Difference between revisions of "Blog articles/Mathematics"

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Articles using Haskell for mathematics, and the mathematics of Haskell.
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== Maths ==
  
   
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For further references see the:
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=== Haskell for mathematics ===
  
   
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* [[Haskell_and_mathematics|Haskell math community]].
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* [[Blog_articles/Monads|Mathematics of monads]]
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== Haskell for mathematics ==
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=== General ===
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* [http://sigfpe.blogspot.com/2006/01/eleven-reasons-to-use-haskell-as.html Eleven Reasons to use Haskell as a Mathematician]
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* [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/learn-maths-with-haskell.html Learn Maths with Haskell]
  
* [http://sigfpe.blogspot.com/2006/09/learn-maths-with-haskell.html Learn Maths with Haskell]
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* [http://blog.mikael.johanssons.org/archive/2006/10/prototyping-thought/ Prototyping thought]
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* [http://scienceblogs.com/goodmath/2006/11/why_haskell.php Why Haskell?]
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=== Calculus and Differential Geometry ===
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* [http://sigfpe.blogspot.com/2006/09/practical-synthetic-differential.html Practical Synthetic Differential Geometry]
  
* [http://sigfpe.blogspot.com/2006/09/practical-synthetic-differential.html Practical Synthetic Differential Geometry]
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* [http://vandreev.wordpress.com/2006/12/04/non-standard-analysis-and-automatic-differentiation/ Non-standard analysis, automatic differentiation, Haskell]
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* [http://sigfpe.blogspot.com/2006/09/more-low-cost-geometric-algebra.html More Low Cost Geometric Algebra]
  
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=== Algebraic Topology and Geometry ===
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* [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell]
  
* [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell]
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* [http://sigfpe.blogspot.com/2006/09/infinitesimal-types.html Infinitesimal Types]
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* [http://sigfpe.blogspot.com/2006/09/more-low-cost-geometric-algebra.html More Low Cost Geometric Algebra]
 
* [http://sigfpe.blogspot.com/2006/08/geometric-algebra-for-free_30.html Geometric Algebra for Free!]
  
* [http://sigfpe.blogspot.com/2006/08/geometric-algebra-for-free_30.html Geometric Algebra for Free!]
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* [http://sigfpe.blogspot.com/2006/01/eleven-reasons-to-use-haskell-as.html Eleven Reasons to use Haskell as a Mathematician]
  
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=== Geometry ===
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* [http://sigfpe.blogspot.com/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion]
  
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* [http://www.alpheccar.org/content/57.html Haskell, PDF and Penrose Tilings]
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* [http://blog.mikael.johanssons.org/archive/2006/11/a-algebras-and-group-cohomology/ <math>A_\infty</math>-algebras and group cohomology]
  
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* [http://www.kennknowles.com/blog/2007/11/20/visualizing-2d-convex-hull-using-gtk-and-opengl-in-haskell/ Visualizing 2D convex hull using Gtk and OpenGL in Haskell]
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* [http://blog.mikael.johanssons.org/archive/2006/10/prototyping-thought/ Prototyping thought]
  
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* [http://www.kennknowles.com/blog/2007/12/03/calculating-the-reflect-rotate-translate-normal-form-for-an-isometry-of-the-plane-in-haskell-and-verifying-it-with-quickcheck/ Calculating the reflect-rotate-translate normal form for an isometry of the plane in Haskell, and verifying it with QuickCheck.]
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* [http://www.kennknowles.com/blog/2008/04/16/drawing-fractals-in-haskell-with-a-cursor-graphics-dsel-and-a-cute-list-representation/ Drawing fractals in Haskell with a cursor graphics DSEL and a cute list representation]
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=== Group theory ===
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* [http://blog.mikael.johanssons.org/archive/2006/10/computational-group-theory-in-haskell-1-in-a-series/ Computational Group Theory in Haskell]
  
* [http://blog.mikael.johanssons.org/archive/2006/10/computational-group-theory-in-haskell-1-in-a-series/ Computational Group Theory in Haskell]
 
* [http://blog.mikael.johanssons.org/archive/2006/07/carry-bits-and-group-cohomology/ Carry bits and group cohomology]
  
* [http://blog.mikael.johanssons.org/archive/2006/07/carry-bits-and-group-cohomology/ Carry bits and group cohomology]
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* [http://sigfpe.blogspot.com/2007/06/monads-from-algebra-and-the-gray-code.html Monads from Algebra and the the Gray Code from Groups]
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* [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials as numbers]
  
