Talk:Blow your mind
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(→Polynomial signum and abs: new section) |
(→Polynomial signum and abs) |
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A sensible option for signum and abs for polynomials (with coefficients from a field) would be | A sensible option for signum and abs for polynomials (with coefficients from a field) would be | ||
| - | signum -> the leading coefficient | + | * signum -> the leading coefficient |
| - | abs -> the monic polynomial obtained by dividing by the leading coefficient | + | * abs -> the monic polynomial obtained by dividing by the leading coefficient |
As with Integer and Data.Complex's abs and signum, the result of signum is then a unit (ie, a value x for which there exists a y such that xy = 1), and we have | As with Integer and Data.Complex's abs and signum, the result of signum is then a unit (ie, a value x for which there exists a y such that xy = 1), and we have | ||
| - | signum a * abs a = a | + | * signum a * abs a = a |
| - | abs 1 = signum 1 = 1 | + | * abs 1 = signum 1 = 1 |
| - | abs (any unit) = 1 | + | * abs (any unit) = 1 |
| - | abs a * abs b = abs (a * b) | + | * abs a * abs b = abs (a * b) |
Revision as of 21:04, 25 August 2012
1 Name?
Is there a better name for this page? —Ashley Y 00:55, 2 March 2006 (UTC)
i completely agree, the name pretty much sucks. but what i really wanted, was to compile a collection of "idioms" that would enlarge the readers perception of what is possible in Haskell and how to go about it. so, i'll have to find a name that reflects this plan. —--J. Ahlmann 14:13, 2 March 2006 (UTC)
2 List / String Operations
Should this:
transpose . unfoldr (\a -> toMaybe (null a) (splitAt 2 a))
be this instead:
transpose . unfoldr (\a -> toMaybe (not $ null a) (splitAt 2 a))
3 Polynomial signum and abs
A sensible option for signum and abs for polynomials (with coefficients from a field) would be
- signum -> the leading coefficient
- abs -> the monic polynomial obtained by dividing by the leading coefficient
As with Integer and Data.Complex's abs and signum, the result of signum is then a unit (ie, a value x for which there exists a y such that xy = 1), and we have
- signum a * abs a = a
- abs 1 = signum 1 = 1
- abs (any unit) = 1
- abs a * abs b = abs (a * b)
