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Science/Mathematics
- a metapackage for GAP documentation
This package contains a definition of a structure for GAP (package)
documentation, based on XML. It also contains conversion programs for
producing text-, PDF- or HTML-versions of such documents, with hyperlinks if
possible.
Formats: [html] [pdf]
- A Tour of NTL
(package: libntl-dev)
- Information about using the Number Theory Library
- A Tutorial for PARI/GP
- This booklet is intended to be a guided tour and a tutorial to the GP
calculator.
Formats: [dvi] [pdf]
- Algebraic number theory and an interface to PARI/GP
The Alnuth package provides various methods to compute with number fields
which are given by a defining polynomial or by generators. Some of the
methods provided in this package are written in GAP code. The other part of
the methods is imported from the computer algebra system PARI/GP. Hence this
package contains some GAP functions and an interface to some functions in the
computer algebra system PARI/GP. The main methods included in Alnuth are:
creating a number field, computing its maximal order (using PARI/GP),
computing its unit group (using PARI/GP) and a presentation of this unit
group, computing the elements of a given norm of the number field (using
PARI/GP), determining a presentation for a finitely generated multiplicative
subgroup (using PARI/GP), and factoring polynomials defined over number
fields (using PARI/GP).
Formats: [html] [pdf]
- An Atlas of Group Representations
The package provides a GAP interface to the Atlas_of_Group_Representations
Formats: [html] [pdf]
- An introduction to GP2C
- This manual describes how to use the GP2C compiler to
run your GP scripts faster.
Formats: [html] [dvi]
- Asymptote User Manual
(package: asymptote-doc)
- This document describes the Asymptote system and programming language.
Formats: [html] [pdf]
- cddlib Reference Manual
- This is a reference manual for cddlib-094. The manual describes the library
functions and data types implemented in the cddlib C-library which is to perform
fundamental polyhedral computations such as representation conversions and linear
programming in both floating-point and GMP rational exact arithmetic. Please read
the accompanying README file and test programs to complement the manual.
The new functions added in this version include dd MatrixCanonicalize to find a non-
redundant proper H- or V-representation, dd FindRelativeInterior to find a relative
interior point of an H-polyhedron, and dd ExistsRestrictedFace (Farkas-type
alternative theorem verifier) to check the existence of a point satisfying a
specified system of linear inequalities possibly including multiple strict
inequalities.
The new functions are particularly important for the development of related software
packages MinkSum (by Ch. Weibel) and Gfan (by Anders Jensen).
- Computation with polycyclic groups
This package provides various algorithms for computations with polycyclic
groups defined by polycyclic presentations.
Formats: [html] [pdf]
- Computing the Automorphism Group of a p-Group
The AutPGrp package introduces a new function to compute the automorphism
group of a finite p-group. The underlying algorithm is a refinement of the
methods described in O'Brien (1995). In particular, this implementation is
more efficient in both time and space requirements and hence has a wider
range of applications than the ANUPQ method. Our package is written in GAP
code and it makes use of a number of methods from the GAP library such as the
MeatAxe for matrix groups and permutation group functions. We have compared
our method to the others available in GAP. Our package usually out-performs
all but the method designed for finite abelian groups. We note that our
method uses the small groups library in certain cases and hence our algorithm
is more effective if the small groups library is installed.
Formats: [html] [pdf]
- Debian Maxima Manual
- This manual documents the maxima computer algebra system.
- Debian Maxima Manual
(package: maxima-doc)
- This manual documents the maxima computer algebra system.
- example help book for GAPDoc
This document tries to use all elements that exist in GAPDoc. In addition,
the final output not only contains the usual content, but also an appendix
with the source text. There are also links from the usual content to the
corresponding source text. This should enable new users to learn GAPDoc
quickly.
Formats: [html] [pdf]
- FactInt: Advanced Methods for Factoring Integers
This package for GAP provides a general-purpose integer factorization
routine, which makes use of a combination of factoring methods.
In particular it contains implementations of the following algorithms:
- Pollard's p-1
- Williams' p+1
- Elliptic Curves Method (ECM)
- Continued Fraction Algorithm (CFRAC)
- Multiple Polynomial Quadratic Sieve (MPQS)
It also contains code by Frank Lübeck for making use of Richard P. Brent's
tables of factors of integers of the form b^k ± 1. FactInt is completely
written in the GAP language and contains / requires no external binaries.
