ringFromFractions -- find presentation for f.g. ring

Synopsis

• Usage:

  (F,G) = ringFromFractions(H,f)

• Inputs:
  • H, a matrix, a one row matrix over a ring $R$
  • f, a ring element
• Optional inputs:
  • Variable => a symbol, default value w, name of symbol used for new variables
  • Index => an integer, default value 0, the starting index for new variables
  • Verbosity => an integer, default value 0, values up to 6 are implemented. Larger values show more output.
• Outputs:
  • F, a ring map, $R \rightarrow S$, where $S$ is the extension ring of $R$ generated by the fractions $1/f H$
  • G, a ring map, $frac S \rightarrow frac R$, the fractions

Description

i1 : R = QQ[x,y]/(y^2-x^3)

o1 = R

o1 : QuotientRing

i2 : H = (y * ideal(x,y)) : ideal(x,y)

                2
o2 = ideal (y, x )

o2 : Ideal of R

i3 : (F,G) = ringFromFractions(((gens H)_{1}), H_0);

i4 : S = target F

o4 = S

o4 : QuotientRing

i5 : F

o5 = map(S,R,{x, y})

o5 : RingMap S <--- R

i6 : G

                        y
o6 = map(frac R,frac S,{-, x, y})
                        x

o6 : RingMap frac R <--- frac S