Internals: Class Hierarchy in the Engine

Work in progress. Contributors: Michael Burr, Anton Leykin, (your-name-here)

Rings

In order to see some of the inheritance of types, run showStructure in M2. There may be further inheritance that is not shown. Running this after typing debug Core (exposed Core unexported symbols) will give additional structure information. To find out information about a specific ring, run <Ring name>.RawRing within debug Core.

Within the d-language, RawRing is a pointer to the struct of a ring. Within the code, sometimes RawRingOrNull is used, often for debugging purposes. RawRingOrNull allows for a null pointer for a nonexistent ring. Since exceptions can't be used between C and C++, this gives a way for error handling. For example, the function toExpr(x:RawRing):Expr produces a ring while toExper(x:RawRingOrNull):Expr produces a ring or an error message. To find the toExpr options, see util.d.

For the C/C++ code, the file e/x-relem.cpp contains Ring Elements and Rings. The file e/ring.hpp has the class for Ring. Here, Rings are mutable engine objects. The way this has been coded, when converting between ring types, a cast must be used, so if a new ring type is added, the conversion has to be added to the Ring class directly.

Linear algebra in the M2 engine

The following are the notes used by Mike Stillman in the M2internals workshop on 3 Feb 2022.

mat.hpp
  MutableMatrix: abstract.
    rank, eigenvalues: member functions.
    
mutablemat-defs.hpp
  MutableMat<MT> : MutableMatrix    
  MT is "MatrixType"
    DMat<RT>  
      DMat<ARingZZpFlint>
      DMat<ARingGFFlint> ... all are managed matrices via flint.
    SMat<RT>
  RT is "RingType" "ARing's": ZZ, QQ, ZZ/p, GF, RR, CC
    ARingZZpFlint
    ARingZZpFFPACK (internal only)
    ARingGFFlint
    ARingGFFlintBig
    ARingZZ (GMP and soon: Flint)
    ARingQQ (GMP and soon: Flint)
    ARingRR
    ARingCC
    ARingRRR
    ARingCCC
    (ARingRRi)

mutablemat-imp.hpp
  MatrixOps::rank(mat)
  MatrixOps::eigenvalues(mat, ...)    

mat-linalg.hpp
  has the MatrixOps namespace

  rank: DMatLinAlg<RT> for doing LU decompositions 
  LUdecomp.rank()
  
  eigenvalues:
  Lapack::eigenvalues(&A, &eigenvals); (lapack.hpp, lapack.cpp)