Blog articles/Mathematics
From HaskellWiki
< Blog articles(Difference between revisions)
DonStewart (Talk  contribs) (→Set theory) 

(19 intermediate revisions by 5 users not shown)  
Line 1:  Line 1:  
−  Haskell and mathematics. See also the [[Haskell_and_mathematicsHaskell math community]]. 
+  Articles using Haskell for mathematics, and the mathematics of Haskell. 
+  
+  For further references see the: 

+  
+  * [[Haskell_and_mathematicsHaskell math community]]. 

+  * [[Blog_articles/MonadsMathematics of monads]] 

== Haskell for mathematics == 
== Haskell for mathematics == 

Line 6:  Line 6:  
* [http://sigfpe.blogspot.com/2006/01/elevenreasonstousehaskellas.html Eleven Reasons to use Haskell as a Mathematician] 
* [http://sigfpe.blogspot.com/2006/01/elevenreasonstousehaskellas.html Eleven Reasons to use Haskell as a Mathematician] 

−  * [http://www.polyomino.f2s.com/ Haskell for Maths]: commutative algebra, combinatorics, number theory, and group theory libraries 
+  * [http://www.polyomino.f2s.com/ Haskell for Maths]: commutative algebra, combinatorics, number theory, and group theory libraries ([http://haskellformaths.blogspot.com/ blog], [http://hackage.haskell.org/package/HaskellForMaths hackage]) 
* [http://sigfpe.blogspot.com/2006/09/learnmathswithhaskell.html Learn Maths with Haskell] 
* [http://sigfpe.blogspot.com/2006/09/learnmathswithhaskell.html Learn Maths with Haskell] 

* [http://blog.mikael.johanssons.org/archive/2006/10/prototypingthought/ Prototyping thought] 
* [http://blog.mikael.johanssons.org/archive/2006/10/prototypingthought/ Prototyping thought] 

Line 23:  Line 23:  
=== Geometry === 
=== Geometry === 

−  * [http://www.alpheccar.org/en/posts/show/57 Haskell, PDF and penrose tilings] 
+  * [http://www.alpheccar.org/content/57.html Haskell, PDF and Penrose Tilings] 
−  +  * [http://www.kennknowles.com/blog/2007/11/20/visualizing2dconvexhullusinggtkandopenglinhaskell/ Visualizing 2D convex hull using Gtk and OpenGL in Haskell] 

+  * [http://www.kennknowles.com/blog/2007/12/03/calculatingthereflectrotatetranslatenormalformforanisometryoftheplaneinhaskellandverifyingitwithquickcheck/ Calculating the reflectrotatetranslate normal form for an isometry of the plane in Haskell, and verifying it with QuickCheck.] 

+  * [http://www.kennknowles.com/blog/2008/04/16/drawingfractalsinhaskellwithacursorgraphicsdselandacutelistrepresentation/ Drawing fractals in Haskell with a cursor graphics DSEL and a cute list representation] 

+  
=== Group theory === 
=== Group theory === 

* [http://blog.mikael.johanssons.org/archive/2006/10/computationalgrouptheoryinhaskell1inaseries/ Computational Group Theory in Haskell] 
* [http://blog.mikael.johanssons.org/archive/2006/10/computationalgrouptheoryinhaskell1inaseries/ Computational Group Theory in Haskell] 

* [http://blog.mikael.johanssons.org/archive/2006/07/carrybitsandgroupcohomology/ Carry bits and group cohomology] 
* [http://blog.mikael.johanssons.org/archive/2006/07/carrybitsandgroupcohomology/ Carry bits and group cohomology] 

+  * [http://sigfpe.blogspot.com/2007/06/monadsfromalgebraandthegraycode.html Monads from Algebra and the the Gray Code from Groups] 

+  * [http://www.kennknowles.com/blog/2007/12/20/infinitelazyknuthbendixcompletionformonoidsinhaskell/ Infinite lazy KnuthBendix completion for monoids in Haskell] 

