71 KiB
71 KiB
In [39]:
reset() load('ZetaFunctionsNewtonND.py') R.<x,y,z> = QQ[] F=z^3 -3*(x^2*y^2 + x^5 + y^5)*z + 2*x^3*y^3 + x^7 + y^7 D=F.discriminant(z) ZF = ZetaFunctions(F)
In [40]:
ZF.is_newton_degenerated()
Out[40]:
True
In [41]:
D
Out[41]:
108*x^15 + 324*x^10*y^5 + 324*x^5*y^10 + 108*y^15 - 27*x^14 + 324*x^12*y^2 + 594*x^7*y^7 + 324*x^2*y^12 - 27*y^14 - 108*x^10*y^3 + 324*x^9*y^4 + 324*x^4*y^9 - 108*x^3*y^10
In [42]:
d = ZetaFunctions(D) d.give_info_newton()
Newton's polyhedron of 108*x^15 + 324*x^10*y^5 + 324*x^5*y^10 + 108*y^15 - 27*x^14 + 324*x^12*y^2 + 594*x^7*y^7 + 324*x^2*y^12 - 27*y^14 - 108*x^10*y^3 + 324*x^9*y^4 + 324*x^4*y^9 - 108*x^3*y^10:
support points = [(15, 0, 0), (10, 5, 0), (5, 10, 0), (0, 15, 0), (14, 0, 0), (12, 2, 0), (7, 7, 0), (2, 12, 0), (0, 14, 0), (10, 3, 0), (9, 4, 0), (4, 9, 0), (3, 10, 0)]
vertices = [(0, 14, 0), (14, 0, 0), (3, 10, 0), (10, 3, 0)]
number of proper faces = 19
Facet 0: 3*x + 4*y - 42 >= 0
Facet 1: x + y - 13 >= 0
Facet 2: x >= 0
Facet 3: 4*x + 3*y - 42 >= 0
Facet 4: y >= 0
Facet 5: z >= 0
In [43]:
F1=F(x=x*y) D1=D(x=x*y)/y^13 F1b=F(y=x*y) D1b=D(y=x*y)/x^13 ZF1 = ZetaFunctions(F1) ZF1b = ZetaFunctions(F1b)
In [44]:
d1=D1(y=0) d1b=D1b(x=0) (d1/x^3).factor(),(d1b/y^3).factor()
Out[44]:
((-108) * (x + 1) * (x^6 - 4*x^5 + 4*x^4 - 4*x^3 + 4*x^2 - 4*x + 1), (-108) * (y + 1) * (y^6 - 4*y^5 + 4*y^4 - 4*y^3 + 4*y^2 - 4*y + 1))
In [45]:
F1t=F1(x=x+1) F1bt=F1b(y=y+1) ZF1t = ZetaFunctions(F1t) ZF1bt = ZetaFunctions(F1bt) ZF1t.is_newton_degenerated(local=True), ZF1bt.is_newton_degenerated(local=True)
Out[45]:
(True, True)
In [46]:
ZF1t.give_info_newton()
Newton's polyhedron of x^7*y^7 + 7*x^6*y^7 + 21*x^5*y^7 + 35*x^4*y^7 - 3*x^5*y^5*z + 35*x^3*y^7 - 15*x^4*y^5*z + 2*x^3*y^6 + 21*x^2*y^7 - 30*x^3*y^5*z + 6*x^2*y^6 + 7*x*y^7 - 30*x^2*y^5*z + 6*x*y^6 + 2*y^7 - 3*x^2*y^4*z - 15*x*y^5*z + 2*y^6 - 6*x*y^4*z - 6*y^5*z - 3*y^4*z + z^3:
support points = [(7, 7, 0), (6, 7, 0), (5, 7, 0), (4, 7, 0), (5, 5, 1), (3, 7, 0), (4, 5, 1), (3, 6, 0), (2, 7, 0), (3, 5, 1), (2, 6, 0), (1, 7, 0), (2, 5, 1), (1, 6, 0), (0, 7, 0), (2, 4, 1), (1, 5, 1), (0, 6, 0), (1, 4, 1), (0, 5, 1), (0, 4, 1), (0, 0, 3)]
vertices = [(0, 0, 3), (0, 6, 0)]
number of proper faces = 11
Facet 0: x >= 0
