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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 "algebra/intersectionform.h"
namespace regina {
IntersectionForm::IntersectionForm(MatrixInt form) :
matrix_(form), rank_(0), signature_(0), even_(true) {
if (form.rows() != form.columns())
throw InvalidArgument("IntersectionForm requires a square matrix.");
size_t n = form.rows();
size_t i;
for (i = 0; i < n; ++i)
if (form.entry(i, i) % 2 != 0) {
even_ = false;
break;
}
// Determine the rank and signature by diagonalising the matrix.
//
// Here we will allow operations that scale individual rows/columns,
// since this lets us stay with in exact integer arithmetic, and it
// will not change either the rank or the signature.
while (rank_ < n) {
// INV: The first rank_ rows and columns contain non-zero entries on
// the diagonal and zero entries everywhere else. These non-zero
// diagonal entries have been added into both rank_ and signature_.
Integer d = form.entry(rank_, rank_);
if (d != 0) {
for (i = rank_ + 1; i < n; ++i) {
Integer e = form.entry(i, rank_);
if (e != 0) {
if (form.entry(rank_, i) != e)
throw InvalidArgument(
"IntersectionForm requires a symmetric matrix.");
Integer gcd = d.gcd(e);
Integer dScaled = d.divExact(gcd);
e.divByExact(gcd);
form.multRow(i, dScaled, rank_);
form.addRow(rank_, i, -e, rank_);
form.multCol(i, dScaled, rank_);
form.addCol(rank_, i, -e, rank_);
}
}
if (d > 0)
++signature_;
else
--signature_;
++rank_;
continue;
}
// The next diagonal entry is zero.
// See if we can find a non-zero diagonal entry further down.
for (i = rank_ + 1; i < n; ++i)
if (form.entry(i, i) != 0)
break;
if (i < n) {
form.swapRows(rank_, i);
form.swapCols(rank_, i);
continue;
}
// All remaining diagonal entries are zero.
// See if we can find a non-zero entry elsewhere to use.
for (size_t r = rank_; r < n; ++r)
for (i = r + 1; i < n; ++i)
if (form.entry(r, i) != 0) {
// Got one.
form.addRow(i, r);
form.addCol(i, r);
if (r != rank_) {
form.swapRows(rank_, r);
form.swapCols(rank_, r);
}
goto loopAgain;
}
// All entries above the main diagonal are zero.
// This should be the end of it, but we will check the below-diagonal
// entries also to finish verifying that the matrix is symmetric.
for (size_t r = rank_; r < n; ++r)
for (i = r + 1; i < n; ++i)
if (form.entry(i, r) != 0)
throw InvalidArgument(
"IntersectionForm requires a symmetric matrix.");
break;
loopAgain:
;
}
}
void IntersectionForm::writeTextShort(std::ostream& out) const {
if (even_)
out << "Even";
else
out << "Odd";
out << ", rank = " << rank_ << ", sig = " << signature_ << ": ";
matrix_.writeTextShort(out);
}
void IntersectionForm::writeTextLong(std::ostream& out) const {
if (even_)
out << "Even";
else
out << "Odd";
out << ", rank = " << rank_ << ", signature = " << signature_ << "\n\n";
matrix_.writeTextLong(out);
}
} // namespace regina
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