graphIdeal(RingMap) -- the ideal of the graph of the regular map corresponding to a ring map

Synopsis

• Usage:

  graphIdeal f

• Function: graphIdeal
• Inputs:

  • f, a ring map
• Outputs:

  • an ideal, the ideal of the graph of regular map corresponding to f
• 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

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 : graphIdeal f

               2                    2
o4 = ideal (- x  + s, - x*y + t, - y  + u)

o4 : Ideal of QQ [x, y, s, t, u, Degrees => {{1}, {1}, {2}, {2}, {2}}]

See also

• graphRing -- the coordinate ring of the graph of the regular map corresponding to a ring map