Facet 1: y >= 0
Facet 2: y + 2*z - 6 >= 0
Facet 3: z >= 0
In [47]:
ZF1bt.give_info_newton()
Newton's polyhedron of x^7*y^7 + 7*x^7*y^6 + 21*x^7*y^5 + 35*x^7*y^4 - 3*x^5*y^5*z + 35*x^7*y^3 - 15*x^5*y^4*z + 21*x^7*y^2 + 2*x^6*y^3 - 30*x^5*y^3*z + 7*x^7*y + 6*x^6*y^2 - 30*x^5*y^2*z + 2*x^7 + 6*x^6*y - 15*x^5*y*z - 3*x^4*y^2*z + 2*x^6 - 6*x^5*z - 6*x^4*y*z - 3*x^4*z + z^3:
support points = [(7, 7, 0), (7, 6, 0), (7, 5, 0), (7, 4, 0), (5, 5, 1), (7, 3, 0), (5, 4, 1), (7, 2, 0), (6, 3, 0), (5, 3, 1), (7, 1, 0), (6, 2, 0), (5, 2, 1), (7, 0, 0), (6, 1, 0), (5, 1, 1), (4, 2, 1), (6, 0, 0), (5, 0, 1), (4, 1, 1), (4, 0, 1), (0, 0, 3)]
vertices = [(0, 0, 3), (6, 0, 0)]
number of proper faces = 11
Facet 0: x + 2*z - 6 >= 0
Facet 1: x >= 0
Facet 2: y >= 0
Facet 3: z >= 0
In [48]:
cF1t = 2*y^6 - 3*y^4*z + z^3 cF1t.factor()
Out[48]:
(2*y^2 + z) * (-y^2 + z)^2
In [49]:
NF1t=F1t(z=z+y^2) ZNF1t = ZetaFunctions(NF1t) ZNF1t.is_newton_degenerated(local=True)
Out[49]:
True
In [50]:
ZNF1t.give_info_newton()
Newton's polyhedron of x^7*y^7 + 7*x^6*y^7 + 18*x^5*y^7 + 20*x^4*y^7 - 3*x^5*y^5*z + 5*x^3*y^7 - 15*x^4*y^5*z + 2*x^3*y^6 - 9*x^2*y^7 - 30*x^3*y^5*z + 3*x^2*y^6 - 8*x*y^7 - 30*x^2*y^5*z - 4*y^7 - 3*x^2*y^4*z - 15*x*y^5*z - 6*x*y^4*z - 6*y^5*z + 3*y^2*z^2 + z^3:
support points = [(7, 7, 0), (6, 7, 0), (5, 7, 0), (4, 7, 0), (5, 5, 1), (3, 7, 0), (4, 5, 1), (3, 6, 0), (2, 7, 0), (3, 5, 1), (2, 6, 0), (1, 7, 0), (2, 5, 1), (0, 7, 0), (2, 4, 1), (1, 5, 1), (1, 4, 1), (0, 5, 1), (0, 2, 2), (0, 0, 3)]
vertices = [(0, 0, 3), (0, 2, 2), (2, 6, 0), (0, 7, 0)]
number of proper faces = 17
Facet 0: y >= 0
Facet 1: x >= 0
Facet 2: x + 2*y + 5*z - 14 >= 0
Facet 3: y + 2*z - 6 >= 0
Facet 4: z >= 0
In [51]:
ZNF1t.newton_plot()
Out[51]:
In [52]:
aux=3*x^2*y^6 - 6*x*y^4*z + 3*y^2*z^2 aux.factor()
Out[52]:
(3) * y^2 * (-x*y^2 + z)^2
In [53]:
NNF1t=NF1t(z=z+x*y^2) ZNNF1t = ZetaFunctions(NNF1t) ZNNF1t.is_newton_degenerated(local=True)
Out[53]:
False
In [54]:
ZNNF1t.give_info_newton()
Newton's polyhedron of x^7*y^7 + 4*x^6*y^7 + 3*x^5*y^7 - 10*x^4*y^7 - 3*x^5*y^5*z - 25*x^3*y^7 - 15*x^4*y^5*z - 24*x^2*y^7 - 30*x^3*y^5*z - 14*x*y^7 - 30*x^2*y^5*z - 4*y^7 - 15*x*y^5*z - 6*y^5*z + 3*x*y^2*z^2 + 3*y^2*z^2 + z^3:
