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Macaulay2 > substitution and maps between rings > graphRing(RingMap)

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

Synopsis

Usage:
graphRing f
Function: graphRing
Inputs:
- f, a ring map
Outputs:
- a quotient ring, the coordinate ring 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 : graphRing f

     QQ [x, y, s, t, u, Degrees => {{1}, {1}, {2}, {2}, {2}}]
o4 = --------------------------------------------------------
                      2                    2
                  (- x  + s, - x*y + t, - y  + u)

o4 : QuotientRing

i5 : Spec oo

          QQ [x, y, s, t, u, Degrees => {{1}, {1}, {2}, {2}, {2}}]
o5 = Spec(--------------------------------------------------------)
                           2                    2
                       (- x  + s, - x*y + t, - y  + u)

o5 : AffineVariety

See also

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