Le GAP et Rubik's Cube
24
Fevr
2024
GAP
GAP est un logiciel de calcul formel, il permet de calculer un certain nombre de caractéristiques du Rubik's Cube, du Pocket, du Skewb, ...
comme le nombre d'états, le nombre de J-conjugaison-classes, ...
Calcul le nombre d'états Revenge
Voici un programme en GAP qui calcule le nombre d'états du Revenge :
Revenge :
#gap_revenge.txt
pH := (64,67,79,76)(65,71,78,72)(66,75,77,68)(69,70,74,73)(96,48,47,16)(1,49,46,17)(2,50,45,18)(3,51,44,19);
pB := (80,83,95,92)(81,87,94,88)(82,91,93,84)(85,86,90,89)(12,28,35,60)(13,29,34,61)(14,30,33,62)(15,31,32,63);
pA := (96,3,15,12)(1,7,14,8)(2,11,13,4)(5,6,10,9)(16,83,63,76)(20,82,59,77)(24,81,55,78)(28,80,51,79);
pP := (32,35,47,44)(33,39,46,40)(34,43,45,36)(37,38,42,41)(64,60,95,19)(65,56,94,23)(66,52,93,27)(67,48,92,31);
pG := (48,51,63,60)(49,55,62,56)(50,59,61,52)(53,54,58,57)(96,80,32,64)(4,84,36,68)(8,88,40,72)(12,92,44,76);
pD := (16,19,31,28)(17,23,30,24)(18,27,29,20)(21,22,26,25)(3,67,35,83)(7,71,39,87)(11,75,43,91)(15,79,47,95);
ph := (4,52,43,20)(5,53,42,21)(6,54,41,22)(7,55,40,23);
pb := (8,24,39,56)(9,25,38,57)(10,26,37,58)(11,27,36,59);
pa := (72,17,87,62)(73,21,86,58)(74,25,85,54)(75,29,84,50);
pp := (68,61,91,18)(69,57,90,22)(70,53,89,26)(71,49,88,30);
pg := (1,81,33,65)(5,85,37,69)(9,89,41,73)(13,93,45,77);
pd := (2,66,34,82)(6,70,38,86)(10,74,42,90)(14,78,46,94);
LAMBDA := Group( pH, pB, pA, pP, pG, pD, ph, pb, pa, pp, pg, pd );
Print( "\n" );
Print( "|LAMBDA| = ", Size( LAMBDA ) , "\n" );
Print( "N = ", 3 * 2 * (2^24) , "\n" );
Print( "C = ", (24^6) / 2 , "\n" );
Print( "|G+| = ", Factorial(8) * (3^8) * Factorial(24) * (2^24) * Factorial(24), "\n" );
Print( "|G#| = |G+|/N = ", (Factorial(8) * (3^8) * Factorial(24) * (2^24) * Factorial(24) )/ (3*2*(2^24)), "\n" ) ;
Print( "|G| = |G#|/C = ", (Factorial(8) * (3^8) * Factorial(24) * (2^24) * Factorial(24) )/ (3*2*(2^24)*(24^6/2)) , "\n" );
Print( "|LAMBDA| = |G#| \n" );
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DMJ: 01/04/2024
