affineMakeRingMaps -- evaluation on points

Synopsis

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

Description

Giving the coordinates of a point in affine space is equivalent to giving a ring map from the polynomial ring to the ground field: evaluation at the point. Given a finite collection of points encoded as the columns of a matrix, this function returns a corresponding list of ring maps.
 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

Ways to use affineMakeRingMaps :

• "affineMakeRingMaps(Matrix,Ring)"

For the programmer

The object affineMakeRingMaps is .