=== Set theory === 
=== Set theory === 

−  * Uncountable ordinals in Haskell 
+  * Ordinals in Haskell 
−  ** [http://japple.blogspot.com/2007/02/countableordinalsinhaskell.html Part 1] 
+  ** [http://japple.blogspot.com/2007/02/countableordinalsinhaskell.html Countable ordinals] 
−  ** [http://japple.blogspot.com/2007/06/ordinalspart2.html Part 2] 
+  ** [http://japple.blogspot.com/2007/06/ordinalspart2.html Uncountable ordinals and better representations for countable ordinals] 
−  * [http://japple.blogspot.com/2007/06/constructabilityuncountabilityand.html Constructability, Uncountability, and �Haskell] 
+  ** [http://blog.jbapple.com/2007/07/ordcountableordinalsandideaof.html Ord, Countable Ordinals, and an Idea of sigfpe] 
+  * [http://japple.blogspot.com/2007/06/constructabilityuncountabilityand.html Constructability, Uncountability, and ωHaskell] 

* [http://community.livejournal.com/evan_tech/220036.html Defining a power set in one line] 
* [http://community.livejournal.com/evan_tech/220036.html Defining a power set in one line] 

+  ** [http://blog.mikedaum.com/2007/06/28/haskellpower/ Commentary on this powerset implementation] 

=== Ring theory === 
=== Ring theory === 

Line 41:  Line 44:  
=== Number theory === 
=== Number theory === 

−  * [http://cdsmith.wordpress.com/2007/06/24/learninghaskellandnumbertheorygcdandhigherorderfunctions/ GCD and Higher Order Functions] 
+  
+  * Number theory and Haskell: 

+  ** [http://cdsmith.wordpress.com/2007/06/02/learningnumbertheoryandhaskellthedivisionalgorithm/ The Division Algorithm] 

+  ** [http://cdsmith.wordpress.com/2007/06/03/learningnumbertheoryandhaskellmorequickcheckanddivisors/ QuickCheck and Divisors] 

+  ** [http://cdsmith.wordpress.com/2007/06/06/learningnumbertheoryandhaskellgreatestcommondivisor/ Greatest Common Divisor] 

+  ** [http://cdsmith.wordpress.com/2007/06/24/learninghaskellandnumbertheorygcdandhigherorderfunctions/ GCD and Higher Order Functions] 

+  ** [http://cdsmith.wordpress.com/2007/07/05/learninghaskellandnumbertheorytheendofgcd/ The End of GCD] 

+  
+  * [http://www.akalin.cx/2007/07/06/aforayintonumbertheorywithhaskell/ A foray into number theory with Haskell] 

=== Cryptography and coding theory === 
=== Cryptography and coding theory === 

Line 75:  Line 78:  
* [http://sigfpe.blogspot.com/2007/03/independenceentanglementand.html Independence, entanglement and decoherence with the quantum monad] 
* [http://sigfpe.blogspot.com/2007/03/independenceentanglementand.html Independence, entanglement and decoherence with the quantum monad] 

* [http://sigfpe.blogspot.com/2007/03/shorquantumerrorcorrectingcodeand.html The Shor Quantum Error Correcting Code (and a Monad for Heat)] 
* [http://sigfpe.blogspot.com/2007/03/shorquantumerrorcorrectingcodeand.html The Shor Quantum Error Correcting Code (and a Monad for Heat)] 

−  * [http://www.alpheccar.org/en/posts/show/68 The Frame Of Reference Monad] 

== Mathematics of Haskell == 
== Mathematics of Haskell == 

Line 82:  Line 84:  
* Category Theory and the Category of Haskell programs: 
* Category Theory and the Category of Haskell programs: 

