The equation H of the model in P3xP5 depend on the variables P3xP53 only quadratically. The constant term of this quadric depends linearly on P3xP54. Thus choosing random integer coordinates of the remaining coordinates allows to compute a point. The input ht specifies the height of the randomly choosen integers
i1 : H = precomputedModelInP3xP5(QQ);
1 1
o1 : Matrix (QQ[w , w , w , w , z , z , z , z , z , z ]) <--- (QQ[w , w , w , w , z , z , z , z , z , z ])
0 1 2 3 0 1 2 3 4 5 0 1 2 3 0 1 2 3 4 5
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i2 : ht=19 o2 = 19 |
i3 : pt=pointOnARationalCodim1Hypersurface(ht)
o3 = | 2 -8 -2 -25/198 -36 -1 -1 6 -1 4 |
1 10
o3 : Matrix QQ <--- QQ
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i4 : substitute(H,pt)
o4 = 0
1 1
o4 : Matrix QQ <--- QQ
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i5 : pt2=fromPointInP3xP5ToPointInP3xP3xP3xP3(pt)
o5 = | 25 -6534 -363 726 -40 33 33 66 25 -2178 363 726 -396 1584 396 25 |
1 16
o5 : Matrix QQ <--- QQ
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i6 : line=fromPointInP3xP3xP3xP3ToLine(pt2)
o6 = | -3267/35 -11/14 8712/35 -35937/175 -39/14 792/7 6171/350 198/7
| -627/280 -125/11088 11/7 99/280 -125/11088 12/7 -55/336 5/28
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-78/7 -9801/25 0 1 |
-25/231 -33/8 1 0 |
2 12
o6 : Matrix QQ <--- QQ
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