Preliminary Implementation in Magma
Tor-mac F5 (Magma code) and some examples in data file (you have to download both files)
To run the examples if you to change the following line in sparse_issac.magma:
// Choose one benchmark
bench:=EX2;
// replace this line by bench:=EX1; or bench:=EX3;
// EX1 is a small example of fewnomials (very sparse random support): 50 variables
// EX2 is a medium size example of fewnomials sparse: 150 variables
// EX3 is a bilinear system: two blocks of variables of size (7,30): 37 variables
You can also replace the prime number p0 by another one (the system is generated randomly with the same support). |
m Bi-Homogeneous equations of bi-degree (2,1) in (nx,ny) variables
| (2,49,65) |
(9,2,29) |
(9,3,36) |
(9,4,43) |
(10,1,26) |
(10,2,33) |
| (10,4,50) |
(10,6,66) |
(11,2,39) |
(11,5,66) |
(11,6,76) |
(12,2,44) |
| (12,6,86) |
(13,2,50) |
(14,1,42) |
(14,2,56) |
(15,1,47) |
(16,1,52) |
| (1,99,101) |
(1,14,16) |
(1,19,21) |
(1,24,26) |
(1,29,31) |
(1,34,36) |
(1,39,41) |
| (1,44,46) |
(1,49,51) |
(2,60,61) |
(2,99,144) |
(2,9,16) |
(2,11,19) |
(2,13,22) |
| (2,15,25) |
(2,17,27) |
(2,19,30) |
(2,24,37) |
(2,34,52) |
(2,44,66) |
| (2,49,73) |
(2,4,9) |
(2,59,87) |
(2,79,115) |
(2,7,13) |
(3,9,22) |
(3,10,24) |
| (3,11,26) |
(3,12,28) |
(3,14,32) |
(3,19,41) |
(3,24,51) |
(3,29,61) |
| (3,39,80) |
(3,59,119) |
(4,6,16) |
(3,7,18) |
(3,8,20) |
(8,2,25) |
(8,3,30) |
| (nx,ny) |
m |
Tor-Mac |
Tor-mac F5 |
FGb |
Size Tor |
Size FGb |
| (1,14) |
16 |
0.02s |
0.01s |
0.4s |
545x545 |
|
| (1,19) |
21 |
0.1s |
0.02s |
3.3s |
967x967 |
25849x12673 |
| (1,24) |
26 |
0.2s |
0.06s |
21.8s |
1511x1511 |
58852x27763 |
| (1,29) |
31 |
0.6s |
0.09s |
112.9s |
2165x2165 |
115830x53161 |
| (1,34) |
36 |
1.3s |
0.2s |
395.1s |
2947x2947 |
205075x91605 |
| (1,39) |
41 |
2.9s |
0.45s |
1641s |
3851x3851 |
373433x163568 |
| (1,44) |
46 |
4.85s |
0.75s |
3168.8s |
4860x4860 |
536245x234118 |
| (1,49) |
51 |
9.0s |
1.6s |
|
6002x6002 |
|
| (2,59) |
61 |
24.5s |
3.7s |
|
8630x8630 |
|
| (1,99) |
101 |
|
22.1s |
|
23961x23961 |
|
CPU Time (MacBook Pro - Core i7 - 16Go RAM
| (nx,ny) |
m |
Tor-Mac |
Tor-mac F5 |
FGb |
Size Tor |
Size FGb |
| (2,4) |
9 |
0.01s |
0.00s |
0.02s |
216x207 |
661x626 |
| (2,7) |
13 |
0.02s |
0.01s |
0.9s |
515x511 |
8860x3679 |
| (2,9) |
16 |
0.06s |
0.02s |
6.5s |
803x788 |
15454x9190 |
| (2,11) |
19 |
0.1s |
0.04s |
25.5s |
1149x1122 |
39941x17098 |
| (2,13) |
22 |
0.25s |
0.3s |
92.5s |
1560x1518 |
38499x27600 |
| (2,15) |
25 |
0.47s |
0.09s |
410.1s |
2030x1970 |
67062x45946 |
| (2,17) |
27 |
1.0s |
0.15s |
1894.7s |
2486x2486 |
115330x82040 |
| (2,19) |
30 |
1.5s |
