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Date: Wed, 15 Jan 92 11:01:42 EST
From: raymond@cps.msu.edu
Message-Id: <9201151601.AA01789@cpss11.cps.msu.edu>
To: DEVO@gdlvm7.vnet.ibm.com, berson@cs.pitt.edu, bosch@mips.com,
        keng@zcar.asd.sgi.com, palmerp@math.orst.edu, schmidtg@astro.pc.ab.com,
        tjj@rolf.helsinki.fi, tout@cps.msu
Subject: Cube software doc
Status: OR

I sent the cube software in a separate message.  It is a tar file that
has been compressed and uuencoded.

  I had some trouble with the lex program on my machine -- it gave
a nonsense warning on the file "scanner", and then gcc wouldn't compile
the lex.yy.c that lex created.  So I used flex on my PC, and then ran
that through gcc with no trouble.

The files are:
  Makefile         Self-explanatory.
  cube.c           Driver.  Has all the permutation manipulating code.
  parser           YACC or BISON parser (both work)
  scanner          LEX or FLEX scanner (my LEX choked.  Don't know why)
  *.h              Function prototypes, struct definitions, etc.
  test.sym         File of two named operators


Start the program by typing "cube".  The program is interactive.  Below is
an example of what you can do.  What you type is shown indented two
spaces.  Comments on the input and output (not to be typed) are in /* */ pairs:

  R;  /* Turn right face a quarter turn clockwise */
(ur br dr fr) (urf urb drb drf)  [4] /* 4 is the order of the permutation */

  UR;   /* U turn followed by R turn */
(uf ul ub br dr fr ur) (urf ulf ulb drb drf)- (urb)+  [105]
/* The + and - indicate CW and CCW corner twists, respectively */

  UR(UR)';  /* UR, followed by inverse of UR */
Identity

  load "test.sym";  /* Load a file of named operators */
joe = (ur br dr fr) (urf urb drb drf)  [4]
bob = (uf ul ub ur br dr fr) (urf)+ (ulf ulb urb drb drf)-  [105]
/* There were two operators int the file, joe and bob.  */

  joe bob;  /* Do a joe, followed by a bob */
(uf ul ub ur dr) (fr br) (urf drb ulf ulb urb drf)  [30]

  FRBL;
(uf ur ub ul fl) (fr df dl bl db br dr) (urf)+ (ulf)+ (ulb)+ (urb)+
(drf dlb drb)+ (dlf)+  [315]

  (FRBL)315;  /* Repeat an FRBL 315 times -- will be back at start */
Identity

  sam=FRBL;  /* Give a name to FRBL */
sam = (uf ur ub ul fl) (fr df dl bl db br dr) (urf)+ (ulf)+ (ulb)+ (urb)+
      (drf dlb drb)+ (dlf)+  [315]

  list;  /* Show all named operators */
sam = (uf ur ub ul fl) (fr df dl bl db br dr) (urf)+ (ulf)+ (ulb)+ (urb)+
      (drf dlb drb)+ (dlf)+  [315]
joe = (ur br dr fr) (urf urb drb drf)  [4]
bob = (uf ul ub ur br dr fr) (urf)+ (ulf ulb urb drb drf)-  [105]

  save "test2.sym";  /* Save sam, joe, and bob in test2.sym */

OK


Note that I am not saving the move sequences -- the permutation is
computed during the parsing, and the input discarded.

Permutations are stored as a 20 by 2 array.  The first row gives the
new location of each cubicle, and the second line indicates the flip
or twist, relative to the principal face of the cubicle.  The principle
face of a cubicle is either the U or D face, if applicable, or the L
or R face.  (See Hofstadter's articles in _Metamagical Themas_ or
Singmaster's _Notes on Rubik's Magic Cube_.)  The principal face of
a cubie the principal face of its home cubicle.  If an operator flips
an edge piece, there is a 1 in the appropriate entry of the second
row of the array.  For corners, there can be a 0, 1, or 2, corresponding
to no twist, CW twist, and CCW twist.  When operators are combined,
the flips and twists are added, and reduced mod 2 or mod 3, as appropriate.

I realize that this documentation is rather sketchy; if you have any
questions, I'll try to answer them.

Feel free to do anything you want with this stuff.

Carl