support points = [(7, 7, 0), (6, 7, 0), (5, 7, 0), (4, 7, 0), (5, 5, 1), (3, 7, 0), (4, 5, 1), (2, 7, 0), (3, 5, 1), (1, 7, 0), (2, 5, 1), (0, 7, 0), (1, 5, 1), (0, 5, 1), (1, 2, 2), (0, 2, 2), (0, 0, 3)]
vertices = [(0, 0, 3), (0, 2, 2), (0, 7, 0)]
number of proper faces = 15
Facet 0: y + 2*z - 6 >= 0
Facet 1: y >= 0
Facet 2: x >= 0
Facet 3: z >= 0
Facet 4: 2*y + 5*z - 14 >= 0
Traslaccion de un golpe
In [57]:
GF1t=F1t(z=z+y^2+x*y^2) ZGF1t = ZetaFunctions(GF1t) ZGF1t.is_newton_degenerated(local=True)
Out[57]:
False
In [58]:
ZGF1t.give_info_newton()
Newton's polyhedron of x^7*y^7 + 4*x^6*y^7 + 3*x^5*y^7 - 10*x^4*y^7 - 3*x^5*y^5*z - 25*x^3*y^7 - 15*x^4*y^5*z - 24*x^2*y^7 - 30*x^3*y^5*z - 14*x*y^7 - 30*x^2*y^5*z - 4*y^7 - 15*x*y^5*z - 6*y^5*z + 3*x*y^2*z^2 + 3*y^2*z^2 + z^3:
support points = [(7, 7, 0), (6, 7, 0), (5, 7, 0), (4, 7, 0), (5, 5, 1), (3, 7, 0), (4, 5, 1), (2, 7, 0), (3, 5, 1), (1, 7, 0), (2, 5, 1), (0, 7, 0), (1, 5, 1), (0, 5, 1), (1, 2, 2), (0, 2, 2), (0, 0, 3)]
vertices = [(0, 0, 3), (0, 2, 2), (0, 7, 0)]
number of proper faces = 15
Facet 0: y + 2*z - 6 >= 0
Facet 1: y >= 0
Facet 2: x >= 0
Facet 3: z >= 0
Facet 4: 2*y + 5*z - 14 >= 0
In [ ]:
In [ ]:
In [ ]:
In [22]:
F1=z^3 -3*(((y^2+2*x^3)^2+x^5*y)*(((x^2+y^3)^2+y^7*x)))*z + 2*((y^4*x^13)*(x^4*y^13)) + x^40 + y^40 D1=F1.discriminant(z) ZD1 = ZetaFunctions(D1) ZD1.is_newton_degenerated()
Out[22]:
True
In [23]:
ZD1.give_info_newton()
Newton's polyhedron of -27*x^80 - 54*x^40*y^40 - 27*y^80 - 108*x^57*y^17 - 108*x^17*y^57 - 108*x^34*y^34 + 6912*x^21*y^21 + 5184*x^20*y^22 + 1296*x^19*y^23 + 108*x^18*y^24 + 20736*x^18*y^23 + 10368*x^17*y^24 + 1296*x^16*y^25 + 20736*x^20*y^20 + 15552*x^19*y^21 + 3888*x^18*y^22 + 324*x^17*y^23 + 25920*x^15*y^25 + 7776*x^14*y^26 + 324*x^13*y^27 + 41472*x^22*y^17 + 31104*x^21*y^18 + 7776*x^20*y^19 + 648*x^19*y^20 + 62208*x^17*y^22 + 31104*x^16*y^23 + 3888*x^15*y^24 + 17280*x^12*y^27 + 2592*x^11*y^28 + 20736*x^24*y^14 + 15552*x^23*y^15 + 3888*x^22*y^16 + 324*x^21*y^17 + 145152*x^19*y^19 + 77760*x^18*y^20 + 11664*x^17*y^21 + 324*x^16*y^22 + 77760*x^14*y^24 + 23328*x^13*y^25 + 972*x^12*y^26 + 6480*x^9*y^29 + 324*x^8*y^30 + 145152*x^21*y^16 + 93312*x^20*y^17 + 19440*x^19*y^18 + 1296*x^18*y^19 + 217728*x^16*y^21 + 77760*x^15*y^22 + 5832*x^14*y^23 + 51840*x^11*y^26 + 7776*x^10*y^27 + 1296*x^6*y^31 + 124416*x^23*y^13 + 93312*x^22*y^14 + 23328*x^21*y^15 + 1944*x^20*y^16 + 333504*x^18*y^18 + 152928*x^17*y^19 + 17820*x^16*y^20 + 108*x^15*y^21 + 181440*x^13*y^23 + 38880*x^12*y^24 + 972*x^11*y^25 + 19440*x^8*y^28 + 972*x^7*y^29 + 108*x^3*y^33 + 82944*x^25*y^10 + 62208*x^24*y^11 + 15552*x^23*y^12 + 1296*x^22*y^13 + 414720*x^20*y^15 + 217728*x^19*y^16 + 31104*x^18*y^17 + 648*x^17*y^18 + 383616*x^15*y^20 + 111456*x^14*y^21 + 5184*x^13*y^22 + 90720*x^10*y^25 + 9720*x^9*y^26 + 3888*x^5*y^30 + 20736*x^27*y^7 + 15552*x^26*y^8 + 3888*x^25*y^9 + 324*x^24*y^10 + 352512*x^22*y^12 + 202176*x^21*y^13 + 34992*x^20*y^14 + 1620*x^19*y^15 + 590976*x^17*y^17 + 202176*x^16*y^18 + 13608*x^15*y^19 + 252720*x^12*y^22 + 39852*x^11*y^23 + 324*x^10*y^24 + 27216*x^7*y^27 + 972*x^6*y^28 + 324*x^2*y^32 + 200448*x^24*y^9 + 134784*x^23*y^10 + 29808*x^22*y^11 + 2160*x^21*y^12 + 622080*x^19*y^14 + 248832*x^18*y^15 + 23328*x^17*y^16 + 466560*x^14*y^19 + 93312*x^13*y^20 + 1944*x^12*y^21 + 98928*x^9*y^24 + 6480*x^8*y^25 + 4536*x^4*y^29 + 103680*x^26*y^6 + 77760*x^25*y^7 + 19440*x^24*y^8 + 1620*x^23*y^9 + 492480*x^21*y^11 + 230688*x^20*y^12 + 26892*x^19*y^13 + 596160*x^16*y^16 + 147744*x^15*y^17 + 4860*x^14*y^18 + 220320*x^11*y^21 + 21384*x^10*y^22 + 22356*x^6*y^26 + 324*x^5*y^27 + 324*x*y^31 + 41472*x^28*y^3 + 31104*x^27*y^4 + 7776*x^26*y^5 + 648*x^25*y^6 + 311040*x^23*y^8 + 155520*x^22*y^9 + 19440*x^21*y^10 + 570240*x^18*y^13 + 163296*x^17*y^14 + 6480*x^16*y^15 + 336960*x^13*y^18 + 42768*x^12*y^19 + 62208*x^8*y^23 + 1944*x^7*y^24 + 2592*x^3*y^28 + 6912*x^30 + 5184*x^29*y + 1296*x^28*y^2 + 108*x^27*y^3 + 124416*x^25*y^5 + 62208*x^24*y^6 + 7776*x^23*y^7 + 388800*x^20*y^10 + 116640*x^19*y^11 + 4860*x^18*y^12 + 365040*x^15*y^15 + 52812*x^14*y^16 + 112752*x^10*y^20 + 4860*x^9*y^21 + 9720*x^5*y^25 + 108*y^30 + 20736*x^27*y^2 + 10368*x^26*y^3 + 1296*x^25*y^4 + 155520*x^22*y^7 + 46656*x^21*y^8 + 1944*x^20*y^9 + 259200*x^17*y^12 + 38880*x^16*y^13 + 133488*x^12*y^17 + 6480*x^11*y^18 + 20736*x^7*y^22 + 648*x^2*y^27 + 25920*x^24*y^4 + 7776*x^23*y^5 + 324*x^22*y^6 + 103680*x^19*y^9 + 15552*x^18*y^10 + 97200*x^14*y^14 + 4860*x^13*y^15 + 26244*x^9*y^19 + 1620*x^4*y^24 + 17280*x^21*y^6 + 2592*x^20*y^7 + 38880*x^16*y^11 + 1944*x^15*y^12 + 19440*x^11*y^16 + 2160*x^6*y^21 + 6480*x^18*y^8 + 324*x^17*y^9 + 7776*x^13*y^13 + 1620*x^8*y^18 + 1296*x^15*y^10 + 648*x^10*y^15 + 108*x^12*y^12:
