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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 = | 6 9 2 7 4 |
     | 0 9 5 0 1 |
     | 1 2 7 3 8 |

              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,{6, 0, 1}), map(QQ,R,{9, 9, 2}), map(QQ,R,{2, 5, 7}),
     ------------------------------------------------------------------------
     map(QQ,R,{7, 0, 3}), map(QQ,R,{4, 1, 8})}

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

o4 = {2, 5, 7}

o4 : List
i5 : phi#2

o5 = map(QQ,R,{2, 5, 7})

o5 : RingMap QQ <--- R

Ways to use makeRingMaps :