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app.cpp
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app.cpp
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#include "app.h"
#include "CoxIter/growthrate.h"
App::App()
: bCheckNR(false), bCheckNREquations(false), bComputeInvariantsQF(false),
bComputeInvariantsPolyhedron(false), bDebug(false), bPrintHelp(false),
iCreateImage(-1), iMaxVectors(0), iMinVectors(0), iFieldSupp(0),
strField("rationals"), strOuputMathematicalFormat("generic") {}
App::~App() {
for (auto c : aiQF)
delete c;
}
void App::readMainParameters(int argc, char **argv) {
string strTemp;
PCRERegexp regexp, regexp2;
PCREResult regexpRes, regexpRes2;
#ifdef _RC7AVAILABLE_
int iRegexpCount;
#endif
// --------------------------------------------------
// Complete parameters
string strParams;
for (int i(0); i < argc; ++i)
strParams += " " + std::string(argv[i]);
// --------------------------------------------------
// Debug?
if (strParams.find("-h") != string::npos ||
strParams.find("-help") != string::npos || argc == 1) {
bPrintHelp = true;
return;
}
// --------------------------------------------------
// Field of definition
if (regexp.preg_match_all(
"([-]*[[:space:]]*k|-[[:space:]]*field)[[:space:]]*[=]*[[[:space:]Q]*"
"[\\[\\(]?[[:space:]]*sqrt[[:space:]\\[\\(]*([0-9]{1,5})",
strParams, regexpRes, PCRE_CASELESS)) {
iFieldSupp = stoi(regexpRes[2][0]);
if (!QuadraticInteger::isDAdmissible(iFieldSupp))
throw(string("Field of definition: quadratic field: the following value "
"is not admissible: " +
regexpRes[2][0]));
strField = "quadratic";
}
#ifdef _RC7AVAILABLE_
else if (regexp.preg_match_all("(-k|-[[:space:]]*k|-[[:space:]]*field)[[:"
"space:]]*[=]*[[:space:]]*RC7",
strParams, regexpRes, PCRE_CASELESS)) {
strField = "rc7";
}
#endif
// --------------------------------------------------
// Debug?
if (strParams.find("-debug") != string::npos) {
str_replace(strParams, "-debug", "");
bDebug = true;
}
// --------------------------------------------------
// Image
if (strParams.find("-noimage") != string::npos) {
str_replace(strParams, "-noimage", "");
iCreateImage = 0;
}
if (strParams.find("-image") != string::npos) {
str_replace(strParams, "-image", "");
iCreateImage = 1;
}
// --------------------------------------------------
// Minimal number of vectors to compute
if (regexp.preg_match_all("-minv[[:space:]]+([[:digit:]]{1,4})", strParams,
regexpRes)) {
str_replace(strParams, regexpRes[0][0], "");
iMinVectors = stoi(regexpRes[1][0]);
}
// --------------------------------------------------
// Maximal number of vectors to compute
if (regexp.preg_match_all("-maxv[[:space:]]+([[:digit:]]{1,4})", strParams,
regexpRes)) {
str_replace(strParams, regexpRes[0][0], "");
iMaxVectors = stoi(regexpRes[1][0]);
}
// --------------------------------------------------
// Non reflective with symmetries
if (regexp.preg_match_all(
"-nr[[:space:]]?\\[[[:space:]]?([[:digit:]]+)[[:space:]]?,[[:space:]]"
"?([[:digit:]]+)\\][[:space:]]?",
strParams, regexpRes, PCRE_CASELESS)) {
bCheckNR = true;
iNRMin = min(stoi(regexpRes[1][0]), stoi(regexpRes[2][0]));
iNRMax = max(stoi(regexpRes[1][0]), stoi(regexpRes[2][0]));
str_replace(strParams, regexpRes[0][0], "");
}
// --------------------------------------------------
