Matrix representations over finite fields

http://www.math.rwth-aachen.de/~MTX/

The MeatAxe is a set of programs for working with matrix representations

over finite fields. Permutation representations are supported to some

extent, too.

cfcomp

After Module has been chopped, you can use this program to determine if a given irreducible module, Irred, is a constituent of Module. If yes, the program finds...

After Module has been chopped, you can use this program to determine if a given irreducible module, Irred, is a constituent of Module. If yes, the program finds...

checksum

Compute the CRC of file. The result is stored in result, if given, else it is printed on stdout.

Compute the CRC of file. The result is stored in result, if given, else it is printed on stdout.

chop

This program calculates the irreducible constituents of a given matrix representation. The representing matrices of the generators are read from input files...

This program calculates the irreducible constituents of a given matrix representation. The representing matrices of the generators are read from input files...

decomp

This program decomposes a module Module into its direct summands, using the head of the endomorphism ring, Endo. It assumes that the endomorphism ring and its...

This program decomposes a module Module into its direct summands, using the head of the endomorphism ring, Endo. It assumes that the endomorphism ring and its...

genmod

This program makes a submodule, i.e., it takes the mountains contained in that submodule and spins them up. The result is written to Name.sNumber. The program...

This program makes a submodule, i.e., it takes the mountains contained in that submodule and spins them up. The result is written to Name.sNumber. The program...

mkcycl

This program is invoked after pwkond(1) has calculated the condensation with respect to the peak words. Mkcycl calculates, for each condensed module, its...

This program is invoked after pwkond(1) has calculated the condensation with respect to the peak words. Mkcycl calculates, for each condensed module, its...

mkdotl

This program calculates a set of dotted lines between the local submodules. More precisely, it computes one dotted line for each submodule with head isomorphic...

This program calculates a set of dotted lines between the local submodules. More precisely, it computes one dotted line for each submodule with head isomorphic...

mkgraph

This program creates a graphical representation of a submodule lattice in PostScript or other formats. The first argument must be the module name. The mksub(1)...

This program creates a graphical representation of a submodule lattice in PostScript or other formats. The first argument must be the module name. The mksub(1)...

mkhom

This program calculates a basis for the vector space of homomorphisms between two kG-modules, Hom_kG(M,N). In the case M=N the program optionally finds a...

This program calculates a basis for the vector space of homomorphisms between two kG-modules, Hom_kG(M,N). In the case M=N the program optionally finds a...

mkhom_old

This program calculates a basis for the vector space of homomorphisms between two kG-modules, Hom_kG(M,N). In the case M=N the program optionally finds a...

This program calculates a basis for the vector space of homomorphisms between two kG-modules, Hom_kG(M,N). In the case M=N the program optionally finds a...

mkinc

This program runs in two steps. During the first step, all cyclic submodules found by mkcycl(1) are uncondensed, giving the local submodules, the "mountains"...

This program runs in two steps. During the first step, all cyclic submodules found by mkcycl(1) are uncondensed, giving the local submodules, the "mountains"...

mksub

This program calculates the submodule lattice using the output generated by mkinc(1) and mkdotl(1). In this final step no matrix operations are involved...

This program calculates the submodule lattice using the output generated by mkinc(1) and mkdotl(1). In this final step no matrix operations are involved...

mktree

This program enumerates all elements of a finitely generated matrix group. By default, the program assumes that the group has two generators, which are read...

This program enumerates all elements of a finitely generated matrix group. By default, the program assumes that the group has two generators, which are read...

orbrep

Given a set of generating permutations, this program find a product of the generators which maps a given point, Seed, to a second given point, Stop. By default...

Given a set of generating permutations, this program find a product of the generators which maps a given point, Seed, to a second given point, Stop. By default...

pseudochop

This program can be used to produce the chop output for a given module without actually doing all the work. To do so, there must be another module (the...

This program can be used to produce the chop output for a given module without actually doing all the work. To do so, there must be another module (the...

rad

This program calculates the radical series of an arbitrary module Name, or the homomorphisms from the projective modules corresponding to the composition...

This program calculates the radical series of an arbitrary module Name, or the homomorphisms from the projective modules corresponding to the composition...

soc

This program determines the Loewy structure of a module by calculating the socles. Before using the program, you must run chop(1) and pwkond(1) with the -t...

