# 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,
• 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 => , default value p, the variable base name, see VariableBaseName
• Outputs:
• , 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 , p , p , p ] 0 1 2 3 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 , p , p , p ] \ | 0 1 2 3 4 | o5 = Spec|-----------------------------------| | 2 2 | |(- p + p , - p p + p , - p + p )| \ 0 2 0 1 3 1 4 / o5 : AffineVariety```