def test_benchmark_coloring():
V = range(1, 12 + 1)
E = [(1, 2), (2, 3), (1, 4), (1, 6), (1, 12), (2, 5), (2, 7), (3, 8), (3, 10),
(4, 11), (4, 9), (5, 6), (6, 7), (7, 8), (8, 9), (9, 10), (10, 11),
(11, 12), (5, 12), (5, 9), (6, 10), (7, 11), (8, 12), (3, 4)]
R, V = xring([ "x%d" % v for v in V ], QQ, lex)
E = [(V[i - 1], V[j - 1]) for i, j in E]
x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12 = V
I3 = [x**3 - 1 for x in V]
Ig = [x**2 + x*y + y**2 for x, y in E]
I = I3 + Ig
assert groebner(I[:-1], R) == [
x1 + x11 + x12,
x2 - x11,
x3 - x12,
x4 - x12,
x5 + x11 + x12,
x6 - x11,
x7 - x12,
x8 + x11 + x12,
x9 - x11,
x10 + x11 + x12,
x11**2 + x11*x12 + x12**2,
x12**3 - 1,
]
assert groebner(I, R) == [1]
def _do_test_benchmark_cyclic_4():
R, a,b,c,d = ring("a,b,c,d", ZZ, lex)
I = [a + b + c + d,
a*b + a*d + b*c + b*d,
a*b*c + a*b*d + a*c*d + b*c*d,
a*b*c*d - 1]
assert groebner(I, R) == [
4*a + 3*d**9 - 4*d**5 - 3*d,
4*b + 4*c - 3*d**9 + 4*d**5 + 7*d,
4*c**2 + 3*d**10 - 4*d**6 - 3*d**2,
4*c*d**4 + 4*c - d**9 + 4*d**5 + 5*d, d**12 - d**8 - d**4 + 1
]
R, a,b,c,d = ring("a,b,c,d", ZZ, grlex)
I = [ i.set_ring(R) for i in I ]
assert groebner(I, R) == [
3*b*c - c**2 + d**6 - 3*d**2,
-b + 3*c**2*d**3 - c - d**5 - 4*d,
-b + 3*c*d**4 + 2*c + 2*d**5 + 2*d,
c**4 + 2*c**2*d**2 - d**4 - 2,
c**3*d + c*d**3 + d**4 + 1,
b*c**2 - c**3 - c**2*d - 2*c*d**2 - d**3,
b**2 - c**2, b*d + c**2 + c*d + d**2,
a + b + c + d
]
def test_benchmark_coloring():
V = range(1, 12 + 1)
E = [(1, 2), (2, 3), (1, 4), (1, 6), (1, 12), (2, 5), (2, 7), (3, 8),
(3, 10), (4, 11), (4, 9), (5, 6), (6, 7), (7, 8), (8, 9), (9, 10),
(10, 11), (11, 12), (5, 12), (5, 9), (6, 10), (7, 11), (8, 12),
(3, 4)]
R, V = xring(["x%d" % v for v in V], QQ, lex)
E = [(V[i - 1], V[j - 1]) for i, j in E]
x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12 = V
I3 = [x**3 - 1 for x in V]
Ig = [x**2 + x * y + y**2 for x, y in E]
I = I3 + Ig
assert groebner(I[:-1], R) == [
x1 + x11 + x12,
x2 - x11,
x3 - x12,
x4 - x12,
x5 + x11 + x12,
x6 - x11,
x7 - x12,
x8 + x11 + x12,
x9 - x11,
x10 + x11 + x12,
x11**2 + x11 * x12 + x12**2,
x12**3 - 1,
]
assert groebner(I, R) == [1]
def _do_test_benchmark_katsura_4():
R, x0,x1,x2,x3 = ring("x:4", ZZ, lex)
I = [x0 + 2*x1 + 2*x2 + 2*x3 - 1,
x0**2 + 2*x1**2 + 2*x2**2 + 2*x3**2 - x0,
2*x0*x1 + 2*x1*x2 + 2*x2*x3 - x1,
x1**2 + 2*x0*x2 + 2*x1*x3 - x2]
assert groebner(I, R) == [
5913075*x0 - 159690237696*x3**7 + 31246269696*x3**6 + 27439610544*x3**5 - 6475723368*x3**4 - 838935856*x3**3 + 275119624*x3**2 + 4884038*x3 - 5913075,
1971025*x1 - 97197721632*x3**7 + 73975630752*x3**6 - 12121915032*x3**5 - 2760941496*x3**4 + 814792828*x3**3 - 1678512*x3**2 - 9158924*x3,
5913075*x2 + 371438283744*x3**7 - 237550027104*x3**6 + 22645939824*x3**5 + 11520686172*x3**4 - 2024910556*x3**3 - 132524276*x3**2 + 30947828*x3,
128304*x3**8 - 93312*x3**7 + 15552*x3**6 + 3144*x3**5 -
1120*x3**4 + 36*x3**3 + 15*x3**2 - x3,
]
R, x0,x1,x2,x3 = ring("x:4", ZZ, grlex)
I = [ i.set_ring(R) for i in I ]
assert groebner(I, R) == [
393*x1 - 4662*x2**2 + 4462*x2*x3 - 59*x2 + 224532*x3**4 - 91224*x3**3 - 678*x3**2 + 2046*x3,
