1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
|
#include "minors.h"
#include "printer.h"
#include <algorithm>
using namespace std;
static int lookup(vector<int> const &v, int i)
{
for(int j=0;j<v.size();j++)
{
if(v[j])
{
if(i==0)
return j;
i--;
}
}
return 0;
}
static int sign(vector<int> const &v)
{
int ret=1;
for(int i=0;i<v.size();i++)
for(int j=i+1;j<v.size();j++)
if(v[i]>v[j])ret=-ret;
return ret;
}
PolynomialSet minors(PolynomialRing const &R, int r, int d, int n, bool withNames, bool M2Convention)
{
int namesOffset=d*n;
int entriesOffset=0;
PolynomialSet ret(R);
vector<int> I;
if(M2Convention)
{
for(int i=0;i<d-r;i++)I.push_back(0);
for(int i=0;i<r;i++)I.push_back(1);
}
else
{
for(int i=0;i<r;i++)I.push_back(1);
for(int i=0;i<d-r;i++)I.push_back(0);
}
do
{
vector<int> J;
if(M2Convention)
{
for(int i=0;i<n-r;i++)J.push_back(0);
for(int i=0;i<r;i++)J.push_back(1);
}
else
{
for(int i=0;i<r;i++)J.push_back(1);
for(int i=0;i<n-r;i++)J.push_back(0);
}
do
{
Polynomial p(R);
if(withNames)
p+=Term(R.getField().zHomomorphism(-1),Monomial(R,IntegerVector::standardVector(R.getNumberOfVariables(),namesOffset++)));
vector<int> K;
for(int i=0;i<r;i++)K.push_back(i);
do
{
IntegerVector v(R.getNumberOfVariables());
vector<int>::const_iterator s=K.begin();
for(int i=0;i<r;i++,s++)
{
int y=lookup(I,i);
int x=lookup(J,*s);
int index=y*n+x;
v+=IntegerVector::standardVector(R.getNumberOfVariables(),index+entriesOffset);
}
p+=Term(R.getField().zHomomorphism(sign(K)),Monomial(R,v));
}
while(next_permutation(K.begin(),K.end()));
ret.push_back(p);
}
while(M2Convention?next_permutation(J.begin(),J.end()):prev_permutation(J.begin(),J.end()));
}
while(M2Convention?next_permutation(I.begin(),I.end()):prev_permutation(I.begin(),I.end()));
return ret;
}
|
