Safe Haskell | Safe-Infered |
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A module of simple utility functions which are used throughout the rest of the library

- toSet :: Ord a => [a] -> [a]
- setUnionAsc :: Ord a => [a] -> [a] -> [a]
- multisetSumAsc :: Ord a => [a] -> [a] -> [a]
- multisetSumDesc :: Ord a => [a] -> [a] -> [a]
- diffAsc :: Ord a => [a] -> [a] -> [a]
- diffDesc :: Ord a => [a] -> [a] -> [a]
- isSubsetAsc :: Ord a => [a] -> [a] -> Bool
- isSubMultisetAsc :: Ord a => [a] -> [a] -> Bool
- pairs :: [a] -> [(a, a)]
- ordpair :: Ord t => t -> t -> (t, t)
- foldcmpl :: (t -> t -> Bool) -> [t] -> Bool
- isWeaklyIncreasing :: Ord t => [t] -> Bool
- isStrictlyIncreasing :: 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]]
- powersetbfs :: [a] -> [[a]]
- combinationsOf :: Int -> [a] -> [[a]]
- choose :: Integral a => a -> a -> a
- class FinSet x where
- elts :: [x]

- class Num a => HasInverses a where
- inverse :: a -> a

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

# Documentation

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

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]Source

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]Source

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]Source

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]Source

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] -> BoolSource

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

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

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

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

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]]Source

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]]Source

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 -> aSource

`choose n k`

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

The class of finite sets

class Num a => HasInverses a whereSource

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.

(Ord a, Show a) => HasInverses (Permutation a) | The HasInverses instance is what enables us to write |

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)) |

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

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