Math.Core.Utils

A module of simple utility functions which are used throughout the rest of the library

Documentation

toSet :: Ord a => [a] -> [a]

mergeSet :: Ord a => [a] -> [a] -> [a]

pairs :: [a] -> [(a, a)]

ordpair :: Ord t => t -> t -> (t, t)

foldcmpl :: (t -> t -> Bool) -> [t] -> Bool

cmpfst :: Ord a => (a, b) -> (a, b1) -> Ordering

eqfst :: Eq a => (a, b) -> (a, b1) -> Bool

fromBase :: Num a => a -> [a] -> a

powersetdfs :: [a] -> [[a]]

Given a set xs, represented as an ordered list, powersetdfs xs returns the list of all subsets of xs, in lex order

powersetbfs :: [a] -> [[a]]

Given a set xs, represented as an ordered list, powersetbfs xs returns the list of all subsets of xs, in shortlex order

combinationsOf :: Int -> [a] -> [[a]]

Given a positive integer k, and a set xs, represented as a list, combinationsOf k xs returns all k-element subsets of xs. The result will be in lex order, relative to the order of the xs.

choose :: Integral a => a -> a -> a

choose n k is the number of ways of choosing k distinct elements from an n-set

class FinSet x where

The class of finite sets

Methods

elts :: [x]

Instances

FinSet F25

FinSet F16

FinSet F9

FinSet F8

FinSet F4

FinSet F23

FinSet F19

FinSet F17

FinSet F13

FinSet F11

FinSet F7

FinSet F5

FinSet F3

FinSet F2

IntegerAsType p => FinSet (Fp p)

(FinSet fp, Eq fp, Num fp, PolynomialAsType fp poly) => FinSet (ExtensionField fp poly)

class Num a => HasInverses a where

A class representing algebraic structures having an inverse operation. Although strictly speaking the Num precondition means that we are requiring the structure also to be a ring, we do sometimes bend the rules (eg permutation groups). Note also that we don't insist that every element has an inverse.

Methods

inverse :: a -> a

Instances

(Ord a, Show a) => HasInverses (Permutation a)

The HasInverses instance is what enables us to write g^-1 for the inverse of a group element.

HasInverses (GroupAlgebra Q)

Note that the inverse of a group algebra element can only be efficiently calculated if the group generated by the non-zero terms is very small (eg <100 elements).

(^-) :: (HasInverses a, Integral b) => a -> b -> a

A trick: x^-1 returns the inverse of x