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NumericalGodeaux :: findPointInP3xP5

findPointInP3xP5 -- find a point on the model in P3xP5

Synopsis

Description

Substituting random values for all but one of the the coordinates we get a quadratic equation for the last coordinate, which in about 50 % of the cases has a kk-rational root.

i1 : kk=ZZ/(nextPrime 10^3)

o1 = kk

o1 : QuotientRing
 
i2 : H = precomputedModelInP3xP5(kk);

                                1                          1
o2 : Matrix (kk[w ..w , z ..z ])  <--- (kk[w ..w , z ..z ])
                 0   3   0   5              0   3   0   5
 
i3 : pt=findPointInP3xP5(kk)

o3 = | 107 -389 280 -176 115 -298 72 378 275 252 |

              1        10
o3 : Matrix kk  <--- kk
 
i4 : substitute(H,pt)

o4 = 0

              1        1
o4 : Matrix kk  <--- kk

See also

Ways to use findPointInP3xP5 :

For the programmer

The object findPointInP3xP5 is a method function.