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ideal, submodule with minimal generators
minimalized(E: IDEAL): IDEAL
minimalized(E: MODULE): MODULE |
It works only in the homogeneous case:
for the inhomogeneous case see
MinSubsetOfGens
.
This function returns the ideal (or submodule) generated by a set of minimal
generators of
E
(with minimal cardinality).
The minimal set of generators is not necessarily a subset of the given
generators.
The coefficient ring is assumed to be a field.
The similar function
minimalize
performs the same
operation, but modifies the argument (
ref
) and returns NULL.
/**/ Use R ::= QQ[x,y,z];
/**/ I := ideal(x^2-y^2, z^4-y^4, x^2-z^2);
/**/ I;
ideal(x^2 -y^2, -y^4 +z^4, x^2 -z^2)
/**/ minimalized(I);
ideal(x^2 -z^2, y^2 -z^2)
/**/ I; -- not modified
ideal(x^2 -y^2, -y^4 +z^4, x^2 -z^2)
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