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D.7.4.1 SL

Procedure from library invar.lib (see invar_lib).

Usage:
SL(<int>)

Returns:
SL(n) sets the current group to SL_n. The following global variables will be set:
group of type <ring>
groupideal of type <ideal>
SLrep of type <matrix>
reynolds of type <proc>
The quotient of of `group` and `groupideal` is the coordinate ring of SL_n. The matrix `SLrep` will be set to the standard representation of SL_n. The basering will be set to 'group'.

Example:
 
LIB "invar.lib";
SL(3);
Invar::group;
==> // coefficients: QQ
==> // number of vars : 9
==> //        block   1 : ordering dp
==> //                  : names    g(1) g(2) g(3) g(4) g(5) g(6) g(7) g(8) g(\
   9)
==> //        block   2 : ordering C
groupideal;
==> groupideal[1]=g(3)*g(5)*g(7)-g(2)*g(6)*g(7)-g(3)*g(4)*g(8)+g(1)*g(6)*g(8)\
   +g(2)*g(4)*g(9)-g(1)*g(5)*g(9)+1
print(SLrep);
==> g(1),g(2),g(3),
==> g(4),g(5),g(6),
==> g(7),g(8),g(9)