#############################################################################
##
#F                             CHEVIE library
##
#Y  Copyright 1992--1993,  Lehrstuhl D f"ur Mathematik,    RWTH Aachen,   and
#Y                         IWR   der   Universit"at    Heidelberg,   Germany.
##
# Orthogonalitaet 
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#                                                                           #
#   Die Greenfunktionen der ^2G2(q^2), q^2 = 3^{2n+1}                        #
#                                                                           #
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##
#A {\sc H. N. Ward}, On Ree's series of simple groups, {\sl Trans.  Am. Math.
#A  Soc. \bf121} (1966), 62--89
##
lprint(`**************************************************************************`);
lprint(`*                                                                        *`);
lprint(`*                                                                        *`);
lprint(`*             Green Functions of ^2G2(q^2), q^2 = 3^{2n+1}               *`);
lprint(`*                                                                        *`);
lprint(`*                                                                        *`);
lprint(`**************************************************************************`);

# tafel der werte

`2G2green` := array(-2..4,-1..7,[

 [`^2G_2(q^2)`, `2G2003green`, q^6*(q^2-1)*(q^2+1)*(q^4-q^2+1), 4, 4, 7, 7], 

 [`classname`, [], [` `], [` `], [` `], [` `], [` `], [` `], [` `]], 

 [`classlength`, 1, 1, (q^2-1)*(q^2+1)*(q^4-q^2+1),
  1/2*q^2*(q^2-1)*(q^2+1)*(q^4-q^2+1),
  1/2*q^2*(q^2-1)*(q^2+1)*(q^4-q^2+1),
  1/3*q^4*(q^2-1)*(q^2+1)*(q^4-q^2+1),
  1/3*q^4*(q^2-1)*(q^2+1)*(q^4-q^2+1),
  1/3*q^4*(q^2-1)*(q^2+1)*(q^4-q^2+1)], 

 [[`T_1`], (q^2+1)*(q^4-q^2+1), (q^2+1)*(q^4-q^2+1), 1, 1, 1, 1, 1, 1], 

 [[`T_2`], -(q^2-1)*(q^4-q^2+1), -(q^2-1)*(q^4-q^2+1), -2*q^2+1, 1, 1, 1, 1,
  1],

 [[`T_3`], -(q^4-1)*(q^2-r3*q+1), -(q^4-1)*(q^2-r3*q+1), q^2-r3*q+1, -r3*q+1,
  -r3*q+1, 1, 1, 1],

 [[`T_4`], -(q^4-1)*(q^2+r3*q+1), -(q^4-1)*(q^2+r3*q+1), q^2+r3*q+1, r3*q+1,
  r3*q+1, 1, 1, 1]
]):

KlassentypOrd2G2003green:=array(1..7,[1,1,1,1,1,1,1]):

NurPolynom2G2003green:=true:

r3 := sqrt(3):

# 5) Informationen:
Information.`2G2003green`:=TEXT(
`- Information about the Green functions of $^2G_2(q^2)$.`,
``,
`- CHEVIE-name of the table: ``2G2green```,
``,
`- The table was first computed in:`,
`  {\\sc H. N. Ward}, On Ree's series of simple groups, {\\em Trans.  Am. Math.`,
`    Soc. \\bf121} (1966), 62--89.`,
``
):

g := `2G2green`;
print(`g := ``2G2green`` `);
