fromCoordinates -- Compute the ideal of a point from its coordinates

Synopsis

• Usage:

  I = fromCoordinates(L,C)

  I = fromCoordinates(x,y,z, C)

• Inputs:
  • L, a list, of three integers or field elements OR a list of lists of that type
  • x, a ring element,
  • y, a ring element,
  • z, a ring element, integer or field coordinates of a point on C (assumed to be a plane curve)
  • C, a ring, the ring in which the ideal of the point will be created
• Outputs:
  • I, an ideal, of C, defining the subscheme corresponding to the list L of points.

Description

i1 : S = ZZ/101[a,b,c]

o1 = S

o1 : PolynomialRing

i2 : C = S/ideal"a3+b3-c3"

o2 = C

o2 : QuotientRing

i3 : P = {0,1,1}

o3 = {0, 1, 1}

o3 : List

i4 : Q = {1,1,0}

o4 = {1, 1, 0}

o4 : List

i5 : fromCoordinates(P,C)

o5 = ideal (a, - b + c)

o5 : Ideal of C

i6 : fromCoordinates({P,P},C)

             2                             2           2
o6 = ideal (a , - a*b + a*c, - a*b + a*c, b  - 2b*c + c )

o6 : Ideal of C

See also

• toCoordinates -- coordinates of a point from its ideal