-x1 + 196*x2**3 - 21*x2**2 + 60*x2*x3 - 18*x2 - 168*x3**3 + 83*x3**2 - 9*x3,
-6*x1 + 1134*x2**2*x3 - 189*x2**2 - 466*x2*x3 + 32*x2 - 630*x3**3 + 57*x3**2 + 51*x3,
33*x1 + 63*x2**2 + 2268*x2*x3**2 - 188*x2*x3 + 34*x2 + 2520*x3**3 - 849*x3**2 + 3*x3,
7*x1**2 - x1 - 7*x2**2 - 24*x2*x3 + 3*x2 - 15*x3**2 + 5*x3,
14*x1*x2 - x1 + 14*x2**2 + 18*x2*x3 - 4*x2 + 6*x3**2 - 2*x3,
14*x1*x3 - x1 + 7*x2**2 + 32*x2*x3 - 4*x2 + 27*x3**2 - 9*x3,
x0 + 2*x1 + 2*x2 + 2*x3 - 1,
]
def _do_test_benchmark_cyclic_4():
R, a, b, c, d = ring("a,b,c,d", ZZ, lex)
I = [
a + b + c + d, a * b + a * d + b * c + b * d,
a * b * c + a * b * d + a * c * d + b * c * d, a * b * c * d - 1
]
assert groebner(I, R) == [
4 * a + 3 * d**9 - 4 * d**5 - 3 * d,
4 * b + 4 * c - 3 * d**9 + 4 * d**5 + 7 * d,
4 * c**2 + 3 * d**10 - 4 * d**6 - 3 * d**2,
4 * c * d**4 + 4 * c - d**9 + 4 * d**5 + 5 * d, d**12 - d**8 - d**4 + 1
]
R, a, b, c, d = ring("a,b,c,d", ZZ, grlex)
I = [i.set_ring(R) for i in I]
assert groebner(I, R) == [
3 * b * c - c**2 + d**6 - 3 * d**2,
-b + 3 * c**2 * d**3 - c - d**5 - 4 * d,
-b + 3 * c * d**4 + 2 * c + 2 * d**5 + 2 * d,
c**4 + 2 * c**2 * d**2 - d**4 - 2, c**3 * d + c * d**3 + d**4 + 1,
b * c**2 - c**3 - c**2 * d - 2 * c * d**2 - d**3, b**2 - c**2,
b * d + c**2 + c * d + d**2, a + b + c + d
]
def _do_test_benchmark_katsura_4():
R, x0,x1,x2,x3 = ring("x:4", ZZ, lex)
I = [x0 + 2*x1 + 2*x2 + 2*x3 - 1,
x0**2 + 2*x1**2 + 2*x2**2 + 2*x3**2 - x0,
2*x0*x1 + 2*x1*x2 + 2*x2*x3 - x1,
x1**2 + 2*x0*x2 + 2*x1*x3 - x2]
assert groebner(I, R) == [
5913075*x0 - 159690237696*x3**7 + 31246269696*x3**6 + 27439610544*x3**5 - 6475723368*x3**4 - 838935856*x3**3 + 275119624*x3**2 + 4884038*x3 - 5913075,
1971025*x1 - 97197721632*x3**7 + 73975630752*x3**6 - 12121915032*x3**5 - 2760941496*x3**4 + 814792828*x3**3 - 1678512*x3**2 - 9158924*x3,
5913075*x2 + 371438283744*x3**7 - 237550027104*x3**6 + 22645939824*x3**5 + 11520686172*x3**4 - 2024910556*x3**3 - 132524276*x3**2 + 30947828*x3,
128304*x3**8 - 93312*x3**7 + 15552*x3**6 + 3144*x3**5 -
1120*x3**4 + 36*x3**3 + 15*x3**2 - x3,
]
R, x0,x1,x2,x3 = ring("x:4", ZZ, grlex)
I = [ i.set_ring(R) for i in I ]
assert groebner(I, R) == [
393*x1 - 4662*x2**2 + 4462*x2*x3 - 59*x2 + 224532*x3**4 - 91224*x3**3 - 678*x3**2 + 2046*x3,
-x1 + 196*x2**3 - 21*x2**2 + 60*x2*x3 - 18*x2 - 168*x3**3 + 83*x3**2 - 9*x3,
-6*x1 + 1134*x2**2*x3 - 189*x2**2 - 466*x2*x3 + 32*x2 - 630*x3**3 + 57*x3**2 + 51*x3,
33*x1 + 63*x2**2 + 2268*x2*x3**2 - 188*x2*x3 + 34*x2 + 2520*x3**3 - 849*x3**2 + 3*x3,
7*x1**2 - x1 - 7*x2**2 - 24*x2*x3 + 3*x2 - 15*x3**2 + 5*x3,
14*x1*x2 - x1 + 14*x2**2 + 18*x2*x3 - 4*x2 + 6*x3**2 - 2*x3,
14*x1*x3 - x1 + 7*x2**2 + 32*x2*x3 - 4*x2 + 27*x3**2 - 9*x3,
x0 + 2*x1 + 2*x2 + 2*x3 - 1,
]
def _do_test_benchmark_katsura_4():
R, x1, x2, x3, x4 = ring("x1:5", QQ, lex)
I = [
x1 + 2 * x2 + 2 * x3 + 2 * x4 - 1,
x1**2 + 2 * x2**2 + 2 * x3**2 + 2 * x4**2 - x1,
2 * x1 * x2 + 2 * x2 * x3 + 2 * x3 * x4 - x2,
x2**2 + 2 * x1 * x3 + 2 * x2 * x4 - x3
]
assert groebner(I, R)
R, x1, x2, x3, x4 = ring("x1:5", QQ, grlex)
