CGT

Combinatorial Game Theory stuff.

This file provides a variety of tools for combinatorial game theory.

Features include: going from finite integer to the corresponding surreal number game going from non-negative integer to the corresponding nimber game adding games, negating games, multiplying game forms simplifying games determining the birthday of games determing the smallest non-negative integer greater or equal to a game an initial attempt at creating an optimization for certain well understood games with the ga class (name potentially not final)

And an interactive calculator function called cgtshell

CGTSHELL

How to use cgtshell: To use cgtshell, call cgtshell() then enter expressions to see the outputs. syntax for various expressions: cgtshell for the most part uses polish notation/prefix notation, so to add the games 2 and 2, one would say

• 2 2 or
• 2,2 or +,2 2 and would recieve the answer four. functions recognized by cgtshell are +:addition (takes 2 arguments) -:negation X:multiplication (takes 2 arguments) ceil:ceiling eq:check for equality (output 1 for true, 0 for false) (takes 2 arguments) sign:sign f:modifies a game so that either player can skip a turn so long as the other player did not just skip a turn

_ represents the result of the previous expression.

To express a game, if the game is a finite integer, use that integer (e.g. 5. -5 would be -5 because - negates the 5. --5==5) if the game is a finite number, use an asterisk followed by that integer (e.g. *4 )

• also works in place of 1 if the game is up or down, use up or down to express a game in terms of its left or right options,
  start with an open curly bracket, list the left options, use a pipe, list the right options, use a close curly bracket e.g. {2,|1,2} or {up |down} (spaces and commas are interchangeable)

Note that games become too large to handle quickly fairly quickly.

Contribute?

would you like to contribute? Feel free to send a pull request for an issue, or submit an issue yourself!