// Non reflective with equations
if (strParams.find("-nrequations") != string::npos) {
str_replace(strParams, "-nrequations", "");
bCheckNREquations = true;
}
// --------------------------------------------------
// Output format
if (regexp.preg_match_all(
"-oformat[[:space:]=]?(mathematica|generic|latex|pari)", strParams,
regexpRes, PCRE_CASELESS)) {
std::transform(regexpRes[1][0].begin(), regexpRes[1][0].end(),
regexpRes[1][0].begin(), ::tolower);
strOuputMathematicalFormat = regexpRes[1][0];
str_replace(strParams, regexpRes[0][0], "");
}
// --------------------------------------------------
// Compute invariants of the polyhedron
if (strParams.find("-ip") != string::npos ||
strParams.find("-ipolyhedron") != string::npos ||
strParams.find("-invariantpolyhedron") != string::npos ||
strParams.find("-invariantspolyhedron") != string::npos) {
str_replace(strParams, "-ip", "");
str_replace(strParams, "-ipolyhedron", "");
str_replace(strParams, "-invariantpolyhedron", "");
str_replace(strParams, "-invariantspolyhedron", "");
bComputeInvariantsPolyhedron = true;
}
// --------------------------------------------------
// Invariants of quadratic form
if (strParams.find("-iqf") != string::npos && strField == "rationals") {
str_replace(strParams, "-iqf", "");
bComputeInvariantsQF = true;
}
regexpRes.clear();
// --------------------------------------------------
// Quadratic form
if (strField == "rationals") {
if (regexp.preg_match_all("(-f|-qf|- f|- qf)([[:digit:]-, ]+)", strParams,
regexpRes)) {
strTemp = regexpRes[2][0];
str_replace(strTemp, " ", "");
vector<string> strQF(explode(",", strTemp));
try {
for (auto strCo : strQF)
aiQF.push_back(new RationalInteger(stoi(strCo)));
} catch (std::exception &ex) {
cout << "Quadratic form: unknown coefficient: " << strTemp << endl;
exit(0);
}
}
} else if (strField == "quadratic") {
if (regexp.preg_match_all(
"(-[[:space:]]*f|-[[:space:]]*qf)([[:digit:],Tt\\+\\-\\* ]+)",
strParams, regexpRes)) {
strTemp = regexpRes[2][0];
str_replace(strTemp, " ", "");
vector<string> strQF(explode(",", strTemp));
for (auto c : strQF) {
if (regexp.preg_match_all("^([-[:digit:]]+)$", c, regexpRes)) // integer
aiQF.push_back(new QuadraticInteger(stoi(c), 0));
else if (regexp.preg_match_all("([+-]{0,1})([[:digit:]]+)([+-]{1,1})([["
":digit:]]*)[\\*]*T",
c, regexpRes)) {
string strN1(regexpRes[1][0] + regexpRes[2][0]),
strN2(regexpRes[3][0]);
strN2 += regexpRes[4][0] == "" ? "1" : regexpRes[4][0];
aiQF.push_back(new QuadraticInteger(stoi(strN1), stoi(strN2)));
} else if (regexp.preg_match_all("([+-]{0,1})([[:digit:]]*)[\\*]*T([+-]"
"{1,1})([[:digit:]]*)",
c, regexpRes)) {
string strN1(regexpRes[1][0]), strN2(regexpRes[3][0]);
strN1 += regexpRes[2][0] == "" ? "1" : regexpRes[2][0];
strN2 += regexpRes[4][0] == "" ? "1" : regexpRes[4][0];
aiQF.push_back(new QuadraticInteger(stoi(strN2), stoi(strN1)));
} else if (regexp.preg_match_all("^([-[:digit:]]+)[*]?(T|t)$", c,
regexpRes)) // non-integer part only
{
if (regexpRes[1][0] == "-")
regexpRes[1][0] = "-1";
aiQF.push_back(new QuadraticInteger(0, stoi(regexpRes[1][0])));
} else
throw(string("Quadratic form: unknown coefficient: " + c));
}
}
}
#ifdef _RC7AVAILABLE_
else if (strField == "rc7") {
if (regexp.preg_match_all(
