Daily Archives: September 23, 2015

flatMap()

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Functors, Applicatives, and Monads

skybrian 70 days ago

If functional languages had called them the Mappable, Applicable, and FlatMappable interfaces, and used map(), apply(), and flatMap() instead of operators, it would have avoided a lot of confusion.

— Hacker News

bind ~ flatMap

— Me@2015-07-22 06:30:25 PM

2015.09.23 Wednesday ACHK

Problem 14.2.2

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A First Course in String Theory
 
 
14.2 Generating function for the unoriented bosonic open string theory.

~~~

How to add “a term that implements the projection to unoriented states”?

What is the projector? \Omega?

f_{os} (x)

= \frac{1}{x} \prod_{n=1}^\infty \frac{1}{(1-x^n)^{24}} 

= \frac{1}{x} \left( 1 + 24 x + 324 x^2 + 3200 x^3 + ... \right)

To keep only the odd-power terms, we should construct an odd function:

f_{uos} (x)

= \frac{1}{2} \left( f_{os} (x) - f_{os} (-x) \right)

= \frac{1}{x} \prod_{n=1}^\infty \frac{1}{(1-x^n)^{24}} - \left( \frac{-1}{x} \prod_{n=1}^\infty \frac{1}{(1-(-x)^n)^{24}} \right)

— Me@2015-09-17 02:27:20 PM
 
 
 
2015.09.23 Wednesday (c) All rights reserved by ACHK