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Points :: makeRingMaps

makeRingMaps -- evaluation on points

Synopsis

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 = | 9 7 8 3 6 |
     | 4 6 2 6 0 |
     | 3 0 7 9 3 |

              3        5
o1 : Matrix ZZ  <--- ZZ
i2 : R = QQ[x,y,z]

o2 = R

o2 : PolynomialRing
i3 : phi = makeRingMaps(M,R)

o3 = {map(QQ,R,{9, 4, 3}), map(QQ,R,{7, 6, 0}), map(QQ,R,{8, 2, 7}),
     ------------------------------------------------------------------------
     map(QQ,R,{3, 6, 9}), map(QQ,R,{6, 0, 3})}

o3 : List
i4 : apply (gens(R),r->phi#2 r)

o4 = {8, 2, 7}

o4 : List
i5 : phi#2

o5 = map(QQ,R,{8, 2, 7})

o5 : RingMap QQ <--- R

Ways to use makeRingMaps :