RequirePackage( name )
RequirePackage will try to initialize the share library name. If the
package name is not installed at your site RequirePackage will signal
an error. If the package name is already initialized RequirePackage
simply returns without any further actions.
gap> CartanMat( "A", 4 );
Error, Variable: 'CartanMat' must have a value
gap> ?CartanMat
CartanMat ________________________ Root systems and finite Coxeter groups
'CartanMat( <type>, <n> )'
returns the Cartan matrix of Dynkin type <type> and rank <n>. Admissible
types are the strings '"A"', '"B"', '"C"', '"D"', '"E"',
'"F"', '"G"', '"H"', '"I"'.
gap> C := CartanMat( "F", 4 );;
gap> PrintArray( C );
[ [ 2, -1, 0, 0 ],
[ -1, 2, -1, 0 ],
[ 0, -2, 2, -1 ],
[ 0, 0, -1, 2 ] ]
For type I_2(m), which is in fact an infinity of types depending on the
number m, a third argument is needed specifying the integer m so the
syntax is in fact 'CartanMat( "I", 2, <m> )':
gap> CartanMat( "I", 2, 5 );
[ [ 2, E(5)^2+E(5)^3 ], [ E(5)^2+E(5)^3, 2 ] ]
'CartanMat( <type1>, <n1>, ... , <typek>, <nk> )'
returns the direct sum of 'CartanMat( <type1>, <n1> )', ldots,
'CartanMat( <typek>, <nk> )'. One can use as argument a computed list of
types by 'ApplyFunc( CartanMat, [ <type1>, <n1>, ... , <typek>, <nk> ] )'.
This function requires the package "chevie" (see "RequirePackage").
gap> RequirePackage( "Chevie" );
Error, share library "Chevie" is not installed in
LoadPackage( name ) called from
RequirePackage( "Chevie" ) called from
main loop
brk> quit;
gap> RequirePackage( "chevie" );
WELCOME to the CHEVIE package, Version 3 (Dec 1996)
Meinolf Geck, Frank Luebeck, Gerhard Hiss,
Gunter Malle, Jean Michel, and Goetz Pfeiffer,
Lehrstuhl D fuer Mathematik, RWTH Aachen,
IWR der Universitaet Heidelberg,
University of St. Andrews and
Universite Paris VII
This replaces the former weyl package. For first help type
?CHEVIE Version 3 -- a short introduction
gap> CartanMat( "A", 4 );;
gap> PrintArray( last );
[ [ 2, -1, 0, 0 ],
[ -1, 2, -1, 0 ],
[ 0, -1, 2, -1 ],
[ 0, 0, -1, 2 ] ]
GAP 3.4.4