I = [i.set_ring(R) for i in I]
assert groebner(I, R)
def test_is_reduced():
R, x, y = ring("x,y", QQ, lex)
f = x**2 + 2 * x * y**2
g = x * y + 2 * y**3 - 1
assert is_reduced([f, g], R) == False
G = groebner([f, g], R)
assert is_reduced(G, R) == True
def _do_test_benchmark_katsura_5():
R, x1, x2, x3, x4, x5 = ring("x1:6", QQ, lex)
I = [
x1 + 2 * x2 + 2 * x3 + 2 * x4 + 2 * x5 - 1,
x1**2 + 2 * x2**2 + 2 * x3**2 + 2 * x4**2 + 2 * x5**2 - x1,
2 * x1 * x2 + 2 * x2 * x3 + 2 * x3 * x4 + 2 * x4 * x5 - x2,
x2**2 + 2 * x1 * x3 + 2 * x2 * x4 + 2 * x3 * x5 - x3,
2 * x2 * x3 + 2 * x1 * x4 + 2 * x2 * x5 - x4
]
assert groebner(I, R)
R, x1, x2, x3, x4, x5 = ring("x1:6", QQ, grlex)
I = [i.set_ring(R) for i in I]
assert groebner(I, R)
def _do_test_benchmark_czichowski():
R, x, t = ring("x,t", ZZ, lex)
I = [
9 * x**8 + 36 * x**7 - 32 * x**6 -
252 * x**5 - 78 * x**4 + 468 * x**3 + 288 * x**2 - 108 * x + 9,
(-72 - 72 * t) * x**7 + (-256 - 252 * t) * x**6 +
(192 + 192 * t) * x**5 + (1280 + 1260 * t) * x**4 +
(312 + 312 * t) * x**3 + (-404 * t) * x**2 + (-576 - 576 * t) * x +
96 + 108 * t
]
assert groebner(I, R)
R, x, t = ring("x,t", ZZ, grlex)
I = [i.set_ring(R) for i in I]
assert groebner(I, R)
def _do_test_benchmark_minpoly():
R, x,y,z = ring("x,y,z", QQ, lex)
F = [x**3 + x + 1, y**2 + y + 1, (x + y) * z - (x**2 + y)]
G = [x + QQ(155,2067)*z**5 - QQ(355,689)*z**4 + QQ(6062,2067)*z**3 - QQ(3687,689)*z**2 + QQ(6878,2067)*z - QQ(25,53),
y + QQ(4,53)*z**5 - QQ(91,159)*z**4 + QQ(523,159)*z**3 - QQ(387,53)*z**2 + QQ(1043,159)*z - QQ(308,159),
z**6 - 7*z**5 + 41*z**4 - 82*z**3 + 89*z**2 - 46*z + 13]
assert groebner(F, R) == G
def _do_test_benchmark_minpoly():
R, x,y,z = ring("x,y,z", QQ, lex)
F = [x**3 + x + 1, y**2 + y + 1, (x + y) * z - (x**2 + y)]
G = [x + QQ(155,2067)*z**5 - QQ(355,689)*z**4 + QQ(6062,2067)*z**3 - QQ(3687,689)*z**2 + QQ(6878,2067)*z - QQ(25,53),
y + QQ(4,53)*z**5 - QQ(91,159)*z**4 + QQ(523,159)*z**3 - QQ(387,53)*z**2 + QQ(1043,159)*z - QQ(308,159),
z**6 - 7*z**5 + 41*z**4 - 82*z**3 + 89*z**2 - 46*z + 13]
assert groebner(F, R) == G
def _do_test_benchmark_czichowski():
R, x,t = ring("x,t", ZZ, lex)
I = [9*x**8 + 36*x**7 - 32*x**6 - 252*x**5 - 78*x**4 + 468*x**3 + 288*x**2 - 108*x + 9,
(-72 - 72*t)*x**7 + (-256 - 252*t)*x**6 + (192 + 192*t)*x**5 + (1280 + 1260*t)*x**4 + (312 + 312*t)*x**3 + (-404*t)*x**2 + (-576 - 576*t)*x + 96 + 108*t]
assert groebner(I, R) == [
-160420835591776763325581422211936558925462474417709511019228211783493866564923546661604487873*t**7 - 1406108495478033395547109582678806497509499966197028487131115097902188374051595011248311352864*t**6 - 5241326875850889518164640374668786338033653548841427557880599579174438246266263602956254030352*t**5 - 10758917262823299139373269714910672770004760114329943852726887632013485035262879510837043892416*t**4 - 13119383576444715672578819534846747735372132018341964647712009275306635391456880068261130581248*t**3 - 9491412317016197146080450036267011389660653495578680036574753839055748080962214787557853941760*t**2 - 3767520915562795326943800040277726397326609797172964377014046018280260848046603967211258368000*t + 3725588592068034903797967297424801242396746870413359539263038139343329273586196480000*x - 632314652371226552085897259159210286886724229880266931574701654721512325555116066073245696000,
