arithm Namespace Reference

Implements useful algebraic structures such as groups, fields, p-subgroups, etc. More...

Classes
class	Field
	Models a mathematical field with a given additive order, multiplicative order, addition, multiplication, unit and zero. More...
class	ModField
	Implements a modular field (i.e. where is prime). More...
class	ArrayOfElmts
	Implements an array of group elements with several mathematical operations depending on the group the associated to it. More...
class	Elmt
	Implements an element of any group. More...
class	Group
	Models a mathematical multiplicative group. More...
class	ModPGrp
	Implements a q-subgroup of a modular field. More...
class	PSubGroup
	Implements a p-subgroup (as defined in Sylow theory) of any multiplicative group. More...

Detailed Description

Implements useful algebraic structures such as groups, fields, p-subgroups, etc.

The simplest classes in this module are Elmt and ArrayOfElmts. These are used to read and write arbitrarily large integers from and to bytetrees as well as to store several such integers into an array.

Then, there are algebraic structures; namely (multiplicative) Group, Field, PSubGroup and ModPGrp). These provide operations as they are performed in these mathematical objects over Elmt's but also over ArrayOfElmt's in which case they are componentwise.