This program determines the Loewy structure of a module by calculating the socles. Before using the program, you must run chop(1) and pwkond(1) with the -t...

symnew

Compute the symmetrized tensor product, where <Mode> is the symmetrization mode, one of e2, e3, e4, s2, or m3. The input matrix is in <Inp> and the output...

Compute the symmetrized tensor product, where <Mode> is the symmetrization mode, one of e2, e3, e4, s2, or m3. The input matrix is in <Inp> and the output...

tcond

This program performs the final steps of the tensor condensation procedure. It calculates, for one or more elements a_1, a_2, ... , the action of e_H·a_i·e_H on...

This program performs the final steps of the tensor condensation procedure. It calculates, for one or more elements a_1, a_2, ... , the action of e_H·a_i·e_H on...

tuc

This program is part of the tensor condensation package. It is used to uncondense one or more vectors, i.e., it calculates the embedding of (M⊗N)e_H into (M⊗N)...

This program is part of the tensor condensation package. It is used to uncondense one or more vectors, i.e., it calculates the embedding of (M⊗N)e_H into (M⊗N)...

zad

This program reads two or more input matrices, calculates their sum or difference and writes the result to a file. The input matrices must be compatible, i.e...

This program reads two or more input matrices, calculates their sum or difference and writes the result to a file. The input matrices must be compatible, i.e...

zbl

This program reads in <Matrix>, zeroizes all entries above the main diagonal, and writes out the result.

This program reads in <Matrix>, zeroizes all entries above the main diagonal, and writes out the result.

zcl

This program "cleans" Mat with Subsp, i.e., it adds suitable linear combinations of rows of Subsp to each row of Mat such that all pivot columns in the result...

This program "cleans" Mat with Subsp, i.e., it adds suitable linear combinations of rows of Subsp to each row of Mat such that all pivot columns in the result...

zcp

This program reads in a square matrix and calculates its characteristic or minimal polynomial. With no options, the characteristic polynomial is computed in a...

This program reads in a square matrix and calculates its characteristic or minimal polynomial. With no options, the characteristic polynomial is computed in a...

zct

This program cuts a piece, specified by Rows and Columns, out of the file Input, and writes the piece to Output. The input may be a matrix or a set of...

This program cuts a piece, specified by Rows and Columns, out of the file Input, and writes the piece to Output. The input may be a matrix or a set of...

zcv

This program converts a text file into binary format. If the input file name is "-", input is read from stdin.Text File Format The text file is interpreted line...

This program converts a text file into binary format. If the input file name is "-", input is read from stdin.Text File Format The text file is interpreted line...

zef

This program reads in a matrix, performs a Gaussian elimination to put the matrix into semi-echelon form, and writes out the result. A matrix is in semi-echelon...

This program reads in a matrix, performs a Gaussian elimination to put the matrix into semi-echelon form, and writes out the result. A matrix is in semi-echelon...

zev

This program reads a matrix from Matrix and a list of polynomials from Poly (or from the standard input). For each input polynomial, it evaluates that function...

This program reads a matrix from Matrix and a list of polynomials from Poly (or from the standard input). For each input polynomial, it evaluates that function...

zfr

This program reads a matrix, applies the Frobenius automorphism x|->x^p, where p is the characteristic of the field, to each entry and writes out the result.

This program reads a matrix, applies the Frobenius automorphism x|->x^p, where p is the characteristic of the field, to each entry and writes out the result.

zkd

This program reads an orbit file (Orbits) and a permutation from Perm. It outputs the condensed form, i.e., a matrix over GF(q) to Kond. The field must be...

This program reads an orbit file (Orbits) and a permutation from Perm. It outputs the condensed form, i.e., a matrix over GF(q) to Kond. The field must be...

zmo

This program calculates the orbits under a set of permutations. By default, the program works with two permutations which are read from Perm.1 and Perm.2. Using...

This program calculates the orbits under a set of permutations. By default, the program works with two permutations which are read from Perm.1 and Perm.2. Using...

zmu

This program reads two matrices or permutations and writes their product to Result. The input files must contain two compatible objects, i.e., their product...

This program reads two matrices or permutations and writes their product to Result. The input files must contain two compatible objects, i.e., their product...

zmw

Zmw calculates an element of the algebra generated by a set of matrices. The word must be specified by its "word number". The first form of the zmw command...

