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Created May 14, 2019 — forked from robert-claypool/app_offline.htm
A simple "app offline" template for ASP.NET
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Created Feb 9, 2019 — forked from pervognsen/clifford.md
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A quadratic space is a real vector space V with a quadratic form Q(x), e.g. V = R^n with Q as the squared length. The Clifford algebra Cl(V) of a quadratic space is the associative algebra that contains V and satisfies x^2 = Q(x) for all x in V. We're imposing by fiat that the square of a vector should be the quadratic form's value and seeing where it takes us. Treat x^2 = Q(x) as a symbolic rewriting rule that lets you replace x^2 or x x with Q(x) and vice versa whenever x is a vector. Beyond that Cl(V) satisfies the standard axioms of an algebra: it lets you multiply by scalars, it's associative and distributive, but not necessarily commutative.

Remarkably, this is all you need to derive everything about Clifford algebras.

Let me show you how easy it is to bootstrap the theory from nothing.

We know Cl(V) contains a copy of V. Since x^2 = Q(x) for all x, it must also contain a copy of some nonnegative reals.

Created Mar 21, 2018 — forked from pirrmann/Differ.fs
Differ
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 type DifferenceType<'TKey, 'T> = | Added of 'TKey * 'T | Removed of 'TKey * 'T | Modified of 'TKey * 'T * 'T * seq with member this.Key = match this with | Added (key, _) | Removed (key, _) | Modified (key, _, _, _) -> key
Created Feb 19, 2018 — forked from CarstenKoenig/Hylo.fs
Factorial using a Hylomorphism in F#
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 type List<'i,'r> = Nil | Cons of 'i*'r type FixList<'i> = FixList of List<'i,FixList<'i>> let rec fmap (f : 'a -> 'b) (l : List<'i,'a>) : List<'i,'b> = match l with | Nil -> Nil | Cons (x, tail) -> Cons (x, f tail) // you can express hylo directly without using ana and cata (by either following the
Created Aug 1, 2017 — forked from battermann/free.fsx
Free Monad like pattern in F#
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 #load @"paket-files/fsprojects/Chessie/src/Chessie/ErrorHandling.fs" type Continuation<'output, 'next> = 'output -> 'next module TerminalDsl = open Chessie.ErrorHandling type Terminal<'next> = | WriteLine of string * Continuation | ReadLine of unit * Continuation
Created Jun 6, 2017 — forked from battermann/io.fsx