|
|
D.13.7.8 tropicalLinkNewton
Procedure from library tropicalNewton.lib (see tropicalNewton_lib).
- Usage:
- tropicalLinkNewton(inI); inI ideal
- Return:
- matrix, a matrix containing generators of all rays of the tropical variety
- Assume:
- constant coefficient case, inI is monomial free,
its tropical variety has codimension one lineality space and
is a polyhedral fan
- Note:
- if printlevel sufficiently high will print intermediate results
Example:
| | LIB "tropicalNewton.lib";
// a 10 valent facet in tropical Grass(3,7)
ring r = (0,t),
(p012,p013,p023,p123,p014,p024,p124,p034,p134,p234,
p015,p025,p125,p035,p135,p235,p045,p145,p245,p345,
p016,p026,p126,p036,p136,p236,p046,p146,p246,p346,
p056,p156,p256,p356,p456),
wp(4,7,5,7,4,4,4,7,5,7,2,1,2,4,4,4,2,1,2,4,7,5,7,7,
5,7,7,5,7,4,4,4,4,4,4);
number uniformizingParameter = t;
export(uniformizingParameter);
ideal inI =
p345*p136+p134*p356, p125*p045+p015*p245, p124*p015-p014*p125,
p135*p245-p125*p345, p135*p045+p015*p345, p124*p045+p014*p245,
p024*p125-p012*p245, p145*p236-p124*p356, p124*p135-p123*p145,
p024*p015+p012*p045, p134*p026+p023*p146-p024*p136,
p145*p036+p014*p356, p014*p135-p013*p145, p234*p145+p124*p345,
p034*p145-p014*p345, p024*p135-p012*p345, p125*p035+p015*p235,
p235*p045-p035*p245, p234*p136-p134*p236, p134*p036-p034*p136,
p146*p356-p136*p456, p135*p146-p134*p156,
p135*p026+p023*p156+p012*p356, p124*p035+p014*p235,
p123*p025+p012*p235, p013*p025-p012*p035, p345*p146+p134*p456,
p125*p036+p015*p236, p345*p026-p023*p456+p024*p356,
p123*p015-p013*p125, p234*p025-p024*p235, p034*p025-p024*p035,
p234*p125+p123*p245, p245*p036-p045*p236, p123*p045+p013*p245,
p034*p125-p013*p245, p234*p015+p013*p245, p245*p156+p125*p456,
p034*p015+p013*p045, p045*p156-p015*p456, p135*p236-p123*p356,
p235*p146-p134*p256, p135*p036+p013*p356, p124*p036+p014*p236,
p123*p014-p013*p124, p035*p146-p134*p056, p145*p126+p124*p156,
p234*p045-p034*p245, p235*p026+p023*p256-p025*p236,
p145*p016+p014*p156, p035*p026+p023*p056-p025*p036,
p345*p236+p234*p356, p234*p135+p123*p345, p345*p036+p034*p356,
p034*p135-p013*p345, p345*p156+p135*p456, p124*p034+p014*p234,
p145*p246-p124*p456, p123*p024+p012*p234, p145*p046+p014*p456,
p013*p024-p012*p034, p024*p156+p012*p456, p125*p056+p015*p256,
p245*p056-p045*p256, p236*p146-p136*p246, p134*p126+p123*p146,
p136*p046-p036*p146, p235*p036-p035*p236, p134*p016+p013*p146,
p123*p035+p013*p235, p235*p156-p135*p256,
p123*p026-p023*p126+p012*p236, p135*p056-p035*p156,
p023*p016-p013*p026+p012*p036, p124*p056+p014*p256,