Formats: [html] [text] [pdf]
- fpLLL: a library for LLL-reduction of Euclidean lattices
- This document describes fpLLL, describing both the tools and the library
- Free Group Algorithms
The FGA package installs methods for computations with finitely generated
subgroups of free groups and provides a presentation for their automorphism
groups.
Formats: [html] [pdf]
- GAP Primitive Permutation Groups Library
The PrimGrp package provides the library of primitive permutation groups
which includes, up to permutation isomorphism (i.e., up to conjugacy in the
corresponding symmetric group), all primitive permutation groups of degree <
4096.
Formats: [html] [pdf]
- GAP reference manual
- This manual contains the official definitions of GAP functions. It
should give all information to someone who wants to use GAP as it is. It is not
intended to be read cover-to-cover.
- Gfan version 0.6: A User’s Manual
- Gfan is a software package for computing Gröbner fans and tropical
varieties. These are polyhedral fans associated to polynomial ideals. The
maximal cones of a Gröbner fan are in bijection with the marked reduced
Gröbner bases of its defining ideal. The software computes all marked
reduced Gröbner bases of an ideal. Their union is a universal Gröbner
basis. The tropical variety of a polynomial ideal is a certain subcomplex
of the Gröbner fan. Gfan contains algorithms for computing this complex
for general ideals and specialized algorithms for tropical curves, tropical
hypersurfaces and tropical varieties of prime ideals. In addition to the
above core functions the package contains many tools which are useful in
the study of Gröbner bases, initial ideals and tropical geometry. The full
list of commands can be found in Appendix B. For ordinary Gröbner basis
computations Gfan is not competitive in speed compared to programs such
as CoCoA, Singular and Macaulay2.
- Gmsh Reference Manual
(package: gmsh-doc)
- This is the reference manual for gmsh.
Formats: [html] [pdf]
- GP2C types and the description system.
- The main feature GP2C adds above GP is the use of types. Types give a
semantic to PARI objects, so that GP2C can generate code that use specialized
(hence faster) PARI functions instead of generic ones.
Formats: [html] [dvi]
- IO: Bindings for low level C library I/O routines
The purpose of this package is to allow efficient and flexible
Input/Output operations from GAP. This is achieved by providing
bindings to the low-level I/O functions in the C-library.
On top of this an implementation of buffered I/O in the GAP language
is provided. Further, a framework for serialisation of arbitrary GAP
objects is implemented. Finally, an implementation of the client side
of the HTTP protocol is included in the package. This package allows one
to use file based I/O, access to links and file systems, pipes, sockets,
and the UDP and TCP/IP protocols.
- LAGUNA: Lie AlGebras and UNits of group Algebras
“LAGUNA” stands for “Lie AlGebras and UNits of group Algebras”. LAGUNA extends
the GAP functionality for computations in group rings. Besides computing some
general properties and attributes of group rings and their elements, LAGUNA is
able to perform two main kinds of computations. Namely, it can verify whether
a group algebra of a finite group satisfies certain Lie properties; and it can
calculate the structure of the normalized unit group of a group algebra of a
finite p-group over the field of p elements.
Formats: [html] [text] [pdf]
- PARI/GP Reference Card
- This is a four-pages reference card of the GP functions.
Formats: [dvi] [pdf]
- PSPP
(package: pspp)
- PSPP is a tool for statistical analysis of sampled data.
It reads a syntax file and a data file, analyzes the data, and writes
the results to a listing file, standard output or various other output formats.
The language accepted by PSPP is similar to those accepted by SPSS
statistical products. The details of PSPP's language are given
in this manual.
Besides the command line tools it also features a GTK+ based GUI named psppire,
that is user friendly and also provides an integrated help system.
Formats: [html] [pdf]
- SageMath Manual
- This is the manual for SageMath.
