Experimenting to find many real points on slices of SO(n)



This website hosts data pertaining to the experiments done in the paper Degree of SO(n).
In short, the experiment involves computing many different linear slices of complementary dimension (or witness sets) for SO(3), SO(4), and SO(5).
For each witness set, we compute the number of real points on it and tally them below.
For an explanation of what the columns in the table mean, click here

Summary Table

Degree Most Real Points # Witness Sets Computed
SO(3) 8 8 1398000
SO(4) 40 30 1004100
SO(5) 384 76 48200







SO(3) Tally Table

#(Real Solutions) FAIL 0 2 4 6 8 Total
SO(3) 2 285676 420049 549875 127699 14699 1398000








Explicit Data

SO(4) Tally Table

#(Real Solutions) FAIL 0 2 4 6 8
SO(4) 51 183427 108273 132143 156010 159630
10 12 14 16 18
124843 76965 38243 16150 5780
20 22 24 26 28
1897 510 145 23 9
30 32 34 36 38
1 0 0 0 0
40 Total
0 1004100



Explicit Data

SO(5) Tally Table

#(Real Solutions) FAIL 0 2 4 6 8
SO(5) 81 6162 2628 2377 2306 2275
10 12 14 16 18
2272 2275 2383 2473 2497
20 22 24 26 28
2527 2504 2485 2280 2009
30 32 34 36 38
1755 1644 1331 1051 802
40 42 44 46 48
591 468 362 235 150
50 52 54 56 58
118 60 44 21 16
60 62 64 66 68
8 4 3 1 0
70 72 74 76 78
0 0 0 2 0
384 Total
0 48200




Explicit Data