−  ** [http://www.alpheccar.org/en/posts/show/74 Category Theory and the category of Haskell programs] 
+  ** [http://www.alpheccar.org/content/74.html Part 1] 
−  ** [http://www.alpheccar.org/en/posts/show/76 Part 2] 
+  ** [http://www.alpheccar.org/content/76.html Part 2] 
+  ** [http://www.alpheccar.org/content/77.html Part 3] 

+  
+  * [http://en.wikibooks.org/wiki/Haskell/Category_theory Category theory and Haskell] 

* [http://sigfpe.blogspot.com/2006/11/whyisntlisttmonad.html Why isn't ListT list a monad?] 
* [http://sigfpe.blogspot.com/2006/11/whyisntlisttmonad.html Why isn't ListT list a monad?] 

Line 101:  Line 103:  
* [http://sigfpe.blogspot.com/2006/09/infinitesimaltypes.html Infinitesimal Types] 
* [http://sigfpe.blogspot.com/2006/09/infinitesimaltypes.html Infinitesimal Types] 

* [http://www.alpheccar.org/en/posts/show/70 Djinn, Coq, Monad and a bit of Haskell] 
* [http://www.alpheccar.org/en/posts/show/70 Djinn, Coq, Monad and a bit of Haskell] 

+  * [http://disparatemathematician.blogspot.com/2007/07/peanosaxiomsivadvancedfunctionsand.html Peano's Axioms IV: Advanced Functions and Integers] 

+  * [http://sigfpe.blogspot.com/2005/07/formalpowerseriesandhaskell.html Formal Power Series and Haskell] 

[[Category:Tutorials]] 
[[Category:Tutorials]] 
Latest revision as of 15:22, 26 January 2012
Articles using Haskell for mathematics, and the mathematics of Haskell.
For further references see the:
Contents 
[edit] 1 Haskell for mathematics
[edit] 1.1 General
 Eleven Reasons to use Haskell as a Mathematician
 Haskell for Maths: commutative algebra, combinatorics, number theory, and group theory libraries (blog, hackage)
 Learn Maths with Haskell
 Prototyping thought
 Why Haskell?
[edit] 1.2 Calculus and Differential Geometry
[edit] 1.3 Algebraic Topology and Geometry
[edit] 1.4 Geometry
 Haskell, PDF and Penrose Tilings
 Visualizing 2D convex hull using Gtk and OpenGL in Haskell
 Calculating the reflectrotatetranslate normal form for an isometry of the plane in Haskell, and verifying it with QuickCheck.
 Drawing fractals in Haskell with a cursor graphics DSEL and a cute list representation
[edit] 1.5 Group theory
 Computational Group Theory in Haskell
 Carry bits and group cohomology
 Monads from Algebra and the the Gray Code from Groups
 Infinite lazy KnuthBendix completion for monoids in Haskell
[edit] 1.6 Set theory
 Ordinals in Haskell
 Constructability, Uncountability, and ωHaskell
 Defining a power set in one line
[edit] 1.7 Ring theory
[edit] 1.8 Number theory
 Number theory and Haskell:
[edit] 1.9 Cryptography and coding theory
 Feistel Ciphers and DES in Haskell
 Arithmetic coding in Haskell
 Twodimensional spatial hashing with spacefilling curves
[edit] 1.10 Logic
[edit] 1.11 Numerics
 The Division Bell
 Overloading Haskell numbers
[edit] 2 Theorem proving
[edit] 3 Quantum computing
 The Essence of Quantum Computing
 Monads for vector spaces, probability and quantum mechanics pt. I
 Monads, Vector Spaces and Quantum Mechanics pt. II
 Independence, entanglement and decoherence with the quantum monad
 The Shor Quantum Error Correcting Code (and a Monad for Heat)
[edit] 4 Mathematics of Haskell
[edit] 4.1 Category theoretic
 Why isn't ListT list a monad?
 Reverse Engineering Machines with the Yoneda Lemma
 Variable substitution gives a...
 Games, Strategies and the SelfComposition of the List Monad.