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* [http://vandreev.wordpress.com/2006/12/04/non-standard-analysis-and-automatic-differentiation/ Non-standard analysis, automatic differentiation, Haskell]
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* [http://www.kennknowles.com/blog/2007/12/20/infinite-lazy-knuth-bendix-completion-for-monoids-in-haskell/ Infinite lazy Knuth-Bendix completion for monoids in Haskell]
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=== Set theory ===
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* Ordinals in Haskell
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** [http://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html Countable ordinals]
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** [http://japple.blogspot.com/2007/06/ordinals-part-2.html Uncountable ordinals and better representations for countable ordinals]
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** [http://blog.jbapple.com/2007/07/ord-countable-ordinals-and-idea-of.html Ord, Countable Ordinals, and an Idea of sigfpe]
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* [http://japple.blogspot.com/2007/06/constructability-uncountability-and.html Constructability, Uncountability, and &omega;-Haskell]
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* [http://community.livejournal.com/evan_tech/220036.html Defining a power set in one line]
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** [http://blog.mikedaum.com/2007/06/28/haskell-power/ Commentary on this powerset implementation]
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=== Ring theory ===
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* [http://sambangu.blogspot.com/2006/12/polynomials-as-numbers Polynomials] ([http://sambangu.blogspot.com/2006/12/questions-on-haskell-style-and update])
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=== Number theory ===
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* Number theory and Haskell:
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** [http://cdsmith.wordpress.com/2007/06/02/learning-number-theory-and-haskell-the-division-algorithm/ The Division Algorithm]
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** [http://cdsmith.wordpress.com/2007/06/03/learning-number-theory-and-haskell-more-quickcheck-and-divisors/ QuickCheck and Divisors]
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** [http://cdsmith.wordpress.com/2007/06/06/learning-number-theory-and-haskell-greatest-common-divisor/ Greatest Common Divisor]
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** [http://cdsmith.wordpress.com/2007/06/24/learning-haskell-and-number-theory-gcd-and-higher-order-functions/ GCD and Higher Order Functions]
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** [http://cdsmith.wordpress.com/2007/07/05/learning-haskell-and-number-theory-the-end-of-gcd/ The End of GCD]
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* [http://www.akalin.cx/2007/07/06/a-foray-into-number-theory-with-haskell/ A foray into number theory with Haskell]
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=== Cryptography and coding theory ===
 
* [http://vandreev.wordpress.com/2007/06/18/feistel-ciphers-and-des-in-haskell/ Feistel Ciphers and DES in Haskell]
  
* [http://vandreev.wordpress.com/2007/06/18/feistel-ciphers-and-des-in-haskell/ Feistel Ciphers and DES in Haskell]
 
* [http://vandreev.wordpress.com/2007/01/07/arithmetic-coding/ Arithmetic coding in Haskell]
  
* [http://vandreev.wordpress.com/2007/01/07/arithmetic-coding/ Arithmetic coding in Haskell]
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* [http://www.polyomino.f2s.com/ Haskell for Maths]: commutative algebra, combinatorics, number theory, and group theory
  
 
* [http://www.serpentine.com/blog/2007/01/11/two-dimensional-spatial-hashing-with-space-filling-curves/ Two-dimensional spatial hashing with space-filling curves]
  
* [http://www.serpentine.com/blog/2007/01/11/two-dimensional-spatial-hashing-with-space-filling-curves/ Two-dimensional spatial hashing with space-filling curves]
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* [http://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html Countable Ordinals in Haskell]
  
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=== Logic ===
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* [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials as numbers]
  
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* [http://sigfpe.blogspot.com/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion]
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* [https://serokell.io/blog/incomplete-and-utter-introduction-to-modal-logic Incomplete and Utter Introduction to Modal Logic, Pt. 1]
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* [https://serokell.io/blog/incomplete-and-utter-introduction-to-modal-logic Incomplete and Utter Introduction to Modal Logic, Pt. 2]
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=== Numerics ===
 
* The Division Bell
  
* The Division Bell
 
** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me.html Part One]
  
** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me.html Part One]
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** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me-part-four.html Part Four (Conclusion)]
  
** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me-part-four.html Part Four (Conclusion)]
 
** [http://praisecurseandrecurse.blogspot.com/2006/12/divisive-aftermath.html The Divisive Aftermath]
  
** [http://praisecurseandrecurse.blogspot.com/2006/12/divisive-aftermath.html The Divisive Aftermath]
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* [http://www.alpheccar.org/en/posts/show/57 Haskell, PDF and penrose tilings]
  
 
* Overloading Haskell numbers
  
* Overloading Haskell numbers
 
** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-1.html Part 1: symbolic expressions]
  
** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-1.html Part 1: symbolic expressions]
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** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-3.html Part 3: Fixed Precision]
  
** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-3.html Part 3: Fixed Precision]
 
** [http://augustss.blogspot.com/2007/05/i-was-asked-if-my-fixed-number-module.html Dynamic epsilons in Haskell with a bit of type hackery]
  
** [http://augustss.blogspot.com/2007/05/i-was-asked-if-my-fixed-number-module.html Dynamic epsilons in Haskell with a bit of type hackery]
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* Number theory
  
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** [http://cdsmith.wordpress.com/2007/06/24/learning-haskell-and-number-theory-gcd-and-higher-order-functions/ GCD and Higher Order Functions]
  
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* [http://www.alpheccar.org/en/posts/show/74 Category theory 1]
  
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* [http://www.alpheccar.org/en/posts/show/76 Category theory 2]
  
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=== Theorem proving ===
  
   
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== Theorem proving ==
 
* [http://vandreev.wordpress.com/2006/12/24/quick-and-dirty-theorem-prover/ Quick and Dirty Theorem Prover]
  