"(-f|-qf|- f|- qf)([[:digit:],\\+\\-\\* \\[\\]\\(\\)]+)", strParams,
regexpRes)) {
str_replace(regexpRes[0][0], " ", "");
str_replace(regexpRes[0][0], "-f", "");
str_replace(regexpRes[0][0], "-qf", "");
regexpRes2.clear();
// -----------------------------------------------
// We replace , inside [] by ;
int iBracketsNumber(0);
char *ptr(const_cast<char *>(regexpRes[0][0].c_str()));
while (*ptr) {
if (*ptr == '[')
iBracketsNumber++;
else if (*ptr == ']')
iBracketsNumber--;
if (iBracketsNumber < 0)
throw(string("The brackets in the quadratic form don't match"));
if (iBracketsNumber && *ptr == ',')
*ptr = ';';
++ptr;
}
if (iBracketsNumber != 0)
throw(string("The brackets in the quadratic form don't match"));
if ((iRegexpCount = regexp2.preg_match_all(
"([[:digit:]\\*\\-]*)\\[([[:digit:];\\-]+)\\]", regexpRes[0][0],
regexpRes2)) > 0) {
for (int i(0); i < iRegexpCount; i++) {
str_replace(regexpRes2[1][i], "*", "");
if (regexpRes2[1][i] == "-")
regexpRes2[1][i] = "-1";
int iCoefficient(regexpRes2[1][i] == "" ? 1 : stoi(regexpRes2[1][i]));
vector<string> strCoeffs(explode(";", regexpRes2[2][i]));
if (strCoeffs.size() != 3)
throw(string("RCyclotomic: Bad integer: " + regexpRes2[0][i]));
aiQF.push_back(new RCyclotomic7Integer(
iCoefficient * (strCoeffs[0] == "" ? 0 : stoi(strCoeffs[0])),
iCoefficient * (strCoeffs[1] == "" ? 0 : stoi(strCoeffs[1])),
iCoefficient * (strCoeffs[2] == "" ? 0 : stoi(strCoeffs[2]))));
str_replace(regexpRes[0][0], regexpRes2[0][i], "");
}
}
vector<string> strQF(explode(",", regexpRes[0][0]));
for (auto c : strQF) {
if (c != "")
aiQF.push_back(new RCyclotomic7Integer(stoi(c)));
}
}
}
#endif
#ifndef _DOT_PROGRAM_FOUND_
iCreateImage = 0;
#endif
}
AlVin *App::instanciateAlVin() {
AlVin *v(nullptr);
if (strField == "rationals") {
vector<int> iQF;
for (auto c : aiQF)
iQF.push_back(dynamic_cast<RationalInteger *>(c)->iVal);
v = new RationalInteger_AlVin(iQF, strOuputMathematicalFormat, true,
bDebug);
} else if (strField == "quadratic") {
QuadraticInteger::set_d(iFieldSupp);
vector<QuadraticInteger> qiQF;
for (auto c : aiQF) {
QuadraticInteger *qi(dynamic_cast<QuadraticInteger *>(c));
qiQF.push_back(*qi);
}
v = new QuadraticInteger_AlVin(qiQF, strOuputMathematicalFormat, true,
bDebug);
}
#ifdef _RC7AVAILABLE_
else if (strField == "rc7") {
vector<RCyclotomic7Integer> rciQF;
for (auto c : aiQF) {
RCyclotomic7Integer *rci(dynamic_cast<RCyclotomic7Integer *>(c));
rciQF.push_back(*rci);
}
v = new RCyclotomic7Integer_AlVin(rciQF, strOuputMathematicalFormat, true,
bDebug);
}
#endif
v->set_bComputeInvariantsPolyhedron(bComputeInvariantsPolyhedron);
v->set_iCreateImage(iCreateImage);
return v;
}
NotReflective *App::instanciateNotReflectiveEquations(AlVin *v) {
NotReflective *nr(nullptr);
if (strField == "rationals") {
nr = new RationalInteger_NotReflective(v);
} else
throw(string("Not implemented for this field"));
return nr;
}
InfiniteNSymetries *App::instanciateInfiniteNSymetries(AlVin *v) {
InfiniteNSymetries *ins(nullptr);
if (!iMaxVectors)
throw(string("Option -nr mut be used with -maxv"));
if (iMaxVectors < v->get_iDimension())
throw(string(
"The number of vectors should be at least equal to the dimension"));
iMaxVectors = max(iNRMax, v->get_iDimension() + 1);
iNRMin = max(iNRMin, v->get_iDimension() + 1);