p234*p146-p134*p246, p025*p126-p012*p256, p134*p046-p034*p146,
p025*p016+p012*p056, p234*p035-p034*p235, p345*p256+p235*p456,
p234*p026+p023*p246-p024*p236, p345*p056+p035*p456,
p034*p026+p023*p046-p024*p036, p125*p016-p015*p126,
p025*p246-p024*p256, p025*p046-p024*p056, p245*p126-p125*p246,
p125*p046+p015*p246, p045*p126+p015*p246, p245*p016-p015*p246,
p045*p016-p015*p046, p123*p036+p013*p236, p236*p156+p126*p356,
p135*p126+p123*p156, p036*p156-p016*p356, p135*p016+p013*p156,
p124*p016-p014*p126, p235*p056-p035*p256, p245*p046-p045*p246,
p234*p036-p034*p236, p123*p034+p013*p234, p246*p356-p236*p456,
p234*p156-p123*p456, p135*p246-p123*p456, p345*p126-p123*p456,
p046*p356-p036*p456, p034*p156+p013*p456, p135*p046+p013*p456,
p345*p016-p013*p456, p124*p046+p014*p246, p024*p126-p012*p246,
p024*p016+p012*p046, p345*p246+p234*p456, p345*p046+p034*p456,
p235*p126+p123*p256, p236*p056-p036*p256, p123*p056+p013*p256,
p035*p126-p013*p256, p235*p016+p013*p256, p035*p016+p013*p056,
p235*p246-p234*p256, p234*p056-p034*p256, p035*p246-p034*p256,
p235*p046-p034*p256, p035*p046-p034*p056, p126*p036+p016*p236,
p123*p016-p013*p126, p234*p126+p123*p246, p236*p046-p036*p246,
p123*p046+p013*p246, p034*p126-p013*p246, p234*p016+p013*p246,
p246*p156+p126*p456, p034*p016+p013*p046, p046*p156-p016*p456,
p234*p046-p034*p246, p126*p056+p016*p256, p246*p056-p046*p256,
p126*p046+p016*p246, p024*p235*p145+p124*p025*p345,
p024*p035*p145-p014*p025*p345, p123*p145*p245-p124*p125*p345,
p013*p145*p245-p014*p125*p345, p013*p045*p145+p014*p015*p345,
p024*p235*p136-p134*p025*p236, p123*p245*p136+p134*p125*p236,
p013*p245*p136+p134*p015*p236, p034*p245*p136-p134*p045*p236,
p134*p156*p356-p135*p136*p456, p123*p145*p146-p124*p134*p156,
p013*p145*p146-p014*p134*p156, p013*p145*p026+p023*p014*p156+p012*p014*p356,
p124*p025*p156+p012*p145*p256, p012*p145*p056-p014*p025*p156,
p024*p145*p256-p124*p025*p456, p024*p145*p056+p014*p025*p456,
p034*p235*p136-p134*p035*p236, p134*p256*p356-p235*p136*p456,
p134*p056*p356-p035*p136*p456, p025*p036*p146-p024*p136*p056,
p013*p125*p026-p023*p015*p126+p012*p015*p236,
p123*p245*p146+p134*p125*p246, p013*p245*p146+p134*p015*p246,
p013*p245*p026-p023*p015*p246-p012*p045*p236,
p013*p045*p026-p023*p015*p046-p012*p045*p036,
p034*p245*p146-p134*p045*p246, p013*p124*p026-p023*p014*p126+p012*p014*p236,
p013*p145*p056-p014*p035*p156, p024*p256*p356-p025*p236*p456,
p024*p056*p356-p025*p036*p456, p234*p256*p356-p235*p236*p456,
p034*p256*p356-p035*p236*p456, p034*p056*p356-p035*p036*p456,
p012*p235*p145*p245+p124*p025*p125*p345,
