# Talk:Blow your mind

### From HaskellWiki

(→Polynomial signum and abs) |
(→Polynomial signum and abs) |
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Line 22: | Line 22: | ||

* abs -> the monic polynomial obtained by dividing by the leading coefficient |
* abs -> the monic polynomial obtained by dividing by the leading coefficient |
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− | As with the abs and signum functions for Integer and Data.Complex's abs, the result of this signum is then a unit (ie, a value x for which there exists a y such that xy = 1), and we have |
+ | As with the abs and signum functions for Integer and for Data.Complex (when restricted to a subring whose intersection with the real numbers is just the integers), the result of this 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 |

## Revision as of 21:52, 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 the abs and signum functions for Integer and for Data.Complex (when restricted to a subring whose intersection with the real numbers is just the integers), the result of this 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)