Mike gave an overview of various parts of the engine (located in M2/Macaulay2/e/), through specific examples and files below.

Subsections:

• Class Hierarchy in the Engine
• Engine Unit tests
• Engine Documentation (Doxygen)

• debug.hpp: Useful for debugging without going into debugger. All objects have a buffer, and text_out() method. One can look up the types of top-level M2-objects which can be displayed this way, and then add print statements (using std::cout) in a source file, e.g. matrix.cpp, to debug methods.

  • For immutable objects (e.g. matrices/vectors), use copy_vec to create copies.

  • Need to add #include files, e.g. #include "debug.hpp", #include <iostream>

  • Project: change occurrences of buffer in debug.hpp to C++ o-streams.

• Various types of objects: Ring, ARing types, ring_elem (a union struct, not as safe, involves virtual function calls, has explicit constructors), RingElement (raw ring element class)

• aring-zz-gmp.hpp: wrapper around gmp

  • mpz: init, clear, set methods
  • Not using C++ interface due to memory allocation/performance issues.
  • elem_text_out: display ring elements

• aring-gf-flint.hpp: similar interface as above, for flint

• mat.hpp

  • MutableMatrix class: abstract class
  • Operations: row/column operations, add/subtract matrices, eigenvalues, SVD, LU, det

• mutablemat-defs.hpp

  • DMat: Dense matrix, takes RT (ring type)

• MutableMatrix : front end object, abstract class

  • MutableMat<MT> : concrete realization

• RT : ARings.

• DMat<RT>

• SMat<RT>

• ConcreteRing type: only has one piece of data, wrapper to allow virtual function calls.

Currently: RT is carried through all types (to work with various interfaces, e.g. flint, LAPACK)

Project: consistent naming system (MutableMatrix and MutableMat vs Ring and ConcreteRing. Proposed fix: MutableMatrix -> M2MutableMatrix, MutableMat -> MutableMatrix.)

Automates creation of code in D language (e.g. for use in interface.dd)

• comp.hpp: Computation class (start, stop conditions). Two types: GBComputation and ResolutionComputation.

• GBComputation (get_gb(), get_mingens(), etc.). If cannot cast to polynomial ring, determine if ring is ZZ (-> Hermite form) or a field (-> Gaussian elimination), else error "GB computation for non-polynomial rings not yet re-implemented". Switch cases for different strategies: default is gbA (binomialGB_comp is defunct). Finally, intern's the result for display.

• ResolutionComputation (betti_init(), betti_display(), etc.). Again cast to polynomial ring, and further checks if Heft vectors are positive, and if the module is homogeneous. Similarly, switch cases: comp(), res_comp, gbres_comp, or fast non-minimal resolution. Betti table display handled in betti.hpp.

• F4 algorithm: associated files in f4 directory.