Zmw calculates an element of the algebra generated by a set of matrices. The word must be specified by its "word number". The first form of the zmw command...

znu

This program reads in a matrix and outputs a basis for its null-space in echelon form. If the Nullspace argument is omitted the null-space is not written out...

This program reads in a matrix and outputs a basis for its null-space in echelon form. If the Nullspace argument is omitted the null-space is not written out...

zor

This program reads a file, containing either permutations, or a square matrix, and calculates the order(s) and prints the message:ORDER IS xxxx There are two...

This program reads a file, containing either permutations, or a square matrix, and calculates the order(s) and prints the message:ORDER IS xxxx There are two...

zpo

This program calculates the Nth power of a matrix or permutation. The exponent N may be negative. For compatibility with the old zsm program, the power may be...

This program calculates the Nth power of a matrix or permutation. The exponent N may be negative. For compatibility with the old zsm program, the power may be...

zpr

This program prints the contents of a MeatAxe data file in readable format. The text produced by zpr can be converted into binary format by the zcv(1) program...

This program prints the contents of a MeatAxe data file in readable format. The text produced by zpr can be converted into binary format by the zcv(1) program...

zpt

This program reads matrices from one or more input files and pastes the pieces together to one matrix. The way in which the pieces are put together is...

This program reads matrices from one or more input files and pastes the pieces together to one matrix. The way in which the pieces are put together is...

zqt

This program reads in a subspace and applies the canonical map to its quotient on a matrix. The result is written out to Quot. Subsp should be a matrix in...

This program reads in a subspace and applies the canonical map to its quotient on a matrix. The result is written out to Quot. Subsp should be a matrix in...

zro

This program calculates the order of Count random elements of the group generated by a set of matrices or permutations. This information can be helpful to find...

This program calculates the order of Count random elements of the group generated by a set of matrices or permutations. This information can be helpful to find...

zsc

This program reads in two or more matrices (generators), a list of seed vectors and a list of operations (the script). Then, zsc applies the script to each seed...

This program reads in two or more matrices (generators), a list of seed vectors and a list of operations (the script). Then, zsc applies the script to each seed...

zsi

This program reads in two spaces from Space1 and Space2 and writes out their sum and intersection, in semi-echelon form, to Sum and Int, respectively. The input...

This program reads in two spaces from Space1 and Space2 and writes out their sum and intersection, in semi-echelon form, to Sum and Int, respectively. The input...

zsp

This program takes as input a set of matrices or permutations (the "generators"), and a list of seed vectors. It uses the spin-up algorithm to find a subspace...

This program takes as input a set of matrices or permutations (the "generators"), and a list of seed vectors. It uses the spin-up algorithm to find a subspace...

zsy

This program reads a matrix or permutation, calculates its symmetrized tensor product according to Mode, and writes out the result. The Mode argument specifies...

This program reads a matrix or permutation, calculates its symmetrized tensor product according to Mode, and writes out the result. The Mode argument specifies...

ztc

This program reads a matrix or permutation, calculates its trace, and outputs this to the user. If the input file is a matrix, it is read row by row and the...

This program reads a matrix or permutation, calculates its trace, and outputs this to the user. If the input file is a matrix, it is read row by row and the...

zte

This program reads in two matrices or permutations and writes out their tensor (Kronecker) product. If A is an mxn matrix, and B is an m'xn' matrix, the result...

This program reads in two matrices or permutations and writes out their tensor (Kronecker) product. If A is an mxn matrix, and B is an m'xn' matrix, the result...

zts

This program is similar to zsp, but it works on the tensor product of two modules, M⊗N. Zts spins up one or more vectors, and optionally calculates a matrix...

This program is similar to zsp, but it works on the tensor product of two modules, M⊗N. Zts spins up one or more vectors, and optionally calculates a matrix...

zuk

This program reads a matrix which is assumed to be a condensed space of a permutation representation whose orbits are in the file Orbits. The vectors in Vectors...

This program reads a matrix which is assumed to be a condensed space of a permutation representation whose orbits are in the file Orbits. The vectors in Vectors...

zvp

This program reads a set of matrices and one or more vectors from Seed, and finds the orbit of the vector under the matrices. The action of the matrices on the...

This program reads a set of matrices and one or more vectors from Seed, and finds the orbit of the vector under the matrices. The action of the matrices on the...