[Next] [Prev] [Right] [Left] [Up] [Index] [Root] 
Release Notes V2.01-1 (21 June 1996)


Release Notes V2.01-1 (21 June 1996)




Magma V2.01-1 (21 June 1996)


Here is a terse summary of the new features installed 
in Magma for version V2.01 since March 5, 1996.  See the release notes
for version V1.30 for all new features introduced into Magma in 1995.


Version V2.01 of Magma features the full release of packages (V1.3 contained
a Beta release of packages), and the new I/O and system facilities.
Version V2.01 also features automatic printing of expressions.








Documentation





  • 
Handbook: Extensive changes and additions

  • 
An Introduction to Magma: extensive revision/updating of the language
and environment chapters; minor revision/updating of most of the
category chapters

  • 
Solving Problems with Magma: reorganization of the chapters; several
additional examples added; several minor amendments and improvements

  • 
First Steps in Magma: documentation that "print" is now optional;
minor revisions

    

    

    
Language and System Features

    

    

  • 
Full release of Packages (see release notes of V1.30-1 for details)

  • 
Automatic printing of expressions without the need of the 'print' statement

  • 
'printf' statment for formatted printing, and Sprint function for
obtaining output as a string

  • 
Automatic loading of multiple files at startup

  • 
Assignment of variables at startup from the command line

  • 
Advanced string manipulation functions including regular expression
matching (Split, Regexp)

  • 
Function Pipe to pass input to an external command and receive
its output as a string

  • 
Function Getpid for obtaining the process ID of the current Magma
process

  • 
File objects for advanced I/O operations, including opening of pipes
and most C standard library I/O functions

  • 
Equality operator 'cmpeq' which returns whether arguments are
comparable as well as equal, thus always returning an answer

  • 
Extension of the where-is operator to expression lists

    

    

    
Aggregate Data Types

    

    

  • 
Multisets, allowing sets with repetitions

  • 
Lists, allowing linear collections of unrelated objects

  • 
Coproducts, allowing mixing of unrelated objects

    

    

    
Permutation Groups

    

    

  • 
New algorithm for finding conjugacy classes in a permutation group

  • 
Solvable radical (SolvableRadical, Radical)

  • 
Algorithm to, given a permutation group G of degree n, construct
a degree n faithful permutation representation of G / Radical(G)

  • 
The parameters for the function ClassMap have changed (see
the Handbook)

    

    

    
Integer Ring

    

    

  • 
Limit of number of factorizations stored for Cunningham factorization
(CunninghamStorageLimit attribute)

    

    

    
Finite Fields

    

    

  • 
Fast trace algorithm due to Eric Rains

    

    

    
Multivariate Polynomial Rings

    

    

  • 
Primary decomposition

  • 
General radical

  • 
Hilbert series and Hilbert polynomial

  • 
Efficient changing of orders

  • 
Extension and contraction of ideals

  • 
Variable extension of ideals

  • 
Computation of varieties over the complex field

  • 
Multivariate factorization of polynomials over finite fields
(and function fields over finite fields)

  • 
Saturation ideal (ColonIdeal: the colon ideal I:f^infinity for
ideal I and polynomial f)

  • 
More general evaluation of multivariate polynomials at elements of
algebras over the coefficient ring

    

    

    
Algebraic Number Fields and their Orders

    

    

  • 
Installation of new KANT V4 (April 3, 1996 version)

  • 
Solution of unit equation

  • 
Construction of exceptional units

  • 
Absolute minimal polynomial of an order element

  • 
Absolute representation matrix of an order element

  • 
Residue field of a prime ideal

  • 
Specification of a fractional ideal as I/n, n an integer

  • 
LCM of ideals belonging to a maximal order

  • 
Ramification index

  • 
Suborders

  • 
Square Root, n-th root of order and ANF elements

  • 
GaloisGroup algorithm fixed so that, for degree 8 to 11 inclusive,
the roots returned (as the second return value) are in the correct
order (i.e are consistent with the permutation group returned)

    

    

    
Matrix Algebras

    

    

  • 
Basis functions (Basis, BasisElement, Coordinates)

    

    

    
Finitely presented Algebras

    

    

  • 
New version of the Linton vector enumerator

    

    

    
Elliptic Curves

    

    

  • 
Function IsEllipticCurve to test whether a sequence of coefficients
defines a valid elliptic curve and to create it if so

  • 
Function SilvermanBound

  • 
Faster rank computation

  • 
Function MordellWeilRankBounds

  • 
Synonym Rank for MordellWeilRank, and synonym RankBounds for
MordellWeilRankBound}

    

    

    
Block Designs

    

    

  • 
Near-linear space functions Restriction, ConnectionNumber, IsPointRegular,
IsLineRegular

    

    

    
Finite Planes

    

    

  • 
Creation of classical and non-classical finite projective
and affine planes

  • 
Subplanes, dual of a projective plane

  • 
Numerical invariants: order, p-rank

  • 
Properties: Desarguesian, self-dual

  • 
Parallel classes of an affine plane

  • 
k-arcs: testing, complete, tangents, secants, passants

  • 
Conics: through given points, knot, exterior, interior

  • 
Unitals: testing, tangents, feet

  • 
Affine to projective plane and vice versa

  • 
Related structures: design, incidence matrix, incidence graph,
linear code

  • 
Collineation group, isomorphism testing

  • 
Central collineations: testing, groups

  • 
Group actions on a plane: orbits and stabilizers of points and
lines 

  • 
Symmetry properties: point transitive, line transitive

    

    • 

    [Next] [Prev] [Right] [Left] [Up] [Index] [Root]