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7.5.10.0. makeUe8
Procedure from library ncalg.lib (see ncalg_lib).

Usage:
makeUe8([p]); p an optional integer (field characteristic)

Return:
a ring, describing U(e_8)

Note:
You have to activate this ring with the 'setring' command. The presentation of U(e_8) is derived from the Chevalley representation of e_8, positive resp. negative roots are denoted by x(i) resp. y(i); Cartan elements are denoted by h(i).

Example:
 
LIB "ncalg.lib";
def ncAlgebra = makeUe8();
ncAlgebra;
==> // coefficients: QQ
==> // number of vars : 248
==> //        block   1 : ordering dp
==> //                  : names    X(1) X(2) X(3) X(4) X(5) X(6) X(7) X(8) X(\
   9) X(10) X(11) X(12) X(13) X(14) X(15) X(16) X(17) X(18) X(19) X(20) X(21\
   ) X(22) X(23) X(24) X(25) X(26) X(27) X(28) X(29) X(30) X(31) X(32) X(33)\
    X(34) X(35) X(36) X(37) X(38) X(39) X(40) X(41) X(42) X(43) X(44) X(45) \
   X(46) X(47) X(48) X(49) X(50) X(51) X(52) X(53) X(54) X(55) X(56) X(57) X\
   (58) X(59) X(60) X(61) X(62) X(63) X(64) X(65) X(66) X(67) X(68) X(69) X(\
   70) X(71) X(72) X(73) X(74) X(75) X(76) X(77) X(78) X(79) X(80) X(81) X(8\
   2) X(83) X(84) X(85) X(86) X(87) X(88) X(89) X(90) X(91) X(92) X(93) X(94\
   ) X(95) X(96) X(97) X(98) X(99) X(100) X(101) X(102) X(103) X(104) X(105)\
    X(106) X(107) X(108) X(109) X(110) X(111) X(112) X(113) X(114) X(115) X(\
   116) X(117) X(118) X(119) X(120) Y(1) Y(2) Y(3) Y(4) Y(5) Y(6) Y(7) Y(8) \
   Y(9) Y(10) Y(11) Y(12) Y(13) Y(14) Y(15) Y(16) Y(17) Y(18) Y(19) Y(20) Y(\
   21) Y(22) Y(23) Y(24) Y(25) Y(26) Y(27) Y(28) Y(29) Y(30) Y(31) Y(32) Y(3\
   3) Y(34) Y(35) Y(36) Y(37) Y(38) Y(39) Y(40) Y(41) Y(42) Y(43) Y(44) Y(45\
   ) Y(46) Y(47) Y(48) Y(49) Y(50) Y(51) Y(52) Y(53) Y(54) Y(55) Y(56) Y(57)\
    Y(58) Y(59) Y(60) Y(61) Y(62) Y(63) Y(64) Y(65) Y(66) Y(67) Y(68) Y(69) \
   Y(70) Y(71) Y(72) Y(73) Y(74) Y(75) Y(76) Y(77) Y(78) Y(79) Y(80) Y(81) Y\
   (82) Y(83) Y(84) Y(85) Y(86) Y(87) Y(88) Y(89) Y(90) Y(91) Y(92) Y(93) Y(\
   94) Y(95) Y(96) Y(97) Y(98) Y(99) Y(100) Y(101) Y(102) Y(103) Y(104) Y(10\
   5) Y(106) Y(107) Y(108) Y(109) Y(110) Y(111) Y(112) Y(113) Y(114) Y(115) \
   Y(116) Y(117) Y(118) Y(119) Y(120) H(1) H(2) H(3) H(4) H(5) H(6) H(7) H(8\
   )
==> //        block   2 : ordering C
==> // noncommutative relations: ...
setring ncAlgebra;
// ...  7752  noncommutative relations
See also: makeUe6; makeUe7; makeUe8; makeUf4; makeUg2; makeUsl; makeUso5; makeUsp1.


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