Welcome to mmgroup’s documentation!
- The mmgroup API reference
- Introduction
- Installation and test
- Basic structures
- The Monster group
- Generators of the monster group \(\mathbb{M}\)
- Representing elements of the monster group
- Implementation of the generators of the monster group
- Multiplication of elements of the monster group
- Python classes implementing the Monster group
- Functions dealing with elements of the Monster group
- Generating random elements of certain subgroups of the Monster
- The representation of the Monster group
- Creating basis vectors of the representation space \(\rho_p\)
- Description of the basis vectors of the representation space
- Representing a vector as a list of tuples
- Operations on vector in the representation \(\rho_p\)
- Special tags for creating vectors in the representation \(\rho_p\)
- Linear order of the basis vectors
- Sparse representation of vectors in \(\rho_p\)
- Other data types accepted as tags for vectors in \(\rho_p\)
- Python classes implementing the representation of the Monster group
- Auxiliary functions for the representation of the Monster group
- The subgroup \(G_{x0}\) of the Monster and the Clifford group
- The Coxeter group \(Y_{555}\) and the Bimonster
- Version history
- The mmgroup guide for developers
- Introduction
- Directory structure
- Some mathematical aspects of the implementation
- Implementing Automorphisms of the Parker loop
- Implementing generators of the Monster group
- Computations in the Leech lattice modulo 2
- Orbits of the group \(N_{x0}\) in the group \(Q_{x0}\)
- Checking equality of monster elements and membership in \(2^{1+24}.\mbox{Co}_1\)
- Subgroups of the Mathieu group \(M_{24}\)
- Installation from a source distribution
- The build process
- Code generation
- Description of some typical bugs
- The C interface of the mmgroup project
- Introduction
- Description of the
mmgroup.mat24
extension- The Golay code
C
and its cocodeC*
- The Mathieu group Mat24
- Operation of the group
Mat24
on vectors - Group operation in the group
Mat24
- The Parker loop
Pl
- The group
AutPl
of standard automorphisms of the Parker loop - Auxiliary functions
- Internal operation
- Abbreviations for functions and parameters in this class
- Conventions for parameters in C functions
- Mapping C functions to python functions
- C interface
- Generating C code for the
mmgroup.mat24
extension
- The Golay code
- Description of the
mmgroup.generators
extension- The Leech lattice and the extraspecial group \(Q_{x0}\)
- Leech lattice encoding of the elements of \(Q_{x0}\)
- Special elements of the group \(Q_{x0}\)
- Computations in the Leech lattice modulo 3
- Header file mmgroup_generators.h
- C functions implementing the group \(N_{0}\)
- C functions for the operation of \(G_{x0}\) on the Leech lattice
- C functions for the generator \(\xi\) of the monster group
- C functions implementing a random generator
- Description of the
mmgroup.clifford12
extension- Quadratic state vectors
- Header file
clifford12.h
- C functions in
bitmatrix64.c
- C functions in
uint_sort.c
- C functions in
qstate12.c
- C functions in
qstate12io.c
- C functions in
qmatrix12.c
- Computing in the subgroup \(G_{x0}\) of the Monster
- C functions in
xsp2co1.c
- C functions in
xsp2co1_word.c
- C functions in
xsp2co1_elem.c
- C functions in
leech3matrix.c
- C functions in
involutions.c
- C functions in
xsp2co1_traces.c
- C functions in
xsp2co1_map.c
- Description of the
mmgroup.mm_op
extension- Representation of a vector in \(\rho_p\)
- Header file mm_basics.h
- Header file mm_op_p.h
- C interface for file mm_index.c
- C interface for file mm_aux.c
- C interface for file mm_tables.c
- C interface for file mm_op_p_vector.c
- C interface for file mm_op_p_axis.c
- Internal operation
- Basic table-providing classes for module
mmgroup.mm_op
- Deprecated stuff
- Description of the
mmgroup.mm_reduce
extension - Shared libraries and dependencies between Cython extensions
- Applications of the mmgroup package
- Demonstration code for the reduction algorithm