610733380717522355121*t**8 + 6243748742141230639968*t**7 + 27761407182086143225024*t**6 + 70066148869420956398592*t**5 + 109701225644313784229376*t**4 + 109009005495588442152960*t**3 + 67072101084384786432000*t**2 + 23339979742629593088000*t + 3513592776846090240000
]
R, x,t = ring("x,t", ZZ, grlex)
I = [ i.set_ring(R) for i in I ]
assert groebner(I, R) == [
16996618586000601590732959134095643086442*t**3*x - 32936701459297092865176560282688198064839*t**3 + 78592411049800639484139414821529525782364*t**2*x - 120753953358671750165454009478961405619916*t**2 + 120988399875140799712152158915653654637280*t*x - 144576390266626470824138354942076045758736*t + 60017634054270480831259316163620768960*x**2 + 61976058033571109604821862786675242894400*x - 56266268491293858791834120380427754600960,
576689018321912327136790519059646508441672750656050290242749*t**4 + 2326673103677477425562248201573604572527893938459296513327336*t**3 + 110743790416688497407826310048520299245819959064297990236000*t**2*x + 3308669114229100853338245486174247752683277925010505284338016*t**2 + 323150205645687941261103426627818874426097912639158572428800*t*x + 1914335199925152083917206349978534224695445819017286960055680*t + 861662882561803377986838989464278045397192862768588480000*x**2 + 235296483281783440197069672204341465480107019878814196672000*x + 361850798943225141738895123621685122544503614946436727532800,
-117584925286448670474763406733005510014188341867*t**3 + 68566565876066068463853874568722190223721653044*t**2*x - 435970731348366266878180788833437896139920683940*t**2 + 196297602447033751918195568051376792491869233408*t*x - 525011527660010557871349062870980202067479780112*t + 517905853447200553360289634770487684447317120*x**3 + 569119014870778921949288951688799397569321920*x**2 + 138877356748142786670127389526667463202210102080*x - 205109210539096046121625447192779783475018619520,
-3725142681462373002731339445216700112264527*t**3 + 583711207282060457652784180668273817487940*t**2*x - 12381382393074485225164741437227437062814908*t**2 + 151081054097783125250959636747516827435040*t*x**2 + 1814103857455163948531448580501928933873280*t*x - 13353115629395094645843682074271212731433648*t + 236415091385250007660606958022544983766080*x**2 + 1390443278862804663728298060085399578417600*x - 4716885828494075789338754454248931750698880
]
def _do_test_benchmark_katsura_3():
R, x0,x1,x2 = ring("x:3", ZZ, lex)
I = [x0 + 2*x1 + 2*x2 - 1,
x0**2 + 2*x1**2 + 2*x2**2 - x0,
2*x0*x1 + 2*x1*x2 - x1]
assert groebner(I, R) == [
-7 + 7*x0 + 8*x2 + 158*x2**2 - 420*x2**3,
7*x1 + 3*x2 - 79*x2**2 + 210*x2**3,
x2 + x2**2 - 40*x2**3 + 84*x2**4,
]
R, x0,x1,x2 = ring("x:3", ZZ, grlex)
I = [ i.set_ring(R) for i in I ]
assert groebner(I, R) == [
7*x1 + 3*x2 - 79*x2**2 + 210*x2**3,
-x1 + x2 - 3*x2**2 + 5*x1**2,
-x1 - 4*x2 + 10*x1*x2 + 12*x2**2,
-1 + x0 + 2*x1 + 2*x2,
