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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2025, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program is free software; you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as *
* published by the Free Software Foundation; either version 2 of the *
* License, or (at your option) any later version. *
* *
* As an exception, when this program is distributed through (i) the *
* App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or *
* (iii) Google Play by Google Inc., then that store may impose any *
* digital rights management, device limits and/or redistribution *
* restrictions that are required by its terms of service. *
* *
* This program is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* General Public License for more details. *
* *
* You should have received a copy of the GNU General Public License *
* along with this program. If not, see <https://www.gnu.org/licenses/>. *
* *
**************************************************************************/
#include "link/link.h"
namespace regina {
Laurent<Integer> Link::affineIndex() const {
if (components_.size() != 1)
throw FailedPrecondition("Regina can only compute affine index "
"polynomials for links with exactly one component");
if (size() == 0)
return {}; // all classical knot have affine index polynomial zero.
// Build a Cheng colouring. This assigns an integer to each strand.
// The starting value does not affect the affine index polynomial, and so
// we choose a starting value of zero.
FixedArray<long> label(2 * size());
StrandRef s = components_.front();
long colour = 0;
do {
if (s.crossing()->sign() > 0) {
if (s.strand() == 0)
++colour;
else
--colour;
} else {
if (s.strand() == 0)
--colour;
else
++colour;
}
label[s.id()] = colour;
++s;
} while (s != components_.front());
Laurent<Integer> ans;
long writhe = 0;
for (auto c : crossings_) {
long exp = label[c->upper().id()] - label[c->lower().id()];
if (c->sign() > 0) {
++exp;
++writhe;
ans.set(exp, ans[exp] + 1);
} else {
--exp;
--writhe;
ans.set(exp, ans[exp] - 1);
}
}
ans.set(0, ans[0] - writhe);
return ans;
}
} // namespace regina
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