# RingFamily

## Description

This family is used to contain classes that correspond to a family of similar rings with a default member.

## Methods that use an object of class RingFamily :

• "diagonalMatrix(RingFamily,List)" -- see diagonalMatrix(Ring,ZZ,ZZ,List) -- make a diagonal matrix from a list
• "diagonalMatrix(RingFamily,ZZ,ZZ,List)" -- see diagonalMatrix(Ring,ZZ,ZZ,List) -- make a diagonal matrix from a list
• "Constant ^ RingFamily" -- see lift -- lift to another ring
• "Number ^ RingFamily" -- see lift -- lift to another ring
• "RingElement ^ RingFamily" -- see lift -- lift to another ring
• "matrix(RingFamily,List)" -- see matrix(Ring,List) -- create a matrix from a doubly nested list of ring elements or matrices
• "mutableIdentity(RingFamily,ZZ)" -- see mutableIdentity(Ring,ZZ) -- make a mutable identity matrix
• "mutableMatrix(RingFamily,ZZ,ZZ)" -- see mutableMatrix(Ring,ZZ,ZZ) -- make a mutable matrix filled with zeroes
• "random(RingFamily)" -- see random(Type) -- random element of a type
• RingFamily _* -- a unary postfix operator, used for indicating pushforward maps
• "substitute(Ideal,RingFamily)" -- see substitute -- substituting values for variables
• "substitute(Matrix,RingFamily)" -- see substitute -- substituting values for variables
• "substitute(Module,RingFamily)" -- see substitute -- substituting values for variables
• "substitute(Number,RingFamily)" -- see substitute -- substituting values for variables
• "substitute(RingElement,RingFamily)" -- see substitute -- substituting values for variables
• "substitute(Vector,RingFamily)" -- see substitute -- substituting values for variables

## Fixed objects of class RingFamily :

• CC -- the class of all complex numbers
• RR -- the class of all real numbers
• RRi -- the class of all real intervals

## For the programmer

The object RingFamily is a type, with ancestor classes Type < MutableHashTable < HashTable < Thing.