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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 <iterator>
#include <sstream>
#include "algebra/grouppresentation.h"
#include "algebra/homgrouppresentation.h"
#include "maths/numbertheory.h"
namespace regina {
HomGroupPresentation::HomGroupPresentation(
const GroupPresentation& groupForIdentity) :
domain_(groupForIdentity), codomain_(groupForIdentity),
map_(groupForIdentity.countGenerators()),
inv_(std::in_place, groupForIdentity.countGenerators()) {
unsigned long i = 0;
for (GroupExpression& e : map_)
e.addTermFirst(i++, 1);
i = 0;
for (GroupExpression& e : *inv_)
e.addTermFirst(i++, 1);
}
HomMarkedAbelianGroup HomGroupPresentation::markedAbelianisation() const {
MarkedAbelianGroup DOM = domain_.markedAbelianisation();
MarkedAbelianGroup RAN = codomain_.markedAbelianisation();
MatrixInt ccMat( RAN.ccRank(), DOM.ccRank() );
for (unsigned long j=0; j<ccMat.columns(); j++) {
GroupExpression COLj( evaluate(j) );
for (unsigned long i=0; i<COLj.countTerms(); i++)
ccMat.entry( COLj.generator(i), j ) += COLj.exponent(i);
}
return HomMarkedAbelianGroup(std::move(DOM), std::move(RAN),
std::move(ccMat));
}
void HomGroupPresentation::writeTextShort(std::ostream& out) const {
if (map_.empty()) {
out << "Trivial map on no generators";
} else {
if (inv_)
out << "Isomorphism: ";
else
out << "Homomorphism: ";
/*
domain_.writeTextShort(out);
out << " to ";
codomain_.writeTextShort(out);
*/
size_t gen = 0;
for (const auto &e : map_) {
if (gen > 0)
out << ", ";
out << 'g' << gen << " -> " << e;
++gen;
}
}
}
void HomGroupPresentation::writeTextLong(std::ostream& out) const {
if (inv_)
out << "Isomorphism with ";
else
out << "Homomorphism with ";
out<<"domain ";
domain_.writeTextCompact(out);
out<<" "; // std::endl;
out<<"map[";
for (unsigned long i=0; i<domain_.countGenerators(); i++) {
if (i!=0)
out<<", ";
if (domain_.countGenerators()<=26)
out<<char('a' + i)<<" --> ";
else
out<<"g"<<i<<" --> ";
map_[i].writeTextShort(out, false, codomain_.countGenerators()<=26);
}
out<<"] ";
out<<"codomain ";
codomain_.writeTextCompact(out);
out<<std::endl;
}
bool HomGroupPresentation::smallCancellation() {
auto codomainMap = codomain_.smallCancellation();
auto domainMap = domain_.smallCancellation();
bool retval = codomainMap || domainMap;
if (! domainMap)
domainMap = HomGroupPresentation(domain_);
if (! codomainMap)
codomainMap = HomGroupPresentation(codomain_);
std::vector< GroupExpression > newMap( domain_.countGenerators() );
for (unsigned long i=0; i<newMap.size(); i++)
newMap[i] = codomainMap->evaluate( evaluate( domainMap->invEvaluate(i) ) );
std::vector< GroupExpression > newInvMap;
if (inv_) {
newInvMap.resize( codomain_.countGenerators() );
for (unsigned long i=0; i<newInvMap.size(); i++)
newInvMap[i] = domainMap->evaluate( invEvaluate(
codomainMap->invEvaluate(i) ) );
}
map_ = std::move(newMap);
/*
for (GroupExpression& e : map_)
retval |= codomain_.simplifyAndConjugate(e); // must not conjugate
*/
if (inv_) {
*inv_ = std::move(newInvMap);
/*
for (GroupExpression& e : *inv_)
retval |= domain_.simplifyAndConjugate(e); // must not conjugate
*/
}
return retval;
}
HomGroupPresentation HomGroupPresentation::operator * (
const HomGroupPresentation& input) const {
std::vector<GroupExpression> evalVec(input.domain_.countGenerators());
for (unsigned long i=0; i<evalVec.size(); i++)
evalVec[i] = evaluate( input.evaluate(i) );
if ( (! inv_) || (! input.inv_) ) {
return HomGroupPresentation(input.domain_, codomain_, evalVec);
} else {
std::vector<GroupExpression> invVec( codomain_.countGenerators());
for (unsigned long i=0; i<invVec.size(); i++)
invVec[i] = input.invEvaluate( invEvaluate(i) );
return HomGroupPresentation(input.domain_, codomain_, evalVec, invVec );
}
}
HomGroupPresentation HomGroupPresentation::operator * (
HomGroupPresentation&& input) const {
std::vector<GroupExpression> evalVec(input.domain_.countGenerators());
for (unsigned long i=0; i<evalVec.size(); i++)
