| Copyright | (c) Erich Gut |
|---|---|
| License | BSD3 |
| Maintainer | zerich.gut@gmail.com |
| Safe Haskell | None |
| Language | Haskell2010 |
OAlg.Entity.Product.ProductSymbol
Contents
Description
free products of symbols in x with index type N.
Synopsis
- newtype ProductSymbol x = ProductSymbol (Product N (U x))
- sy :: Entity x => x -> ProductSymbol x
- psyShow :: Entity x => ProductSymbol x -> String
- psyxs :: ProductSymbol x -> [(x, N)]
- psywrd :: Entity x => ProductSymbol x -> Word N x
- wrdpsy :: Entity x => Word N x -> ProductSymbol x
- nProxy :: Proxy N
- psyJoin :: Entity x => ProductSymbol (ProductSymbol x) -> ProductSymbol x
- productSymbol :: Entity x => [x] -> ProductSymbol x
- psyLength :: ProductSymbol x -> N
- psyFactor :: ProductSymbol x -> N -> x
- psyMap :: Entity y => (x -> y) -> ProductSymbol x -> ProductSymbol y
- xProductSymbol :: Entity x => N -> X x -> X (ProductSymbol x)
ProductSymbol
newtype ProductSymbol x Source #
free product of symbols in x with index type N.
Example
The expression sy 'a'Char
consisting just of the character 'a'.
>>>sy 'a'ProductSymbol['a']
they are Total Multiplicative
>>>sy 'a' * sy 'b' * sy 'c'ProductSymbol['a'*'b'*'c']
and admit a listing
>>>list (Proxy :: Proxy N) (sy 'a' * sy 'b' * sy 'c')[('a',0),('b',1),('c',2)]
they have a compact representation for repetitions
>>>sy 'a' * sy 'b' * sy 'b' * sy 'a' * sy 'c'ProductSymbol['a'*'b'^2*'a'*'c']
>>>sy 'a' * sy 'b' * sy 'b' * sy 'a' * sy 'c' == sy 'a' * sy 'b' ^ 2 * sy 'a' * sy 'c'True
but they are not Commutative
>>>sy 'a' * sy 'b' ^ 2 * sy 'a' * sy 'c' == sy 'a' ^ 2 * sy 'b' ^ 2 * sy 'c'False
and they admit a total right operation <* of
Permutation N
>>>(sy 'a' * sy 'b' ^ 2 * sy 'a' * sy 'c') <* (pmtSwap 1 3 :: Permutation N)ProductSymbol['a'^2*'b'^2*'c']
Note
- Free products of symbols are finite complete sequences and allow a compact representation for repetitions and serve merely as dimensions for matrices (see OAlg.Entity.Matrix.Dim).
- Possibly infinite complete sequences are represented by
[x].
Constructors
| ProductSymbol (Product N (U x)) |
Instances
sy :: Entity x => x -> ProductSymbol x Source #
symbol of an entity, i.e. the complete sequence of psyLength one consisting
just of it.
Example
>>>sy 'a'ProductSymbol['a']
>>>sy 'a' * sy 'b' * sy 'b' ^ 5 * sy 'c'ProductSymbol['a'*'b'^6*'c']
psyxs :: ProductSymbol x -> [(x, N)] Source #
the indexed listing of the symbols.
psyJoin :: Entity x => ProductSymbol (ProductSymbol x) -> ProductSymbol x Source #
joining complete sequences.
productSymbol :: Entity x => [x] -> ProductSymbol x Source #
the induced product of symbols.
psyLength :: ProductSymbol x -> N Source #
the length of a complete sequence.
psyFactor :: ProductSymbol x -> N -> x Source #
the symbol for the given index.
psyMap :: Entity y => (x -> y) -> ProductSymbol x -> ProductSymbol y Source #
mapping free products of symbols.
X
xProductSymbol :: Entity x => N -> X x -> X (ProductSymbol x) Source #
random variable of complete sequences with the given maximal length.