homogenize -- homogenize with respect to a variable

homogenize -- homogenize with respect to a variable

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 :

homogenize(Ideal,RingElement)

homogenize(Matrix,RingElement)

homogenize(Matrix,RingElement,List)

homogenize(Module,RingElement)

homogenize(Module,RingElement,List)

homogenize(RingElement,RingElement)

homogenize(RingElement,RingElement,List)

homogenize(Vector,RingElement)

homogenize(Vector,RingElement,List)