support points = [(80, 0, 0), (40, 40, 0), (0, 80, 0), (57, 17, 0), (17, 57, 0), (34, 34, 0), (21, 21, 0), (20, 22, 0), (19, 23, 0), (18, 24, 0), (18, 23, 0), (17, 24, 0), (16, 25, 0), (20, 20, 0), (19, 21, 0), (18, 22, 0), (17, 23, 0), (15, 25, 0), (14, 26, 0), (13, 27, 0), (22, 17, 0), (21, 18, 0), (20, 19, 0), (19, 20, 0), (17, 22, 0), (16, 23, 0), (15, 24, 0), (12, 27, 0), (11, 28, 0), (24, 14, 0), (23, 15, 0), (22, 16, 0), (21, 17, 0), (19, 19, 0), (18, 20, 0), (17, 21, 0), (16, 22, 0), (14, 24, 0), (13, 25, 0), (12, 26, 0), (9, 29, 0), (8, 30, 0), (21, 16, 0), (20, 17, 0), (19, 18, 0), (18, 19, 0), (16, 21, 0), (15, 22, 0), (14, 23, 0), (11, 26, 0), (10, 27, 0), (6, 31, 0), (23, 13, 0), (22, 14, 0), (21, 15, 0), (20, 16, 0), (18, 18, 0), (17, 19, 0), (16, 20, 0), (15, 21, 0), (13, 23, 0), (12, 24, 0), (11, 25, 0), (8, 28, 0), (7, 29, 0), (3, 33, 0), (25, 10, 0), (24, 11, 0), (23, 12, 0), (22, 13, 0), (20, 15, 0), (19, 16, 0), (18, 17, 0), (17, 18, 0), (15, 20, 0), (14, 21, 0), (13, 22, 0), (10, 25, 0), (9, 26, 0), (5, 30, 0), (27, 7, 0), (26, 8, 0), (25, 9, 0), (24, 10, 0), (22, 12, 0), (21, 13, 0), (20, 14, 0), (19, 15, 0), (17, 17, 0), (16, 18, 0), (15, 19, 0), (12, 22, 0), (11, 23, 0), (10, 24, 0), (7, 27, 0), (6, 28, 0), (2, 32, 0), (24, 9, 0), (23, 10, 0), (22, 11, 0), (21, 12, 0), (19, 14, 0), (18, 15, 0), (17, 16, 0), (14, 19, 0), (13, 20, 0), (12, 21, 0), (9, 24, 0), (8, 25, 0), (4, 29, 0), (26, 6, 0), (25, 7, 0), (24, 8, 0), (23, 9, 0), (21, 11, 0), (20, 12, 0), (19, 13, 0), (16, 16, 0), (15, 17, 0), (14, 18, 0), (11, 21, 0), (10, 22, 0), (6, 26, 0), (5, 27, 0), (1, 31, 0), (28, 3, 0), (27, 4, 0), (26, 5, 0), (25, 6, 0), (23, 8, 0), (22, 9, 0), (21, 10, 0), (18, 13, 0), (17, 14, 0), (16, 15, 0), (13, 18, 0), (12, 19, 0), (8, 23, 0), (7, 24, 0), (3, 28, 0), (30, 0, 0), (29, 1, 0), (28, 2, 0), (27, 3, 0), (25, 5, 0), (24, 6, 0), (23, 7, 0), (20, 10, 0), (19, 11, 0), (18, 12, 0), (15, 15, 0), (14, 16, 0), (10, 20, 0), (9, 21, 0), (5, 25, 0), (0, 30, 0), (27, 2, 0), (26, 3, 0), (25, 4, 0), (22, 