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--- status: DRAFT
--- author(s): L.Gold
--- notes: needs good example, maybe:
--- dim of scheme is degree of reduced denominator
document {
Key => {reduceHilbert, (reduceHilbert,Divide)},
Headline => "reduce a Hilbert series expression",
Usage => "reduceHilbert H",
Inputs => {
"H" => Divide
},
Outputs => {
Divide => {"the Hilbert series reduced by removing common factors"}
},
PARA {
"This function is used to reduce the rational expression
given by the command ", TO "hilbertSeries",
". It is not automatically reduced, but sometimes it is
useful to write it in reduced form. For instance, one might
not notice that the series is a polynomial until it is
reduced."
},
EXAMPLE {
"R = ZZ/101[x, Degrees => {2}];",
"I = ideal x^2;",
"s = hilbertSeries I",
"reduceHilbert s"
},
PARA {
"The reduction is partial, in the sense that the explicit factors of
the denominator are cancelled entirely or not at all."
},
EXAMPLE lines ///
M = R^{0,-1}
hilbertSeries M
f = reduceHilbert oo
gcd( value numerator f, value denominator f )
///
}
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