Math.Core.Utils

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

Documentation

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

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

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

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

The set union of two ascending lists. If both inputs are strictly increasing, then the output is their union and is strictly increasing. The code does not check that the lists are strictly increasing.

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

The multiset sum of two ascending lists. If xs and ys are ascending, then multisetSumAsc xs ys == sort (xs++ys). The code does not check that the lists are ascending.

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

The multiset sum of two descending lists. If xs and ys are descending, then multisetSumDesc xs ys == sort (xs++ys). The code does not check that the lists are descending.

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

The multiset or set difference between two ascending lists. If xs and ys are ascending, then diffAsc xs ys == xs \ ys, and diffAsc is more efficient. If xs and ys are sets (that is, have no repetitions), then diffAsc xs ys is the set difference. The code does not check that the lists are ascending.

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

The multiset or set difference between two descending lists. If xs and ys are descending, then diffDesc xs ys == xs \ ys, and diffDesc is more efficient. If xs and ys are sets (that is, have no repetitions), then diffDesc xs ys is the set difference. The code does not check that the lists are descending.

isSubsetAsc :: Ord a => [a] -> [a] -> Bool

isSubMultisetAsc :: Ord a => [a] -> [a] -> Bool

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

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

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

isWeaklyIncreasing :: Ord t => [t] -> Bool

isStrictlyIncreasing :: Ord t => [t] -> Bool

isWeaklyDecreasing :: Ord t => [t] -> Bool

isStrictlyDecreasing :: Ord t => [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 HasInverses a where

A class representing algebraic structures having an inverse operation. Note that in some cases not every element has an inverse.

Methods

inverse :: a -> a

Instances

HasInverses SSymF

(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).

(Eq k, Fractional k, Ord a, Show a) => HasInverses (Vect k (Interval a))

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

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