7, 0), (21, 8, 0), (20, 9, 0), (17, 12, 0), (16, 13, 0), (12, 17, 0), (11, 18, 0), (7, 22, 0), (2, 27, 0), (24, 4, 0), (23, 5, 0), (22, 6, 0), (19, 9, 0), (18, 10, 0), (14, 14, 0), (13, 15, 0), (9, 19, 0), (4, 24, 0), (21, 6, 0), (20, 7, 0), (16, 11, 0), (15, 12, 0), (11, 16, 0), (6, 21, 0), (18, 8, 0), (17, 9, 0), (13, 13, 0), (8, 18, 0), (15, 10, 0), (10, 15, 0), (12, 12, 0)]
vertices = [(0, 30, 0), (30, 0, 0), (12, 12, 0)]
number of proper faces = 15
Facet 0: 2*x + 3*y - 60 >= 0
Facet 1: 3*x + 2*y - 60 >= 0
Facet 2: x >= 0
Facet 3: y >= 0
Facet 4: z >= 0
In [ ]:
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In [25]:
F2=z^3 -3*x^4+x^5*z + 2*x^6 + y^13 D2=F2.discriminant(z) ZD2 = ZetaFunctions(D1) ZD2.is_newton_degenerated() ZD2.give_info_newton()
Newton's polyhedron of -27*x^80 - 54*x^40*y^40 - 27*y^80 - 108*x^57*y^17 - 108*x^17*y^57 - 108*x^34*y^34 + 6912*x^21*y^21 + 5184*x^20*y^22 + 1296*x^19*y^23 + 108*x^18*y^24 + 20736*x^18*y^23 + 10368*x^17*y^24 + 1296*x^16*y^25 + 20736*x^20*y^20 + 15552*x^19*y^21 + 3888*x^18*y^22 + 324*x^17*y^23 + 25920*x^15*y^25 + 7776*x^14*y^26 + 324*x^13*y^27 + 41472*x^22*y^17 + 31104*x^21*y^18 + 7776*x^20*y^19 + 648*x^19*y^20 + 62208*x^17*y^22 + 31104*x^16*y^23 + 3888*x^15*y^24 + 17280*x^12*y^27 + 2592*x^11*y^28 + 20736*x^24*y^14 + 15552*x^23*y^15 + 3888*x^22*y^16 + 324*x^21*y^17 + 145152*x^19*y^19 + 77760*x^18*y^20 + 11664*x^17*y^21 + 324*x^16*y^22 + 77760*x^14*y^24 + 23328*x^13*y^25 + 972*x^12*y^26 + 6480*x^9*y^29 + 324*x^8*y^30 + 145152*x^21*y^16 + 93312*x^20*y^17 + 19440*x^19*y^18 + 1296*x^18*y^19 + 217728*x^16*y^21 + 77760*x^15*y^22 + 5832*x^14*y^23 + 51840*x^11*y^26 + 7776*x^10*y^27 + 1296*x^6*y^31 + 124416*x^23*y^13 + 93312*x^22*y^14 + 23328*x^21*y^15 + 1944*x^20*y^16 + 333504*x^18*y^18 + 152928*x^17*y^19 + 17820*x^16*y^20 + 108*x^15*y^21 + 181440*x^13*y^23 + 38880*x^12*y^24 + 972*x^11*y^25 + 19440*x^8*y^28 + 972*x^7*y^29 + 108*x^3*y^33 + 82944*x^25*y^10 + 62208*x^24*y^11 + 15552*x^23*y^12 + 1296*x^22*y^13 + 414720*x^20*y^15 + 217728*x^19*y^16 + 31104*x^18*y^17 + 648*x^17*y^18 + 383616*x^15*y^20 + 111456*x^14*y^21 + 5184*x^13*y^22 + 90720*x^10*y^25 + 9720*x^9*y^26 + 3888*x^5*y^30 + 20736*x^27*y^7 + 15552*x^26*y^8 + 3888*x^25*y^9 + 324*x^24*y^10 + 