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document {
Key => {
homogenize,
(homogenize, Ideal, RingElement),
--(homogenize, Ideal, RingElement, List), ??
(homogenize, Matrix, RingElement),
(homogenize, Matrix, RingElement, List),
(homogenize, Module, RingElement),
(homogenize, Module, RingElement, List),
(homogenize, Vector, RingElement),
(homogenize, Vector, RingElement, List),
(homogenize, RingElement, RingElement),
(homogenize, RingElement, RingElement, List),
},
Headline => "homogenize with respect to a variable",
TT "homogenize(m,v)", " -- homogenize the ring element, vector,
matrix, or module ", TT "m", " using the variable ", TT "v", " in the ring of ", TT "m", ".",
BR{},
TT "homogenize(m,v,w)", " -- homogenize ", TT "m", " using the variable ", TT "v", ",
so that the result is homogeneous with respect to the given list ", TT "w", " of
integers provided as weights for the variables.",
PARA{},
EXAMPLE {
"R = ZZ/101[x,y,z,Degrees => {1,2,3}]",
"f = 1 + y + z^2",
"homogenize(f,x)",
"homogenize(f,x,{1,0,-1})",
},
PARA{},
"The weights that may be used are limited (roughly) to the range -2^30 .. 2^30.",
PARA{},
Caveat => {
"If the homogenization overflows the monomial, this is not
reported as an error."
}
}
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