]
def _do_test_benchmark_katsura_3():
R, x0,x1,x2 = ring("x:3", ZZ, lex)
I = [x0 + 2*x1 + 2*x2 - 1,
x0**2 + 2*x1**2 + 2*x2**2 - x0,
2*x0*x1 + 2*x1*x2 - x1]
assert groebner(I, R) == [
-7 + 7*x0 + 8*x2 + 158*x2**2 - 420*x2**3,
7*x1 + 3*x2 - 79*x2**2 + 210*x2**3,
x2 + x2**2 - 40*x2**3 + 84*x2**4,
]
R, x0,x1,x2 = ring("x:3", ZZ, grlex)
I = [ i.set_ring(R) for i in I ]
assert groebner(I, R) == [
7*x1 + 3*x2 - 79*x2**2 + 210*x2**3,
-x1 + x2 - 3*x2**2 + 5*x1**2,
-x1 - 4*x2 + 10*x1*x2 + 12*x2**2,
-1 + x0 + 2*x1 + 2*x2,
]
def time_vertex_color_12_vertices_23_edges():
assert groebner(F_1, R) != [1]
def _do_test_benchmark_cyc442():
R, x1, x2, x3, x4, x5, x6, x7, x8 = ring("x1:9", QQ, lex)
I = [
23476 * x1**2 + 14715 * x1 * x2 + 23476 * x2**2 + 50124 * x1 * x3 +
14715 * x2 * x3 + 23476 * x3**2 + 14715 * x1 * x4 + 50124 * x2 * x4 +
14715 * x3 * x4 + 23476 * x4**2 + 3250 * x1 * x5 + 3250 * x2 * x5 +
3250 * x3 * x5 + 3250 * x4 * x5 + 63946 * x5**2 + 3250 * x1 * x6 +
3250 * x2 * x6 + 3250 * x3 * x6 + 3250 * x4 * x6 + 64414 * x5 * x6 +
63946 * x6**2 + 3250 * x1 * x7 + 3250 * x2 * x7 + 3250 * x3 * x7 +
3250 * x4 * x7 + 65369 * x5 * x7 + 64414 * x6 * x7 + 63946 * x7**2 +
3250 * x1 * x8 + 3250 * x2 * x8 + 3250 * x3 * x8 + 3250 * x4 * x8 +
64414 * x5 * x8 + 65369 * x6 * x8 + 64414 * x7 * x8 + 63946 * x8**2 +
25135 * x1 + 25135 * x2 + 25135 * x3 + 25135 * x4 + 50952 * x5 +
50952 * x6 + 50952 * x7 + 50952 * x8 + 44161, 49110 * x1**2 +
44186 * x1 * x2 + 49110 * x2**2 + 32144 * x1 * x3 + 44186 * x2 * x3 +
49110 * x3**2 + 44186 * x1 * x4 + 32144 * x2 * x4 + 44186 * x3 * x4 +
49110 * x4**2 + 2181 * x1 * x5 + 2181 * x2 * x5 + 2181 * x3 * x5 +
2181 * x4 * x5 + 60239 * x5**2 + 2181 * x1 * x6 + 2181 * x2 * x6 +
2181 * x3 * x6 + 2181 * x4 * x6 + 16370 * x5 * x6 + 60239 * x6**2 +
2181 * x1 * x7 + 2181 * x2 * x7 + 2181 * x3 * x7 + 2181 * x4 * x7 +
9899 * x5 * x7 + 16370 * x6 * x7 + 60239 * x7**2 + 2181 * x1 * x8 +
2181 * x2 * x8 + 2181 * x3 * x8 + 2181 * x4 * x8 + 16370 * x5 * x8 +
9899 * x6 * x8 + 16370 * x7 * x8 + 60239 * x8**2 + 10103 * x1 +
10103 * x2 + 10103 * x3 + 10103 * x4 + 29709 * x5 + 29709 * x6 +
29709 * x7 + 29709 * x8 + 19872, 2486 * x1**2 + 10248 * x1 * x2 +
2486 * x2**2 + 38090 * x1 * x3 + 10248 * x2 * x3 + 2486 * x3**2 +
10248 * x1 * x4 + 38090 * x2 * x4 + 10248 * x3 * x4 + 2486 * x4**2 +
62189 * x1 * x5 + 62189 * x2 * x5 + 62189 * x3 * x5 + 62189 * x4 * x5 +
25668 * x5**2 + 62189 * x1 * x6 + 62189 * x2 * x6 + 62189 * x3 * x6 +
62189 * x4 * x6 + 4404 * x5 * x6 + 25668 * x6**2 + 62189 * x1 * x7 +
62189 * x2 * x7 + 62189 * x3 * x7 + 62189 * x4 * x7 + 57891 * x5 * x7 +
4404 * x6 * x7 + 25668 * x7**2 + 62189 * x1 * x8 + 62189 * x2 * x8 +
62189 * x3 * x8 + 62189 * x4 * x8 + 4404 * x5 * x8 + 57891 * x6 * x8 +
4404 * x7 * x8 + 25668 * x8**2 + 28022 * x1 + 28022 * x2 + 28022 * x3 +
28022 * x4 + 63038 * x5 + 63038 * x6 + 63038 * x7 + 63038 * x8 + 48379,
55159 * x1**2 + 24927 * x1 * x2 + 55159 * x2**2 + 3744 * x1 * x3 +
24927 * x2 * x3 + 55159 * x3**2 + 24927 * x1 * x4 + 3744 * x2 * x4 +
24927 * x3 * x4 + 55159 * x4**2 + 53739 * x1 * x5 + 53739 * x2 * x5 +