evalVec[i] = evaluate( input.evaluate(i) );
if ( (! inv_) || (! input.inv_) ) {
return HomGroupPresentation(std::move(input.domain_), codomain_, evalVec);
} else {
std::vector<GroupExpression> invVec( codomain_.countGenerators());
for (unsigned long i=0; i<invVec.size(); i++)
invVec[i] = input.invEvaluate( invEvaluate(i) );
return HomGroupPresentation(std::move(input.domain_), codomain_,
evalVec, invVec );
}
}
bool HomGroupPresentation::nielsen() {
// modelled on simplify()
auto codomainMap = codomain_.nielsen();
auto domainMap = domain_.nielsen();
bool retval = codomainMap || domainMap;
if (! domainMap)
domainMap = HomGroupPresentation(domain_);
if (! codomainMap)
codomainMap = HomGroupPresentation(codomain_);
std::vector< GroupExpression > newMap( domain_.countGenerators() );
for (unsigned long i=0; i<newMap.size(); i++)
newMap[i] = codomainMap->evaluate(evaluate(domainMap->invEvaluate(i)));
std::vector< GroupExpression > newInvMap;
if (inv_) {
newInvMap.resize( codomain_.countGenerators() );
for (unsigned long i=0; i<newInvMap.size(); i++)
newInvMap[i] = domainMap->evaluate( invEvaluate(
codomainMap->invEvaluate(i) ) );
}
map_ = std::move(newMap);
/*
for (GroupExpression& e : map_)
retval |= codomain_.simplifyAndConjugate(e); // must not conjugate
*/
if (inv_) {
*inv_ = std::move(newInvMap);
/*
for (GroupExpression& e : *inv_)
retval |= domain_.simplifyAndConjugate(e); // must not conjugate
*/
}
return retval;
}
bool HomGroupPresentation::simplify() {
// step 1: simplify presentation of domain and codomain
auto codomainMap = codomain_.simplify();
auto domainMap = domain_.simplify();
bool retval = codomainMap || domainMap;
// build identity maps if either of the above is null.
if (! domainMap)
domainMap = HomGroupPresentation(domain_);
if (! codomainMap)
codomainMap = HomGroupPresentation(codomain_);
// step 2: compute codomainMap*(*oldthis)*domainMap.inverse() and replace
// "map" appropriately. Simplify the words in the codomain.
// Do the same for the inverse map if we have one.
std::vector< GroupExpression > newMap( domain_.countGenerators() );
for (unsigned long i=0; i<newMap.size(); i++)
newMap[i] = codomainMap->evaluate(evaluate(domainMap->invEvaluate(i)));
std::vector< GroupExpression > newInvMap;
if (inv_) {
newInvMap.resize( codomain_.countGenerators() );
for (unsigned long i=0; i<newInvMap.size(); i++)
newInvMap[i] = domainMap->evaluate(
invEvaluate( codomainMap->invEvaluate(i) ) );
}
// step 3: rewrite this map, and simplify
map_ = std::move(newMap);
/*
for (GroupExpression& e : map_)
retval |= codomain_.simplifyAndConjugate(e); // must not conjugate
*/
if (inv_) {
*inv_ = std::move(newInvMap);
/*
for (GroupExpression& e : *inv_)
retval |= domain_.simplifyAndConjugate(e); // must not conjugate
*/
}
return retval;
}
bool HomGroupPresentation::invert() {
if (inv_) {
domain_.swap(codomain_);
map_.swap(*inv_);
return true;
}
return false;
}
bool HomGroupPresentation::verify() const {
for (const auto& r : domain_.relations()) {
GroupExpression imgRel( evaluate(r) );
codomain_.simplifyAndConjugate(imgRel);
if (!imgRel.isTrivial())
return false;
}
return true;
}
bool HomGroupPresentation::verifyIsomorphism() const {
if (! inv_)
return false;
if (inv_->size() != codomain_.countGenerators())
return false;
// for every generator in the domain compute f^-1(f(x))x^-1 and reduce
for (unsigned long i=0; i<domain_.countGenerators(); i++) {
GroupExpression tempW( invEvaluate(evaluate(i)) );
tempW.addTermLast( i, -1 );
domain_.simplifyAndConjugate(tempW);
if (! tempW.isTrivial())
return false;
}
// for every generator in the codomain compute f(f^-1(x))x^-1 and reduce
for (unsigned long i=0; i<codomain_.countGenerators(); i++) {
GroupExpression tempW( evaluate(invEvaluate(i)) );
tempW.addTermLast( i, -1 );
codomain_.simplifyAndConjugate(tempW);
if (! tempW.isTrivial())
return false;
}
return true;
}
} // namespace regina
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