Difference between revisions of "CoCoA:Minimalized"
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Minimalized
remove redundant generators
Description
In the inhomogeneous case it returns the ideal or module
obtained by removing redundant generators from E.
In the homogeneous case, it obtains a generating set with smallest
possible cardinality. The minimal set of generators found by CoCoA is
not necessarily a subset of the given generators. It returns the minimalized ideal or module.
The coefficient ring is assumed to be a field.
The similar function <ttref>Minimalize</ttref> performs the same
operation, but modifies the argument and returns NULL.
Example
Use R ::= Q[x,y,z]; I := Ideal(x-y^2,z-y^5,x^5-z^2); I; Ideal(-y^2 + x, -y^5 + z, x^5 - z^2) ------------------------------- Minimalized(I); Ideal(-y^2 + x, -y^5 + z) ------------------------------- I; Ideal(-y^2 + x, -y^5 + z, x^5 - z^2) ------------------------------- Minimalize(I); I; Ideal(-y^2 + x, -y^5 + z) ------------------------------- J := Ideal(x, x-y, y-z, z^2); Minimalized(J); Ideal(y - z, x - z, z) -------------------------------
Syntax
Minimalized(E:IDEAL):IDEAL Minimalized(E:MODULE):MODULE where X is a variable containing an ideal or module.
<type>ideal</type> <type>module</type>