53739 * x3 * x5 + 53739 * x4 * x5 + 44289 * x5**2 + 53739 * x1 * x6 +
53739 * x2 * x6 + 53739 * x3 * x6 + 53739 * x4 * x6 + 3420 * x5 * x6 +
44289 * x6**2 + 53739 * x1 * x7 + 53739 * x2 * x7 + 53739 * x3 * x7 +
53739 * x4 * x7 + 45104 * x5 * x7 + 3420 * x6 * x7 + 44289 * x7**2 +
53739 * x1 * x8 + 53739 * x2 * x8 + 53739 * x3 * x8 + 53739 * x4 * x8 +
3420 * x5 * x8 + 45104 * x6 * x8 + 3420 * x7 * x8 + 44289 * x8**2 +
63145 * x1 + 63145 * x2 + 63145 * x3 + 63145 * x4 + 56087 * x5 +
56087 * x6 + 56087 * x7 + 56087 * x8 + 6681,
43228 * x1**2 + 21944 * x1 * x2 + 43228 * x2**2 + 51728 * x1 * x3 +
21944 * x2 * x3 + 43228 * x3**2 + 21944 * x1 * x4 + 51728 * x2 * x4 +
21944 * x3 * x4 + 43228 * x4**2 + 30646 * x1 * x5 + 30646 * x2 * x5 +
30646 * x3 * x5 + 30646 * x4 * x5 + 40094 * x5**2 + 30646 * x1 * x6 +
30646 * x2 * x6 + 30646 * x3 * x6 + 30646 * x4 * x6 + 46610 * x5 * x6 +
40094 * x6**2 + 30646 * x1 * x7 + 30646 * x2 * x7 + 30646 * x3 * x7 +
30646 * x4 * x7 + 57385 * x5 * x7 + 46610 * x6 * x7 + 40094 * x7**2 +
30646 * x1 * x8 + 30646 * x2 * x8 + 30646 * x3 * x8 + 30646 * x4 * x8 +
46610 * x5 * x8 + 57385 * x6 * x8 + 46610 * x7 * x8 + 40094 * x8**2 +
53245 * x1 + 53245 * x2 + 53245 * x3 + 53245 * x4 + 13928 * x5 +
13928 * x6 + 13928 * x7 + 13928 * x8 + 55454, 65262 * x1**2 +
6014 * x1 * x2 + 65262 * x2**2 + 21339 * x1 * x3 + 6014 * x2 * x3 +
65262 * x3**2 + 6014 * x1 * x4 + 21339 * x2 * x4 + 6014 * x3 * x4 +
65262 * x4**2 + 55081 * x1 * x5 + 55081 * x2 * x5 + 55081 * x3 * x5 +
55081 * x4 * x5 + 20275 * x5**2 + 55081 * x1 * x6 + 55081 * x2 * x6 +
55081 * x3 * x6 + 55081 * x4 * x6 + 38604 * x5 * x6 + 20275 * x6**2 +
55081 * x1 * x7 + 55081 * x2 * x7 + 55081 * x3 * x7 + 55081 * x4 * x7 +
1791 * x5 * x7 + 38604 * x6 * x7 + 20275 * x7**2 + 55081 * x1 * x8 +
55081 * x2 * x8 + 55081 * x3 * x8 + 55081 * x4 * x8 + 38604 * x5 * x8 +
1791 * x6 * x8 + 38604 * x7 * x8 + 20275 * x8**2 + 34133 * x1 +
34133 * x2 + 34133 * x3 + 34133 * x4 + 57403 * x5 + 57403 * x6 +
57403 * x7 + 57403 * x8 + 37546, 44187 * x1**2 + 43904 * x1 * x2 +
44187 * x2**2 + 22080 * x1 * x3 + 43904 * x2 * x3 + 44187 * x3**2 +
43904 * x1 * x4 + 22080 * x2 * x4 + 43904 * x3 * x4 + 44187 * x4**2 +
12927 * x1 * x5 + 12927 * x2 * x5 + 12927 * x3 * x5 + 12927 * x4 * x5 +
9924 * x5**2 + 12927 * x1 * x6 + 12927 * x2 * x6 + 12927 * x3 * x6 +
12927 * x4 * x6 + 64529 * x5 * x6 + 9924 * x6**2 + 12927 * x1 * x7 +
12927 * x2 * x7 + 12927 * x3 * x7 + 12927 * x4 * x7 + 55702 * x5 * x7 +
64529 * x6 * x7 + 9924 * x7**2 + 12927 * x1 * x8 + 12927 * x2 * x8 +
12927 * x3 * x8 + 12927 * x4 * x8 + 64529 * x5 * x8 + 55702 * x6 * x8 +
64529 * x7 * x8 + 9924 * x8**2 + 45703 * x1 + 45703 * x2 + 45703 * x3 +
45703 * x4 + 22994 * x5 + 22994 * x6 + 22994 * x7 + 22994 * x8 + 65108,
6275 * x1**2 + 56393 * x1 * x2 + 6275 * x2**2 + 54764 * x1 * x3 +
56393 * x2 * x3 + 6275 * x3**2 + 56393 * x1 * x4 + 54764 * x2 * x4 +
56393 * x3 * x4 + 6275 * x4**2 + 53580 * x1 * x5 + 53580 * x2 * x5 +
53580 * x3 * x5 + 53580 * x4 * x5 + 42217 * x5**2 + 53580 * x1 * x6 +
