graphRing(RingMap) -- the coordinate ring of the graph of the regular map corresponding to a ring map

Synopsis

• Function: graphRing

• Usage:

  graphRing f

• Inputs:
  • f, a ring map
• Optional inputs:
  • MonomialOrder => ..., default value {GRevLex, Position => Up}, a monomial ordering, see monomial orderings
  • MonomialSize => an integer, default value 32, the monomial size, see MonomialSize
  • VariableBaseName => a symbol, default value "p", the variable base name, see VariableBaseName
• Outputs:
  • a quotient ring, the coordinate ring of the graph of regular map corresponding to f

Description

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : S = QQ[s,t,u]

o2 = S

o2 : PolynomialRing

i3 : f = map(R,S,{x^2,x*y,y^2})

                  2        2
o3 = map (R, S, {x , x*y, y })

o3 : RingMap R <-- S

i4 : graphRing f

                  QQ[p ..p ]
                      0   4
o4 = -----------------------------------
         2                       2
     (- p  + p , - p p  + p , - p  + p )
         0    2     0 1    3     1    4

o4 : QuotientRing

i5 : Spec oo

         /             QQ[p ..p ]            \
         |                 0   4             |
o5 = Spec|-----------------------------------|
         |    2                       2      |
         |(- p  + p , - p p  + p , - p  + p )|
         \    0    2     0 1    3     1    4 /

o5 : AffineVariety

See also

• graphIdeal -- the ideal of the graph of the regular map corresponding to a ring map