0.4s |
5866.1s |
3075x3060 |
179401x123139 |
| (2,24) |
37 |
5.0s |
1.2s |
|
4760x4751 |
|
| (2,44) |
66 |
128.0s |
12.4s |
|
15377x15227 |
|
| (2,99) |
144 |
|
789.0s |
|
74984x74630 |
|
CPU Time (MacBook Pro - Core i7 - 16Go RAM
| (nx,ny) |
m |
Tor-Mac |
Tor-mac F5 |
FGb |
Size Tor |
Size FGb |
| (14,1) |
42 |
51.6s |
4.1s |
100.7s |
9142x9103 |
37791x18119 |
| (15,1) |
47 |
100.9s |
7.9s |
|
11613x11538 |
50619x23751 |
| (16,1) |
52 |
|
14.9s |
|
14490x14439 |
|
|
| (nx,ny) |
m |
Tor-Mac |
Tor-mac F5 |
FGb |
Size Tor |
Size FGb |
| (8,2) |
25 |
2.1s |
0.3s |
2.4s |
3031x2926 |
17135x6929 |
| (9,2) |
29 |
6.1s |
0.7s |
8.05s |
4325x4236 |
29579x11510 |
| (10,2) |
33 |
|
1.6s |
25.65s |
5947x5947 |
14481x10942 |
| (11,2) |
39 |
|
3.8s |
162.0s |
8313x8118 |
29831x20909 |
| (12,2) |
44 |
|
8.5s |
204.3s |
10988x10842 |
29831x20909 |
| (13,2) |
50 |
|
18.1s |
439.8s |
14433x14188 |
41162x27926 |
| (14,2) |
56 |
|
36.0s |
967.7s |
18513x18253 |
55501x37035 |
CPU Time (MacBook Pro - Core i7 - 16Go RAM
| (nx,ny) |
m |
Tor-Mac |
Tor-mac F5 |
FGb |
Size Tor |
Size FGb |
| (8,3) |
30 |
9.5s |
1.1s |
13.30s |
4910x4895 |
|
| (9,3) |
36 |
26.7s |
3.1s |
36.1s |
7221x7081 |
16047x12871 |
CPU Time (MacBook Pro - Core i7 - 16Go RAM
| (nx,ny) |
m |
Tor-Mac |
Tor-mac F5 |
FGb |
Size Tor |
Size FGb |
| (8,2) |
25 |
2.1s |
0.3s |
2.4s |
3031x2926 |
17135x6929 |
| (9,3) |
36 |
26.7s |
3.1s |
36.1s |
7221x7081 |
16047x12871 |
| (10,4) |
50 |
|
23.1s |
1687.3s |
15184x14924 |
35729x28590 |
| (11,5) |
66 |
|
155.1s |
6265.8s |
28616x28538 |
308931x128567 |
| (12,6) |
86 |
|
872.2s |
27093.3s |
50969x50802 |
601239x252664 |
CPU Time (MacBook Pro - Core i7 - 16Go RAM
| (nx,ny) |
m |
Tor-Mac |
Tor-mac F5 |
FGb |
Size Tor |
Size FGb |
| (8,3) |
30 |
9.5s |
1.1s |
13.30s |
4910x4895 |
|
| (9,4) |
43 |
|
9.0s |
135.6s |
10846x10649 |
90475x38327 |
CPU Time (MacBook Pro - Core i7 - 16Go RAM
m Bi-Homogeneous equations of bi-degree (1,1) in (nx,ny) variables
| (2,29,40) |
(2,39,53) |
(2,49,65) |
| (2,59,78) |
(2,69,91) |
(6,19,52) |
| (6,21,56) |
(6,27,71) |
(6,29,76) |
| (nx,ny) |
m |
Tor-Mac |
Tor-mat F5 |
FGb |
Size Tor |
Size FGb |
| (2,29) |
40 |
0.7s |
|
5.2s |
2576x2546 |
42655x19375 |
| (2,39) |
53 |
2.6s |
|
36.7s |
4708x4646 |
110012x48684 |
| (2,49) |
65 |
7.6s |
1.36s |
298.5s |
6784x6764 |
271115x117390 |
| (2,59) |
78 |
19.3s |
4.86s |
852.3s |
9804x9747 |
499888x213391 |
| (6,19) |
52 |
3.65s |
1.10s |
25.2s |
5496x5422 |
100952x41849 |
| (6,21) |
56 |
5.7s |
1.96s |
51.5s |
6566x6566 |
141112x57884 |
| (6,27) |
71 |
18.2s |
7.07s |
236.0s |
10700x10637 |
300290x121981 |
CPU Time (MacBook Pro - Core i7 - 16Go RAM
|
