next | previous | forward | backward | up | top | index | toc | Macaulay2 web site

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 = | 1 6 8 9 8 |
     | 9 9 4 7 9 |
     | 0 6 8 4 9 |

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

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

o4 = {8, 4, 8}

o4 : List
i5 : phi#2

o5 = map(QQ,R,{8, 4, 8})

o5 : RingMap QQ <--- R

Ways to use makeRingMaps :