Category Archives: math

Themes on Streams

> {-# LANGUAGE DeriveFunctor, FlexibleInstances #-} Recall that a stream is a countably infinite sequence of values: > data Stream a = a :> Stream a > deriving (Functor, Show) > > sHead (a :> _) = a > sTail … Continue reading

Posted in haskell, math | Tagged , , , , , | 3 Comments

Math.OEIS needs a new maintainer

Summary: the OEIS has switched servers and the oeis package needs updating to match, so I’m looking for someone to take over development. All the rest is padding in the form of entertaining stories. Recently, Michael Snoyman’s wonderful packdeps tool … Continue reading

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Things I have learned about vector spaces

Work on the diagrams library is coming along rather nicely. I’ll have more to say about it soon, but for now here are two things I have learned recently: Normals transform as the inverse transpose (see Subject 5.27). Be very … Continue reading

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Species and Functors and Types, Oh My!

My paper on combinatorial species and the species library (an improved version of my previous ICFP submission) has been accepted to the 2010 Haskell Symposium! I look forward to seeing people in Baltimore in September, and in the meantime the … Continue reading

Posted in combinatorics, haskell, math, writing | Tagged , , , , , | 2 Comments

Math.Combinatorics.Multiset and Sawada’s algorithm

I’ve uploaded a new version of my Math.Combinatorics.Multiset library (see the previous announcement here). I’ve added a few more fairly simple algorithms (splitting a multiset into two pieces in all possible ways; finding all size-k submultisets of a multiset), and … Continue reading

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How to solve this differential equation?

How would you solve the differential equation with the initial condition ? I know what the answer is supposed to be, but I don’t know how to directly solve it. In case you’re wondering, is the exponential generating function for … Continue reading

Posted in combinatorics, math | Tagged , , , , | 15 Comments

Mgu’s and universal properties

Warning, poorly-explained categorical rambling follows… The most general unifier (mgu) of two expressions and is a substitution for which , such that every other substitution for which can be expressed as for some . For example, the most general unifier … Continue reading

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Species operations: differentiation

Continuing my series describing my new combinatorial species library, today we’ll take a look at the operation of differentiation. You may remember that the Species type class has an Algebra.Differential constraint, which, as I previously explained, transitively implies an Algebra.Ring … Continue reading

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Primitive species and species operations, part II

In my previous post, I began describing the primitive species and species operations supported by my combinatorial species library; we looked at the ring structure on species, that is, the primitive species and , and the operations of species sum … Continue reading

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Primitive species and species operations

In this second post about my new combinatorial species library, I plan to begin writing about the species DSL itself: what are the primitive combinatorial species and the primitive operations on species? (The first post described the concept of combinatorial … Continue reading

Posted in combinatorics, haskell, math | Tagged , , , | 3 Comments