352512*x^22*y^12 + 202176*x^21*y^13 + 34992*x^20*y^14 + 1620*x^19*y^15 + 590976*x^17*y^17 + 202176*x^16*y^18 + 13608*x^15*y^19 + 252720*x^12*y^22 + 39852*x^11*y^23 + 324*x^10*y^24 + 27216*x^7*y^27 + 972*x^6*y^28 + 324*x^2*y^32 + 200448*x^24*y^9 + 134784*x^23*y^10 + 29808*x^22*y^11 + 2160*x^21*y^12 + 622080*x^19*y^14 + 248832*x^18*y^15 + 23328*x^17*y^16 + 466560*x^14*y^19 + 93312*x^13*y^20 + 1944*x^12*y^21 + 98928*x^9*y^24 + 6480*x^8*y^25 + 4536*x^4*y^29 + 103680*x^26*y^6 + 77760*x^25*y^7 + 19440*x^24*y^8 + 1620*x^23*y^9 + 492480*x^21*y^11 + 230688*x^20*y^12 + 26892*x^19*y^13 + 596160*x^16*y^16 + 147744*x^15*y^17 + 4860*x^14*y^18 + 220320*x^11*y^21 + 21384*x^10*y^22 + 22356*x^6*y^26 + 324*x^5*y^27 + 324*x*y^31 + 41472*x^28*y^3 + 31104*x^27*y^4 + 7776*x^26*y^5 + 648*x^25*y^6 + 311040*x^23*y^8 + 155520*x^22*y^9 + 19440*x^21*y^10 + 570240*x^18*y^13 + 163296*x^17*y^14 + 6480*x^16*y^15 + 336960*x^13*y^18 + 42768*x^12*y^19 + 62208*x^8*y^23 + 1944*x^7*y^24 + 2592*x^3*y^28 + 6912*x^30 + 5184*x^29*y + 1296*x^28*y^2 + 108*x^27*y^3 + 124416*x^25*y^5 + 62208*x^24*y^6 + 7776*x^23*y^7 + 388800*x^20*y^10 + 116640*x^19*y^11 + 4860*x^18*y^12 + 365040*x^15*y^15 + 52812*x^14*y^16 + 112752*x^10*y^20 + 4860*x^9*y^21 + 9720*x^5*y^25 + 108*y^30 + 20736*x^27*y^2 + 10368*x^26*y^3 + 1296*x^25*y^4 + 155520*x^22*y^7 + 46656*x^21*y^8 + 1944*x^20*y^9 + 259200*x^17*y^12 + 38880*x^16*y^13 + 133488*x^12*y^17 + 6480*x^11*y^18 + 20736*x^7*y^22 + 648*x^2*y^27 + 25920*x^24*y^4 + 7776*x^23*y^5 + 324*x^22*y^6 + 103680*x^19*y^9 + 15552*x^18*y^10 + 97200*x^14*y^14 + 4860*x^13*y^15 + 26244*x^9*y^19 + 1620*x^4*y^24 + 17280*x^21*y^6 + 2592*x^20*y^7 + 38880*x^16*y^11 + 1944*x^15*y^12 + 19440*x^11*y^16 + 2160*x^6*y^21 + 6480*x^18*y^8 + 324*x^17*y^9 + 7776*x^13*y^13 + 1620*x^8*y^18 + 1296*x^15*y^10 + 648*x^10*y^15 + 108*x^12*y^12:
support points = [(80, 0, 0), (40, 40, 0), (0, 80, 0), (57, 17, 0), (17, 57, 0), (34, 34, 0), (21, 21, 0), (20, 22, 0), (19, 23, 0), (18, 24, 0), (18, 23, 0), (17, 24, 0), (16, 25, 0), (20, 20, 0), (19, 21, 0), (18, 22, 0), (17, 23, 0), (15, 25, 0), (14, 26, 0), (13, 27, 0), (22, 17, 0), (21, 18, 0), (20, 19, 0), (19, 20, 0), (17, 22, 0), (16, 23, 0), (15, 24, 0), (12, 27, 0), (11, 28, 0), (24, 14, 0), (23, 15, 0), (22, 