* [http://vandreev.wordpress.com/2006/12/24/quick-and-dirty-theorem-prover/ Quick and Dirty Theorem Prover]
   
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=== Quantum computing ===
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== Quantum computing ==
   
 
* [http://sigfpe.blogspot.com/2007/02/essence-of-quantum-computing.html The Essence of Quantum Computing]
  
* [http://sigfpe.blogspot.com/2007/02/essence-of-quantum-computing.html The Essence of Quantum Computing]
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* [http://sigfpe.blogspot.com/2007/03/independence-entanglement-and.html Independence, entanglement and decoherence with the quantum monad]
  
* [http://sigfpe.blogspot.com/2007/03/independence-entanglement-and.html Independence, entanglement and decoherence with the quantum monad]
 
* [http://sigfpe.blogspot.com/2007/03/shor-quantum-error-correcting-code-and.html The Shor Quantum Error Correcting Code (and a Monad for Heat)]
  
* [http://sigfpe.blogspot.com/2007/03/shor-quantum-error-correcting-code-and.html The Shor Quantum Error Correcting Code (and a Monad for Heat)]
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* [http://www.alpheccar.org/en/posts/show/68 The Frame Of Reference Monad]
  
   
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=== Mathematics of Haskell ===
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== Mathematics of Haskell ==
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=== Category theoretic ===
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* Category Theory and the Category of Haskell programs:
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** [http://www.alpheccar.org/content/74.html Part 1]
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** [http://www.alpheccar.org/content/76.html Part 2]
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** [http://www.alpheccar.org/content/77.html Part 3]
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* [http://en.wikibooks.org/wiki/Haskell/Category_theory Category theory and Haskell]
   
 
* [http://sigfpe.blogspot.com/2006/11/why-isnt-listt-monad.html Why isn't ListT list a monad?]
  
* [http://sigfpe.blogspot.com/2006/11/why-isnt-listt-monad.html Why isn't ListT list a monad?]
 
* [http://sigfpe.blogspot.com/2006/11/yoneda-lemma.html Reverse Engineering Machines with the Yoneda Lemma]
  
* [http://sigfpe.blogspot.com/2006/11/yoneda-lemma.html Reverse Engineering Machines with the Yoneda Lemma]
 
* [http://sigfpe.blogspot.com/2006/11/variable-substitution-gives.html Variable substitution gives a...]
  
* [http://sigfpe.blogspot.com/2006/11/variable-substitution-gives.html Variable substitution gives a...]
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* [http://sigfpe.blogspot.com/2006/11/from-l-theorem-to-spreadsheet.html From Löb's Theorem to Spreadsheet Evaluation]
  
 
* [http://sigfpe.blogspot.com/2006/10/games-strategies-and-self-composition.html Games, Strategies and the Self-Composition of the List Monad.]
  
* [http://sigfpe.blogspot.com/2006/10/games-strategies-and-self-composition.html Games, Strategies and the Self-Composition of the List Monad.]
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=== Lambda and combinator calculi ===
 
* [http://scienceblogs.com/goodmath/2006/09/programs_are_proofs_models_and_1.php Programs are Proofs: Models and Types in Lambda Calculus]
  
* [http://scienceblogs.com/goodmath/2006/09/programs_are_proofs_models_and_1.php Programs are Proofs: Models and Types in Lambda Calculus]
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* [http://scienceblogs.com/goodmath/2006/11/why_haskell.php Why Haskell?]
  
 
* [http://www.onebadseed.com/blog/?p=51 Don't need the Y combinator]
  
* [http://www.onebadseed.com/blog/?p=51 Don't need the Y combinator]
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=== Other formal logics ===
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* [http://sigfpe.blogspot.com/2006/11/from-l-theorem-to-spreadsheet.html From Löb's Theorem to Spreadsheet Evaluation]
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=== Miscellaneous ===
 
* [http://www.rubrication.net/2007/04/21/how-a-real-module-system-should-work/ ML, Haskell and Coq]
  
* [http://www.rubrication.net/2007/04/21/how-a-real-module-system-should-work/ ML, Haskell and Coq]
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* [http://sigfpe.blogspot.com/2006/09/infinitesimal-types.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]
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* [http://disparatemathematician.blogspot.com/2007/07/peanos-axioms-iv-advanced-functions-and.html Peano's Axioms IV: Advanced Functions and Integers]
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* [http://www.alpheccar.org/en/posts/show/74 Category Theory and the category of Haskell programs]
  
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* [http://sigfpe.blogspot.com/2005/07/formal-power-series-and-haskell.html Formal Power Series and Haskell]
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[[Category:Tutorials]]
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[[Category:Mathematics|*]]

Latest revision as of 07:20, 16 April 2020

Articles using Haskell for mathematics, and the mathematics of Haskell.

For further references see the:

Haskell for mathematics

General

Calculus and Differential Geometry

Algebraic Topology and Geometry

Geometry

Group theory

Set theory

Ring theory

Number theory

Cryptography and coding theory

Logic

Numerics

Theorem proving

Quantum computing

Mathematics of Haskell

Category theoretic

Lambda and combinator calculi

Other formal logics

Miscellaneous

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