iNRMax = min(iMaxVectors, iNRMax);
if (strField == "rationals") {
ins = new RationalInteger_InfiniteNSymetries(v);
} else if (strField == "quadratic") {
ins = new QuadraticInteger_InfiniteNSymetries(v);
}
#ifdef _RC7AVAILABLE_
else if (strField == "rc7") {
ins = new RCyclotomic7Integer_InfiniteNSymetries(v);
}
#endif
else
throw(string("Not implemented for this field"));
return ins;
}
void App::Run() {
if (bPrintHelp) {
printHelp();
return;
}
if (!aiQF.size())
throw(string("No quadratic form given"));
try {
AlVin *v(instanciateAlVin());
NotReflective *nrEquations(nullptr);
InfiniteNSymetries *ins(nullptr);
chrono::time_point<std::chrono::system_clock> timeStart(
chrono::system_clock::now());
if (!v->Run(iMinVectors, iMaxVectors)) {
cout << "\nThe algorithm did not terminate; the polyhedron may be of "
"infinite volume\n"
<< endl;
if (bCheckNREquations) {
if (iMaxVectors) {
nrEquations = instanciateNotReflectiveEquations(v);
nrEquations->Run();
delete nrEquations;
} else
cout << "Option -nrequations mut be used with -maxv" << endl;
}
if (bCheckNR) {
try {
ins = instanciateInfiniteNSymetries(v);
cout << "Checking if the form is non-reflective..." << endl;
if (ins->Run(iNRMin, iNRMax)) {
cout << "\tThe form is non-reflective" << endl;
if (bDebug) {
vector<GraphInvolution> grui(ins->get_usefulInvolutions());
cout << "\tList of used involutions:" << endl;
for (auto inv : grui) {
unsigned int iSize(inv.iPermutation.size());
if (strOuputMathematicalFormat == "latex") {
for (unsigned int i(0); i < iSize; i++) {
if (inv.iPermutation[i] == i)
cout << (i ? ", " : "\t\t") << "e_"
<< (inv.iVertices[i] < 9 ? "" : "{")
<< (inv.iVertices[i] + 1)
<< (inv.iVertices[i] < 9 ? "" : "}");
else if (i < inv.iPermutation[i])
cout << (i ? ", " : "\t\t") << "e_"
<< (inv.iVertices[i] < 9 ? "" : "{")
<< (inv.iVertices[i] + 1)
<< (inv.iVertices[i] < 9 ? "" : "}")
<< " \\leftrightarrow e_"
<< (inv.iVertices[inv.iPermutation[i]] < 9 ? ""
: "{")
<< (inv.iVertices[inv.iPermutation[i]] + 1)
<< (inv.iVertices[inv.iPermutation[i]] < 9 ? ""
: "}");
}
} else {
for (unsigned int i(0); i < iSize; i++) {
if (inv.iPermutation[i] == i)
cout << (i ? ", " : "\t\t") << "e"
<< (inv.iVertices[i] + 1);
else if (i < inv.iPermutation[i])
cout << (i ? ", " : "\t\t") << "e"
<< (inv.iVertices[i] + 1) << " <-> e"
<< (inv.iVertices[inv.iPermutation[i]] + 1);
}
}
cout << endl;
}
}
} else {
cout << "\tCannot decide" << endl;
if (bDebug) {
cout << "\tFor the found involutions, a basis of the fixed "
"points space is:"
<< endl;
ins->print_basisFixedPoints("\t\t");
}
}
delete ins;
} catch (string strE) {
cout << strE << endl;
}
}
} else {
if (bComputeInvariantsPolyhedron) {
CoxIter *ci(v->get_ptrCI());
ci->set_ouputMathematicalFormat(strOuputMathematicalFormat);
ci->computeEulerCharacteristicFVector();
unsigned int iDimension(v->get_iDimension());
cout << "\n---------------------------------\nInformation about the "
"polyhedron:\n---------------------------------"
<< endl;
cout << "Euler characteristic: " << ci->get_brEulerCaracteristic()
<< endl;
// ----------------------------------------------
// Covolume
if (iDimension % 2 == 0) {
cout << "Volume: ";
MPZ_rational cov((iDimension / 2) % 2 ? -1 : 1);
for (unsigned int i(1); i <= iDimension; i++) {
cov *= 2;
