homogenize(PolySystem,Ring,RingElement) -- homogenize a polynomial system

Synopsis

• Function: homogenize

• Usage:

  G = sub(F,R,t)

• Inputs:
  • F, a polynomial system
  • R, a ring
  • t, a ring element, a ring element, a variable in R
• Outputs:
  • G, a polynomial system

Description

Constructs a polynomial system that is a homogenization of the given system.

i1 : R = CC[x,y]; S := polySystem {x^2+y^2-6, 2*x^4-y}

o2 = {-2} | x2+y2-6 |
     {-4} | 2x4-y   |

o2 : PolySystem

i3 : T := homogenize(S,CC[x,y,t],t)

o3 = {-2} | x2+y2-6t2 |
     {-4} | 2x4-yt3   |

o3 : PolySystem

i4 : ring T

o4 = CC  [x..y, t]
       53

o4 : PolynomialRing

See also

• homogenize -- homogenize with respect to a variable
• PolySystem -- a polynomial system