(W_{})^{8} = 126 on Gr(4;8) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
type | # real solutions | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 | 32 | 34 | 36 | 38 | 40 | 42 | 44 | 46 | 48 | 50 | 52 | 54 | 56 | 58 | 60 | 62 | 64 | 66 | 68 | 70 | 72 | 74 | 76 | 78 | 80 | 82 | 84 | 86 | 88 | 90 | 92 | 94 | 96 | 98 | 100 | 102 | 104 | 106 | 108 | 110 | 112 | 114 | 116 | 118 | 120 | 122 | 124 | 126 | total | |
8r0c | 1000 | 1000 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
6r1c | 6 | 6 | 10 | 88 | 616 | 830 | 554 | 1888 | 1832 | 1747 | 2916 | 2744 | 4160 | 3187 | 3589 | 2732 | 2383 | 1846 | 3150 | 1409 | 5135 | 1222 | 917 | 814 | 675 | 681 | 697 | 930 | 868 | 2020 | 671 | 648 | 1023 | 236 | 408 | 734 | 262 | 380 | 346 | 196 | 162 | 270 | 155 | 110 | 416 | 100 | 77 | 174 | 61 | 72 | 103 | 63 | 56 | 42 | 133 | 52 | 50 | 182 | 76 | 69 | 2021 | 59000 | |||
4r2c | 2614 | 3771 | 2497 | 1512 | 3285 | 1579 | 1378 | 1074 | 974 | 567 | 848 | 523 | 650 | 338 | 268 | 235 | 377 | 183 | 239 | 105 | 89 | 72 | 74 | 83 | 64 | 69 | 55 | 64 | 46 | 41 | 44 | 23 | 23 | 31 | 13 | 14 | 20 | 7 | 11 | 14 | 3 | 10 | 15 | 4 | 3 | 8 | 6 | 5 | 6 | 3 | 2 | 1 | 9 | 4 | 1 | 3 | 4 | 1 | 38 | 24000 | |||||
2r3c | 8896 | 4479 | 1667 | 1620 | 1079 | 721 | 2586 | 595 | 478 | 215 | 292 | 188 | 163 | 106 | 63 | 56 | 62 | 27 | 55 | 29 | 16 | 16 | 11 | 15 | 3 | 4 | 7 | 6 | 7 | 7 | 6 | 2 | 3 | 5 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 23500 | ||||||||||||||||||
0r4c | 19134 | 1585 | 606 | 287 | 361 | 158 | 123 | 32 | 35 | 28 | 40 | 28 | 20 | 7 | 4 | 12 | 2 | 8 | 1 | 6 | 2 | 4 | 1 | 1 | 1 | 1 | 2 | 3 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 23500 |
>: ./Shapiro.out >: bertini Shapiro.bertini >: alphaCertified Shapiro.poly nonsingular_solutions settings > output >: sh scour.sh
[MTV] | E. Mukhin, V. Tarasov, A. Varchenko, The B and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz, Annals of Mathematics, 170 (2009), 863—991. |
[S00] | F. Sottile, Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro, Experimental Mathematics, 9 (2000), 161—182. |
[S10] | F. Sottile, Frontiers of Reality in Schubert Calculus, Bulletin of the American Mathematical Society, 47 (2010), 31—71. |