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D.7.4.5 sympower
Procedure from library invar.lib (see invar_lib).
- Usage:
- sympower(<matrix>,<int>)
- Returns:
- If m is a matrix with coefficients in the ring 'group', representing
the action on some vector space V, then sympower(m,n) gives the
matrix of the representation of the group on the n-th symmetric
power of V.
Example:
| | LIB "invar.lib";
SL(2);
print(SLrep);
==> g(1),g(2),
==> g(3),g(4)
print(sympower(SLrep,3));
==> g(1)^3, 3*g(1)^2*g(2), 3*g(1)*g(2)^2, g(2)^3,
==> g(1)^2*g(3),3*g(1)^2*g(4)-2*g(1), 3*g(1)*g(2)*g(4)-g(2),g(2)^2*g(4),
==> g(1)*g(3)^2,3*g(1)*g(3)*g(4)-g(3),3*g(1)*g(4)^2-2*g(4), g(2)*g(4)^2,
==> g(3)^3, 3*g(3)^2*g(4), 3*g(3)*g(4)^2, g(4)^3
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