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D.7.4.3 torusrep
Procedure from library invar.lib (see invar_lib).
- Usage:
- torusrep(<list>), <list> must be a list of integer vectors of length
n, where n is the dimension of the current torusgroup.
- Returns:
- torusrep(m) gives a matrix with entries in 'group'. This matrix
represents the action of the torus with weights
m[1],m[2],...,m[size(m)]
Example:
| | LIB "invar.lib";
torus(1); // Take the 1-dimensional torus, the multiplicative group.
list weights=-2,-3,7; // 3-dimensial action with weights -2,-3,7
matrix m=torusrep(weights);// compute the matrix of the representation
invar(m); // compute the invariant ring
==>
==> Ideal B:
==> x(1)^2*x(2)*x(3)-y(1)^2*y(2)*y(3),
==> x(2)^2*y(1)^3-x(1)^3*y(2)^2,
==> x(2)^3*x(3)*y(1)-x(1)*y(2)^3*y(3),
==> x(1)^5*x(3)*y(2)-x(2)*y(1)^5*y(3),
==> x(1)*x(2)^4*x(3)^2-y(1)*y(2)^4*y(3)^2,
==> x(1)^7*x(3)^2-y(1)^7*y(3)^2,
==> x(2)^7*x(3)^3-y(2)^7*y(3)^3
==>
==> Zero Fiber Ideal:
==> x(1)^2*x(2)*x(3),
==> x(1)*x(2)^4*x(3)^2,
==> x(1)^7*x(3)^2,
==> x(2)^7*x(3)^3
==>
==> Generating Invariants:
==> x(1)^2*x(2)*x(3),
==> x(1)*x(2)^4*x(3)^2,
==> x(1)^7*x(3)^2,
==> x(2)^7*x(3)^3
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