affineMakeRingMaps -- evaluation on points

Synopsis

• Usage:

  affineMakeRingMaps(M,R)

• Inputs:
  • M, a matrix, in which each column consists of the coordinates of a point
  • R, a polynomial ring, coordinate ring of the affine space containing the points
• Outputs:
  • a list, of ring maps corresponding to evaluations at each point

Description

i1 : M = random(ZZ^3, ZZ^5)

o1 = | 8 7 3 8 8 |
     | 1 8 7 5 5 |
     | 3 3 8 7 2 |

              3        5
o1 : Matrix ZZ  <--- ZZ

i2 : R = QQ[x,y,z]

o2 = R

o2 : PolynomialRing

i3 : phi = affineMakeRingMaps(M,R)

o3 = {map(QQ,R,{8, 1, 3}), map(QQ,R,{7, 8, 3}), map(QQ,R,{3, 7, 8}), map(QQ,R,{8, 5, 7}), map(QQ,R,{8, 5, 2})}

o3 : List

i4 : apply (gens(R),r->phi#2 r)

o4 = {3, 7, 8}

o4 : List

i5 : phi#2

o5 = map(QQ,R,{3, 7, 8})

o5 : RingMap QQ <--- R