53580 * x2 * x6 + 53580 * x3 * x6 + 53580 * x4 * x6 + 23516 * x5 * x6 +
42217 * x6**2 + 53580 * x1 * x7 + 53580 * x2 * x7 + 53580 * x3 * x7 +
53580 * x4 * x7 + 4442 * x5 * x7 + 23516 * x6 * x7 + 42217 * x7**2 +
53580 * x1 * x8 + 53580 * x2 * x8 + 53580 * x3 * x8 + 53580 * x4 * x8 +
23516 * x5 * x8 + 4442 * x6 * x8 + 23516 * x7 * x8 + 42217 * x8**2 +
25434 * x1 + 25434 * x2 + 25434 * x3 + 25434 * x4 + 46919 * x5 +
46919 * x6 + 46919 * x7 + 46919 * x8 + 58727
]
assert groebner(I, R)
R, x1, x2, x3, x4, x5, x6, x7, x8 = ring("x1:9", QQ, grlex)
I = [i.set_ring(R) for i in I]
assert groebner(I, R)
def _do_test_groebner():
R, x, y = ring("x,y", QQ, lex)
f = x**2 + 2 * x * y**2
g = x * y + 2 * y**3 - 1
assert groebner([f, g], R) == [x, y**3 - QQ(1, 2)]
R, y, x = ring("y,x", QQ, lex)
f = 2 * x**2 * y + y**2
g = 2 * x**3 + x * y - 1
assert groebner([f, g], R) == [y, x**3 - QQ(1, 2)]
R, x, y, z = ring("x,y,z", QQ, lex)
f = x - z**2
g = y - z**3
assert groebner([f, g], R) == [f, g]
R, x, y = ring("x,y", QQ, grlex)
f = x**3 - 2 * x * y
g = x**2 * y + x - 2 * y**2
assert groebner([f, g], R) == [x**2, x * y, -QQ(1, 2) * x + y**2]
R, x, y, z = ring("x,y,z", QQ, lex)
f = -x**2 + y
g = -x**3 + z
assert groebner([f, g],
R) == [x**2 - y, x * y - z, x * z - y**2, y**3 - z**2]
R, x, y, z = ring("x,y,z", QQ, grlex)
f = -x**2 + y
g = -x**3 + z
assert groebner([f, g],
R) == [y**3 - z**2, x**2 - y, x * y - z, x * z - y**2]
R, x, y, z = ring("x,y,z", QQ, lex)
f = -x**2 + z
g = -x**3 + y
assert groebner([f, g],
R) == [x**2 - z, x * y - z**2, x * z - y, y**2 - z**3]
R, x, y, z = ring("x,y,z", QQ, grlex)
f = -x**2 + z
g = -x**3 + y
assert groebner([f, g],
R) == [-y**2 + z**3, x**2 - z, x * y - z**2, x * z - y]
R, x, y, z = ring("x,y,z", QQ, lex)
f = x - y**2
g = -y**3 + z
assert groebner([f, g], R) == [x - y**2, y**3 - z]
R, x, y, z = ring("x,y,z", QQ, grlex)
f = x - y**2
g = -y**3 + z
assert groebner([f, g], R) == [x**2 - y * z, x * y - z, -x + y**2]
R, x, y, z = ring("x,y,z", QQ, lex)
f = x - z**2
g = y - z**3
assert groebner([f, g], R) == [x - z**2, y - z**3]
R, x, y, z = ring("x,y,z", QQ, grlex)
f = x - z**2
g = y - z**3
assert groebner([f, g], R) == [x**2 - y * z, x * z - y, -x + z**2]
R, x, y, z = ring("x,y,z", QQ, lex)
f = -y**2 + z
g = x - y**3
assert groebner([f, g], R) == [x - y * z, y**2 - z]
R, x, y, z = ring("x,y,z", QQ, grlex)
f = -y**2 + z
g = x - y**3
assert groebner([f, g],
R) == [-x**2 + z**3, x * y - z**2, y**2 - z, -x + y * z]
R, x, y, z = ring("x,y,z", QQ, lex)
f = y - z**2
g = x - z**3
assert groebner([f, g], R) == [x - z**3, y - z**2]
R, x, y, z = ring("x,y,z", QQ, grlex)
f = y - z**2
g = x - z**3
assert groebner([f, g],
R) == [-x**2 + y**3, x * z - y**2, -x + y * z, -y + z**2]
R, x, y, z = ring("x,y,z", QQ, lex)
f = 4 * x**2 * y**2 + 4 * x * y + 1
g = x**2 + y**2 - 1
assert groebner([f, g], R) == [
x - 4 * y**7 + 8 * y**5 - 7 * y**3 + 3 * y,
y**8 - 2 * y**6 + QQ(3, 2) * y**4 - QQ(1, 2) * y**2 + QQ(1, 16),
]
def time_vertex_color_12_vertices_24_edges():
assert groebner(F_2, R) == [1]
def _do_test_groebner():
R, x,y = ring("x,y", QQ, lex)