cov /= i;
if (i <= (iDimension / 2))
cov *= i;
}
cout << "pi^" << (iDimension / 2) << " * "
<< cov * ci->get_brEulerCaracteristic() << endl;
}
// ----------------------------------------------
// f-vector
vector<unsigned int> iFVector(ci->get_fVector());
cout << "f-vector: (";
for (unsigned int i(0); i <= iDimension; i++)
cout << (i ? ", " : "") << iFVector[i];
cout << ")" << endl;
cout << "Number of vertices at infinity: "
<< ci->get_verticesAtInfinityCount() << endl;
// ---------------------------------------------
// Number of faces with x vertices
/*
cout << "Number of facets with x vertices (x>=3): ";
vector< unsigned int > iFacesAppears( ci->get_iVerticesCount(), 0 );
auto pG( ci->get_ptr_graphsProducts() );
for( auto it : (*pG)[2] )
{
for( auto v : it.get_iVertices() )
iFacesAppears[v]++;
}
for( unsigned int i(3); i < iFVector[0]; i++ )
{
unsigned int iTemp(0);
for( auto it : iFacesAppears )
{
if( it == i )
iTemp++;
}
cout << iTemp << ", ";
}
cout << endl;*/
// ---------------------------------------------
// Growth series and growth rate
cout << "\nGrowth series: " << endl;
ci->printGrowthSeries();
cout << endl;
GrowthRate gr;
GrowthRate_Result grr(
gr.grrComputations(ci->get_growthSeries_denominator()));
if (grr.isComputed && ci->get_isGrowthSeriesReduced()) {
cout << "\nGrowth rate: " << grr.growthRate << endl;
cout << "\tPerron number: "
<< (grr.perron < 0 ? "?" : (grr.perron > 0 ? "yes" : "no"))
<< endl;
cout << "\tPisot number: "
<< (grr.pisot < 0 ? "?" : (grr.pisot > 0 ? "yes" : "no"))
<< endl;
cout << "\tSalem number: "
<< (grr.salem < 0 ? "?" : (grr.salem > 0 ? "yes" : "no"))
<< endl;
}
}
}
// Here we have K=Q
if (bComputeInvariantsQF) {
cout << "\nCommensurability invariant:" << endl;
vector<int> iQF;
for (auto ai : aiQF)
iQF.push_back(dynamic_cast<RationalInteger *>(ai)->get_iValue());
InvariantsQF invqf(iQF);
cout << "\t" << invqf.get_strInvariant() << endl;
}
string strFinalInformation(v->get_strFinalInformation());
if (strFinalInformation != "")
cout << "\n" << strFinalInformation << endl;
cout << "\nComputation time: "
<< chrono::duration<double, milli>(chrono::system_clock::now() -
timeStart)
.count() /
1000
<< "s" << endl;
if (v != nullptr)
delete v;
} catch (string &strE) {
cout << "Error: " << strE << endl;
return;
}
}
void App::printHelp() const {
cout << " _ __ __ _ \n"
" /\\ | |\\ \\ / /(_) \n"
" / \\ | | \\ \\ / / _ _ ___ \n"
" / /\\ \\ | | \\ \\/ / | || '_ \\ \n"
" / ____ \\ | | \\ / | || | | |\n"
"/_/ \\_\\|_| \\/ |_||_| |_|\n"
<< endl;
cout << "AlVin is an implementation of the Vinberg algorithm\n"
"for the fields Q, Q[sqrt(d)] and Q(cos(2*pi/7))\n\n"
"One basic example is the following: \n"
"\t./alvin -qf -1,2,2,3\n"
"\tHere, we applied the algorithm to the diagonal quadratic"
"\n\tform <-1,2,2,3>\n\n"
"If we want to work over the quadratic field Q[sqrt(2)], we can use\n"
"\t./alvin -k=Q[sqrt 2] -qf -1-T,1,1,1,1\n"
"\twhere T denotes the generator of the ring of integers\n\n"
"Another example over Q[sqrt(3)] is given by\n"
"\t./alvin -k=Q[sqrt 3] -qf -3-2T,1,1,1,1 -ip\n"
"\tthe -ip parameter asks AlVin to compute the Invariants of the\n"
"\tcorresponding Polyhedron\n\n"
"The complete documentation is available here:\n"
"\thttps://rgugliel.github.io/AlVin/\n"
<< endl;
}