>	read `maple/coxeter2.4v.txt`;

coxeter and weyl 2.4v loaded.

Run 'withcoxeter()' or 'withweyl()' to use abbreviated names.

>	withcoxeter(); withweyl();

Warning: new definition for  tensor

>	diagram(A4);

   1---2---3---4

>	diagram(F4);

   1---2=<=3---4

>	diagram(G2);

   1=<<=2

>	pos_roots(F4);

nops gives number of elements in a list. 24 positive roots implies the dim of F4 is 52.

>

nops(%);

weights gives fundamental weights

>	W := weights(F4);

weyl_dim computes dim of irrep given heighest weight.

>	weyl_dim(W[1],F4);

weight_mults gives weights and their multiplicities within Weyl chamber

>	weight_mults(W[1],F4);

orbit gives orbit under Weyl group

>	o1 := orbit(W[1],F4);

X[a,b,c,d] represents character of irrep with highest weight a,b,c,d w.r.t. fundmental weights.

tensor gives tensor product:

>	tensor(W[1],W[1],F4);

same thing can be done with toX (cp with tos in symmetric function package.)

>	toX(X[1,0,0,0]*X[1,0,0,0],F4);

toM is same as weight_mults. cp with tom in symmetric functions package.

>	toM(X[2,0,0,0],F4);

>