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

RandomPlaneCurves (missing documentation) :: imageUnderRationalMap

imageUnderRationalMap -- Compute the image of the scheme under a rational map

Synopsis

Usage:
I = imageUnderRationalMap(J,L)
Inputs:
- J, an ideal, in a polynomial ring
- L, a matrix, of homogeneous polynomials of equal degrees
Outputs:
- I, an ideal, of the image of the scheme defined by J under the rational map defined by L

Description

i1 : p=nextPrime 10000

o1 = 10007

i2 : kk=ZZ/p

o2 = kk

o2 : QuotientRing

i3 : R=kk[t_0,t_1]

o3 = R

o3 : PolynomialRing

i4 : I=ideal 0_R

o4 = ideal 0

o4 : Ideal of R

i5 : L=matrix{{t_0^4,t_0^3*t_1,t_0*t_1^3,t_1^4}}

o5 = | t_0^4 t_0^3t_1 t_0t_1^3 t_1^4 |

             1       4
o5 : Matrix R  <--- R

i6 : J=imageUnderRationalMap(I,L)

                          3      2     2    2     3    2
o6 = ideal (x x  - x x , x  - x x , x x  - x x , x  - x x )
             1 2    0 3   2    1 3   0 2    1 3   1    0 2

o6 : Ideal of kk[x , x , x , x ]
                  0   1   2   3

i7 : betti J

            0 1
o7 = total: 1 4
         0: 1 .
         1: . 1
         2: . 3

o7 : BettiTally

Ways to use `imageUnderRationalMap` :

imageUnderRationalMap(Ideal,Matrix)