: advanced undergraduate
• Reason(s) to participate: learn Macaulay2 internals, provide a faster implementation of ZZ/n to yourself and to other researchers

Project Description

Currently ZZ/n "works" only for prime n. Implementing ZZ/n for composite n in the engine would allow fast operations (e.g., linear algebra) over ZZ/n for arbitrary n. It would be simpler if this ring were a base ring. This requires changes in the c++ engine and also requires implementation of linear algebra over such rings.

This should possibly be implemented as two different engine rings: one for machine length integers, and one for larger integers.

Workaround

Currently one can create a quotient of a polynomial ring with no variables: ZZ[]/n. This "works", albeit slowly.