This function is a variant of the randomKRationalPoint function, which has been further improved and extended in the package MultiprojectiveVarieties, see point(MultiprojectiveVariety).
Below we verify the birationality of a rational map.
i1 : f = inverseMap specialQuadraticTransformation(9,ZZ/33331); o1 : RationalMap (cubic rational map from 8-dimensional subvariety of PP^11 to PP^8) |
i2 : time p = point source f
-- used 0.322125 seconds
o2 = ideal (y - 9235y , y + 11075y , y - 5847y , y + 7396y , y +
10 11 9 11 8 11 7 11 6
------------------------------------------------------------------------
13530y , y + 4359y , y - 2924y , y + 13040y , y + 6904y , y -
11 5 11 4 11 3 11 2 11 1
------------------------------------------------------------------------
12227y , y - 5653y )
11 0 11
ZZ
-----[y ..y ]
33331 0 11
o2 : Ideal of -------------------------------------------------------------------------------------------------------
(y y - y y + y y , y y - y y + y y , y y - y y + y y , y y - y y + y y , y y - y y + y y )
6 7 5 8 4 11 3 7 2 8 1 11 3 5 2 6 0 11 3 4 1 6 0 8 2 4 1 5 0 7
|
i3 : time p == f^* f p
-- used 0.239661 seconds
o3 = true
|
The object point is a method function.