- The GAP Character Table Library
- There are three different kinds of character tables in the GAP
library, namely ordinary character tables, Brauer tables, and generic
character tables. Note that the Brauer table and the corresponding
ordinary table of a group determine the decomposition matrix of the
group (or the decomposition matrices of its blocks). These
decomposition matrices can be computed with GAP (see Operations
Concerning Blocks in the GAP Reference Manual for details).
Formats: [html] [pdf]
- The GAP Library of Tables of Marks
The concept of a Table of Marks was introduced by W.Burnside in his book
"Theory of Groups of Finite Order". Therefore a table of marks is
sometimes called a Burnside matrix. The table of marks of a finite group G
is a matrix whose rows and columns are labelled by the conjugacy classes of
subgroups of G and where for two subgroups H and K the (H, K)-entry is the
number of fixed points of K in the transitive action of G on the cosets of H
in G. So the table of marks characterizes the set of all permutation
representations of G. Moreover, the table of marks gives a compact
description of the subgroup lattice of G, since from the numbers of fixed
points the numbers of conjugates of a subgroup K contained in a subgroup H
can be derived. For small groups the table of marks of G can be constructed
directly in GAP by first computing the entire subgroup lattice of G.
However, for larger groups this method is unfeasible. The GAP Table of Marks
library provides access to several hundred table of marks and their maximal
subgroups.
Formats: [html] [pdf]
- The GAP Small Groups Library
The SmallGrp package provides the library of groups of certain "small"
orders. The groups are sorted by their orders and they are listed up to
isomorphism; that is, for each of the available orders a complete and
irredundant list of isomorphism type representatives of groups is given.
Formats: [html] [pdf]
- The GAP Tutorial
- This manual contains a tutorial introduction to GAP.
- The GNU BC arbitrary precision calculator
(package: bc)
- bc is a language that supports arbitrary precision numbers
with interactive execution of statements. There are some similarities
in the syntax to the C programming language. A standard math library is
available by command line option. If requested, the math library is
defined before processing any files. bc starts by processing code from
all the files listed on the command line in the order listed. After all
files have been processed, bc reads from the standard input. All code
is executed as it is read. (If a file contains a command to halt the
processor, bc will never read from the standard input.)
- The GNU DC arbitrary precision calculator
(package: dc)
- GNU dc is a reverse-polish desk calculator which supports unlimited
precision arithmetic. It also allows you to define and call macros.
Normally DC reads from the standard input; if any command arguments are
given to it, they are filenames, and DC reads and executes the contents
of the files instead of reading from standard input. All normal output
is to standard output; all error messages are written to standard error.
- The GNU GSL Reference Manual in html format
(package: gsl-ref-html)
- The GNU Scientific Library (GSL) is a collection of routines for
numerical computing. The routines have been written from scratch in C, and
present a modern Applications Programming Interface (API) for C
programmers, allowing wrappers to be written for very high level languages.
The source code is distributed under the GNU General Public License.
- The GNU Octave Library
(package: octave-doc)
- This document describes the Octave libraries. Octave is a
(mostly MATLAB® compatible) high-level language, primarily intended
for numerical computations. It provides a convenient command-line
interface for solving linear and nonlinear problems numerically.
Formats: [html] [info] [pdf]
- The GNU Octave Manual
(package: octave-doc)
- Octave is a (mostly MATLAB® compatible) high-level
language, primarily intended for numerical computations. It provides
a convenient command-line interface for solving linear and nonlinear
problems numerically.
Formats: [html] [info] [pdf]
- The GNU Octave Reference Card
(package: octave-doc)
- Octave is a (mostly MATLAB® compatible) high-level
language, primarily intended for numerical computations. It provides
a convenient command-line interface for solving linear and nonlinear
problems numerically.
- Transitive Groups Library
The TransGrp package provides the library of transitive groups.
Formats: [html] [pdf]
- User's Guide to PARI/GP
- This manual describe the interface to the PARI library and the GP
calculator.
Formats: [dvi] [pdf]
- User's Guide to the PARI library
- The first part of this book introduces the general concepts of PARI
programming and describe useful general purpose functions. The second
part describes all available public low-level functions.
Formats: [dvi] [pdf]
- Utility functions in GAP
The Utils package provides a collection of utility functions gleaned from
many packages.
Formats: [html] [pdf]
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