D.16.1.6 lowerHomogeneitySpace

Syntax:

lowerHomogeneitySpace( poly g )
lowerHomogeneitySpace( ideal I )

Type:

cone

Purpose:

the cone of all weight vectors with non-positive first entry with respect to whom g or I is homogeneous.

Example:

LIB "gfanlib.so"; ring r = integer,(t,x,y,z),dp; poly g = tx+t2y; cone homogSpace = lowerHomogeneitySpace(g); rays(homogSpace); ==> -2,-1,1,0 generatorsOfLinealitySpace(homogSpace); ==> 0,-1,-1, 0, ==> 0, 0, 0,-1 ideal I = tx+y, t2y+z; homogSpace = lowerHomogeneitySpace(I); rays(homogSpace); ==> -3,4,1,-5 generatorsOfLinealitySpace(homogSpace); ==> 0,-1,-1,-1