p012*p035*p145*p245-p014*p025*p125*p345,
p012*p035*p045*p145+p014*p015*p025*p345,
p012*p235*p245*p136-p134*p025*p125*p236,
p012*p035*p245*p136+p134*p015*p025*p236,
p024*p035*p245*p136-p134*p025*p045*p236,
p014*p025*p125*p156+p012*p015*p145*p256,
p012*p145*p245*p256-p124*p025*p125*p456,
p012*p045*p145*p256+p014*p025*p125*p456,
p012*p245*p256*p356-p025*p125*p236*p456,
p012*p045*p256*p356+p015*p025*p236*p456,
p012*p045*p056*p356+p015*p025*p036*p456,
p123*p245*p256*p356+p125*p235*p236*p456,
p013*p245*p256*p356+p015*p235*p236*p456,
p013*p045*p256*p356+p015*p035*p236*p456,
p013*p045*p056*p356+p015*p035*p036*p456;
system("--random",1337);
printlevel = 3;
list TinI = tropicalLinkNewton(inI);
==> reducing to one-dimensional fan
==> intersecting with pairs of affine hyperplanes
==> 1: empty
==> 2: empty
==> 3: empty
==> 4: empty
==> 5: empty
==> 6: empty
==> 7: empty
==> 8: empty
==> 9: empty
==> 10: empty
==> 11: non-empty, computing tropical variety
==> total number of rays: 2
==> 12: empty
==> 13: non-empty, computing tropical variety
==> total number of rays: 4
==> 14: non-empty, computing tropical variety
==> total number of rays: 6
==> 15: non-empty, computing tropical variety
==> total number of rays: 8
==> 16: empty
==> 17: empty
==> 18: empty
==> 19: empty
==> 20: empty
==> 21: empty
==> 22: non-empty, computing tropical variety
==> total number of rays: 10
==> 23: empty
for (int i=1; i<=size(TinI); i++)
{ print(TinI[i]); }
==> 0,0,0,0,0,0,-1,-1,0,1,0,0,-1,-1,0,1,1,-1,-1,-1,0,1,-1,(-t+1),(-t+1),(t-1)\
,1,1,
==> -1,0,1,1,-1,(t-1),-1
==> 0,0,0,0,0,0,-1,-1,0,1,0,0,-1,-1,0,1,1,-1,-1,-1,0,-1,-1,_[1,24],_[1,25],_[\
1,26],
==> 1,1,-1,0,1,1,-1,_[1,34],-1
==> 0,0,0,0,0,0,-1,-1,0,1,0,0,-1,-1,0,1,1,-1,-1,-1,0,(-t-1),-1,1,(-t),(t),1,1\
,-1,0,
==> 1,1,-1,(t),-1
==> 0,0,0,0,0,0,-1,-1,0,1,0,0,-1,-1,0,1,1,-1,-1,-1,0,_[1,22],-1,-1,-1/(t),1/(\
t),1,1,
==> -1,0,1,1,-1,1/(t),-1
==> 0,0,0,0,0,0,-1,-1,0,1,0,0,-1,-1,0,1,1,-1,-1,-1,0,(-t-1),-1,(-t),1,(t),1,1\
,-1,0,
==> 1,1,-1,(t),-1
==> 0,0,0,0,0,0,-1,-1,0,1,0,0,-1,-1,0,1,1,-1,-1,-1,0,_[1,22],-1,-1/(t),-1,1/(\
t),1,1,
==> -1,0,1,1,-1,1/(t),-1
==> 0,0,0,0,0,0,-1,-1,0,1,0,0,-1,-1,0,1,1,-1,-1,-1,0,(t-1),-1,(t),(t),1,1,1,-\
1,0,1,
==> 1,-1,(-t),-1
==> 0,0,0,0,0,0,-1,-1,0,1,0,0,-1,-1,0,1,1,-1,-1,-1,0,_[1,22],-1,1/(t),1/(t),-\
1,1,1,
==> -1,0,1,1,-1,-1/(t),-1
==> 0,0,0,0,0,0,-1,-1,0,1,0,0,-1,-1,0,1,1,-1,-1,-1,0,(t-1),-1,(t),(t),(-t),1,\
1,-1,0,
==> 1,1,-1,1,-1
==> 0,0,0,0,0,0,-1,-1,0,1,0,0,-1,-1,0,1,1,-1,-1,-1,0,_[1,22],-1,1/(t),1/(t),-\
1/(t),
==> 1,1,-1,0,1,1,-1,-1,-1
|
|