16, 0), (21, 17, 0), (19, 19, 0), (18, 20, 0), (17, 21, 0), (16, 22, 0), (14, 24, 0), (13, 25, 0), (12, 26, 0), (9, 29, 0), (8, 30, 0), (21, 16, 0), (20, 17, 0), (19, 18, 0), (18, 19, 0), (16, 21, 0), (15, 22, 0), (14, 23, 0), (11, 26, 0), (10, 27, 0), (6, 31, 0), (23, 13, 0), (22, 14, 0), (21, 15, 0), (20, 16, 0), (18, 18, 0), (17, 19, 0), (16, 20, 0), (15, 21, 0), (13, 23, 0), (12, 24, 0), (11, 25, 0), (8, 28, 0), (7, 29, 0), (3, 33, 0), (25, 10, 0), (24, 11, 0), (23, 12, 0), (22, 13, 0), (20, 15, 0), (19, 16, 0), (18, 17, 0), (17, 18, 0), (15, 20, 0), (14, 21, 0), (13, 22, 0), (10, 25, 0), (9, 26, 0), (5, 30, 0), (27, 7, 0), (26, 8, 0), (25, 9, 0), (24, 10, 0), (22, 12, 0), (21, 13, 0), (20, 14, 0), (19, 15, 0), (17, 17, 0), (16, 18, 0), (15, 19, 0), (12, 22, 0), (11, 23, 0), (10, 24, 0), (7, 27, 0), (6, 28, 0), (2, 32, 0), (24, 9, 0), (23, 10, 0), (22, 11, 0), (21, 12, 0), (19, 14, 0), (18, 15, 0), (17, 16, 0), (14, 19, 0), (13, 20, 0), (12, 21, 0), (9, 24, 0), (8, 25, 0), (4, 29, 0), (26, 6, 0), (25, 7, 0), (24, 8, 0), (23, 9, 0), (21, 11, 0), (20, 12, 0), (19, 13, 0), (16, 16, 0), (15, 17, 0), (14, 18, 0), (11, 21, 0), (10, 22, 0), (6, 26, 0), (5, 27, 0), (1, 31, 0), (28, 3, 0), (27, 4, 0), (26, 5, 0), (25, 6, 0), (23, 8, 0), (22, 9, 0), (21, 10, 0), (18, 13, 0), (17, 14, 0), (16, 15, 0), (13, 18, 0), (12, 19, 0), (8, 23, 0), (7, 24, 0), (3, 28, 0), (30, 0, 0), (29, 1, 0), (28, 2, 0), (27, 3, 0), (25, 5, 0), (24, 6, 0), (23, 7, 0), (20, 10, 0), (19, 11, 0), (18, 12, 0), (15, 15, 0), (14, 16, 0), (10, 20, 0), (9, 21, 0), (5, 25, 0), (0, 30, 0), (27, 2, 0), (26, 3, 0), (25, 4, 0), (22, 7, 0), (21, 8, 0), (20, 9, 0), (17, 12, 0), (16, 13, 0), (12, 17, 0), (11, 18, 0), (7, 22, 0), (2, 27, 0), (24, 4, 0), (23, 5, 0), (22, 6, 0), (19, 9, 0), (18, 10, 0), (14, 14, 0), (13, 15, 0), (9, 19, 0), (4, 24, 0), (21, 6, 0), (20, 7, 0), (16, 11, 0), (15, 12, 0), (11, 16, 0), (6, 21, 0), (18, 8, 0), (17, 9, 0), (13, 13, 0), (8, 18, 0), (15, 10, 0), (10, 15, 0), (12, 12, 0)]
vertices = [(0, 30, 0), (30, 0, 0), (12, 12, 0)]
number of proper faces = 15
Facet 0: 2*x + 3*y - 60 >= 0
Facet 1: 3*x + 2*y - 60 >= 0
Facet 2: x >= 0
Facet 3: y >= 0
Facet 4: z >= 0
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