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Macaulay2Doc :: homogenize

homogenize -- homogenize with respect to a variable

Description

homogenize(m,v) -- homogenize the ring element, vector, matrix, or module m using the variable v in the ring of m.
homogenize(m,v,w) -- homogenize m using the variable v, so that the result is homogeneous with respect to the given list w of integers provided as weights for the variables.

i1 : R = ZZ/101[x,y,z,Degrees => {1,2,3}]

o1 = R

o1 : PolynomialRing
i2 : f = 1 + y + z^2

      2
o2 = z  + y + 1

o2 : R
i3 : homogenize(f,x)

      6    4     2
o3 = x  + x y + z

o3 : R
i4 : homogenize(f,x,{1,0,-1})

      2 2
o4 = x z  + y + 1

o4 : R

The weights that may be used are limited (roughly) to the range -2^30 .. 2^30.

Caveat

If the homogenization overflows the monomial, this is not reported as an error.

Ways to use homogenize :