f = x**2 + 2*x*y**2
g = x*y + 2*y**3 - 1
assert groebner([f, g], R) == [x, y**3 - QQ(1,2)]
R, y,x = ring("y,x", QQ, lex)
f = 2*x**2*y + y**2
g = 2*x**3 + x*y - 1
assert groebner([f, g], R) == [y, x**3 - QQ(1,2)]
R, x,y,z = ring("x,y,z", QQ, lex)
f = x - z**2
g = y - z**3
assert groebner([f, g], R) == [f, g]
R, x,y = ring("x,y", QQ, grlex)
f = x**3 - 2*x*y
g = x**2*y + x - 2*y**2
assert groebner([f, g], R) == [x**2, x*y, -QQ(1,2)*x + y**2]
R, x,y,z = ring("x,y,z", QQ, lex)
f = -x**2 + y
g = -x**3 + z
assert groebner([f, g], R) == [x**2 - y, x*y - z, x*z - y**2, y**3 - z**2]
R, x,y,z = ring("x,y,z", QQ, grlex)
f = -x**2 + y
g = -x**3 + z
assert groebner([f, g], R) == [y**3 - z**2, x**2 - y, x*y - z, x*z - y**2]
R, x,y,z = ring("x,y,z", QQ, lex)
f = -x**2 + z
g = -x**3 + y
assert groebner([f, g], R) == [x**2 - z, x*y - z**2, x*z - y, y**2 - z**3]
R, x,y,z = ring("x,y,z", QQ, grlex)
f = -x**2 + z
g = -x**3 + y
assert groebner([f, g], R) == [-y**2 + z**3, x**2 - z, x*y - z**2, x*z - y]
R, x,y,z = ring("x,y,z", QQ, lex)
f = x - y**2
g = -y**3 + z
assert groebner([f, g], R) == [x - y**2, y**3 - z]
R, x,y,z = ring("x,y,z", QQ, grlex)
f = x - y**2
g = -y**3 + z
assert groebner([f, g], R) == [x**2 - y*z, x*y - z, -x + y**2]
R, x,y,z = ring("x,y,z", QQ, lex)
f = x - z**2
g = y - z**3
assert groebner([f, g], R) == [x - z**2, y - z**3]
R, x,y,z = ring("x,y,z", QQ, grlex)
f = x - z**2
g = y - z**3
assert groebner([f, g], R) == [x**2 - y*z, x*z - y, -x + z**2]
R, x,y,z = ring("x,y,z", QQ, lex)
f = -y**2 + z
g = x - y**3
assert groebner([f, g], R) == [x - y*z, y**2 - z]
R, x,y,z = ring("x,y,z", QQ, grlex)
f = -y**2 + z
g = x - y**3
assert groebner([f, g], R) == [-x**2 + z**3, x*y - z**2, y**2 - z, -x + y*z]
R, x,y,z = ring("x,y,z", QQ, lex)
f = y - z**2
g = x - z**3
assert groebner([f, g], R) == [x - z**3, y - z**2]
R, x,y,z = ring("x,y,z", QQ, grlex)
f = y - z**2
g = x - z**3
assert groebner([f, g], R) == [-x**2 + y**3, x*z - y**2, -x + y*z, -y + z**2]
R, x,y,z = ring("x,y,z", QQ, lex)
f = 4*x**2*y**2 + 4*x*y + 1
g = x**2 + y**2 - 1
assert groebner([f, g], R) == [
x - 4*y**7 + 8*y**5 - 7*y**3 + 3*y,
y**8 - 2*y**6 + QQ(3,2)*y**4 - QQ(1,2)*y**2 + QQ(1,16),
]
def time_vertex_color_12_vertices_24_edges():
assert groebner(F_2, R) == [1]
def time_vertex_color_12_vertices_23_edges():
assert groebner(F_1, R) != [1]
for i in range(len(var_str_list)):
new_var = r_v[1][i]
exec(var_str_list[i] + ' = ' + 'new_var')
exec('var_list.append({})'.format(var_str_list[i]))
I = None
R = r_v[0]
exec('I = ' + sys_string)
print(fname + ' Starting ...')
print(I)
print(R)
start_f5b = time.time()
res_f5b = groebner(I, R, method="f5b")
end_f5b = time.time()
f5b_runtime = end_f5b - start_f5b
start_cp_gpu = time.time()
res_cp_gpu = f5b_gpu.run(I, R, True, False) # Only GPU CP
end_cp_gpu = time.time()
cp_gpu_runtime = end_cp_gpu - start_cp_gpu
cp_match = res_f5b == res_cp_gpu
start_sp_gpu = time.time()
res_sp_gpu = f5b_gpu.run(I, R, False, True) # Only GPU Spoly
end_sp_gpu = time.time()
sp_gpu_runtime = end_sp_gpu - start_sp_gpu
sp_match = res_f5b == res_sp_gpu
