Le GAP (logiciel calcul formel)

[Morphocode]

GAP est un logiciel calcul formel, qui nous permet de calculer certains nombres de Rubik's Cube.
On télécharge le GAP 4.4.12 ici

https://www.gap-system.org/Releases/4.4.12.html

Dans la fenêtre de commande cmd , on se place dans le dossier GAP4R4/bin

cd \
cd GAP4R4
cd bin

c:\GAP4R4\bin >gap < ficher.txt

Code : Tout sélectionner

# gap_rubik.txt
#         5  6  7
#         4  H  8
#         3  2  1
#25 28 23|21 26 19|17 32 31|29 30 27
#38 G  36|12 A  10|34 D  40|16 P  14
#43 44 37|39 42 33|35 48 45|47 46 41
#         11 18 9
#         20 B  24
#         13 22 15

pH := (2,4,6,8)(26,28,30,32) (1,3,5,7)(17,21,25,29)(19,23,27,31) ;
pB := (18,24,22,20)(42,48,46,44) (9,15,13,11)(33,45,41,37)(35,47,43,39);
pA := (2,34,18,36)(26,10,42,12) (1,35,11,23)(17,9,37,3)(19,33,39,21);
pP := (6,38,22,40)(30,14,46,16) (7,25,13,45)(29,27,41,47)(31,5,43 ,15);
pG := (4,12,20,14)(28,36,44,38) (3,39,13,27)(21,11,41,5)(23,37,43,25);
pD := (8,16,24,10)(32,40,48,34) (1,29,15,33)(17,31,45,35)(19,7,47,9);
pGamma := (2,26);
pPsi := (1,17,19);
pOmega := (2,8)(26,32);
ph := (10,36,14,40)(34,12,38,16);
pd := (2,30,22,42)(26,6,46,18);
pa :=  (4,32,24,44)(28,8,48,20);
LAMBDAPLUS :=  Group( pH, pB, pA, pP, pG, pD, pGamma, pPsi, pOmega );
LAMBDA := Group( pH, pB, pA, pP, pG, pD );

Print( "\n" );
Print( "|LAMBDA+| = ",Size( LAMBDAPLUS ), "\n" );
Print( "|LAMBDA| = ", Size( LAMBDA ) , "\n" );
Print( "N = ", 2 * 3 * 2 , "\n" );
Print( "|G+| = ", Factorial(12) * (2^12) * Factorial(8) * (3^8) , "\n" );
Print( "|G| = |G+|/N = ",( Factorial(12) * (2^12) * Factorial(8) * (3^8) ) / ( 2 * 3 * 2 ), "\n" );