Verification of perioidcity congruences is finished
Verification of periodicity congruences is finished and works ok.
This commit is contained in:
Wojciech Politarczyk
parent
bfe339cb0f
commit
7cde96e48f
1
.gitignore
vendored
1
.gitignore
vendored
@ -1,5 +1,6 @@
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#*
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*~
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.*
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*.o
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GPATH
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GRTAGS
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4
Makefile
4
Makefile
@ -11,7 +11,7 @@ CXX = g++ -std=c++11
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INCLUDES = -I. -I/opt/local/include
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# OPTFLAGS = -g
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OPTFLAGS = -O2 -g -pg
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OPTFLAGS = -O2 -g
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# OPTFLAGS = -O2 -g -DNDEBUG
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LDFLAGS = -L/opt/local/lib
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@ -120,6 +120,6 @@ realclean: clean
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$(LIB_OBJS): $(LIB_HEADERS)
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$(ALGEBRA_OBJS): $(ALGEBRA_HEADERS) $(LIB_HEADERS)
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$(KNOTKIT_OBJS) main.o mpimain.o kk.o: $(KNOTKIT_HEADERS) $(ALGEBRA_HEADERS) $(LIB_HEADERS) $(PERIODICITY_HEADERS)
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$(PERIODICITY_OBJS) : $(PERIODICITY_HEADERS)
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$(PERIODICITY_OBJS) : $(PERIODICITY_HEADERS) $(ALGEBRA_HEADERS) $(LIB_HEADERS)
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mpimain.o mpi_aux.o: mpi_aux.h
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19
algebra/Z.h
19
algebra/Z.h
@ -14,6 +14,7 @@ class Z
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private:
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std::shared_ptr<mpz_class> impl;
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#ifdef DEBUG_Z
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void write_state() const {
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std::cout << "I store the following value " << *this << "\n";
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std::cout << "Number of objects pointing to the same value " << impl.use_count() << "\n";
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@ -22,6 +23,7 @@ class Z
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/* std::cout << "Size of std::shared_ptr<mpz_class> " << sizeof(impl) << "\n"; */
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/* std::cout << "Size of mpz_class " << sizeof(*impl) << "\n"; */
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}
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#endif
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public:
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Z() : impl(new mpz_class) {
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@ -52,6 +54,12 @@ class Z
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#ifdef DEBUG_Z
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std::cout << "Z(const Z& z)" << "\n";
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write_state();
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#endif
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}
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Z(copy, const Z& z) : impl(z.impl) {
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#ifdef DEBUG_Z
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std::cout << "Z(COPY, const Z& z)\n";
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write_state();
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#endif
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}
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Z(Z&& z) : impl(std::move(z.impl)) {
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@ -115,6 +123,17 @@ class Z
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return *impl.get() < *z.impl.get();
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}
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bool operator <= (const Z& z) const {
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return *this < z || *this == z;
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}
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bool operator > (const Z& z) const {
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return !(*this <= z);
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}
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bool operator >= (const Z& z) const {
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return !(*this < z);
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}
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bool is_unit () const
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{
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return *this == 1 || *this == -1;
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@ -548,7 +548,6 @@ multivariate_laurentpoly<T> invert_variable(const multivariate_laurentpoly<T>& p
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return result;
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}
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<<<<<<< HEAD
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template<class T>
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multivariate_laurentpoly<T>
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multivariate_laurentpoly<T>::evaluate(T val, unsigned index) const {
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@ -569,6 +568,4 @@ multivariate_laurentpoly<T>::evaluate(T val, unsigned index) const {
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return res;
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}
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=======
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>>>>>>> 297e02dc05d79c4546d04aeb720680a9c231284e
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#endif // _KNOTKIT_ALGEBRA_MULTIVARIATE_LAURENPOLY_H
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111
kk.cpp
111
kk.cpp
@ -1,10 +1,6 @@
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#include <knotkit.h>
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<<<<<<< HEAD
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#include <periodicity.h>
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#include <fstream>
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=======
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>>>>>>> 297e02dc05d79c4546d04aeb720680a9c231284e
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#include <vector>
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#include <utility>
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@ -322,6 +318,17 @@ int compute_s_inv(knot_diagram& kd) {
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}
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void check_periodicity(std::string out_file) {
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if(periodicity_test == "all") {
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Kh_periodicity_checker Kh_pc(kd);
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Przytycki_periodicity_checker P_pc(Kh_pc.get_KhP().evaluate(-1, eval_index));
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for(auto& p : primes_list) {
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std::cout << "Przytycki's criterion: "
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<< P_pc(p) << std::endl
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<< "Kh criterion: "
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<< Kh_pc(p) << std::endl;
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}
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}
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else {
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if(period == 2 || period == 3) {
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std::cout << "Sorry, the criteria don't work for period "
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<< period << "...\n";
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@ -332,73 +339,26 @@ void check_periodicity(std::string out_file) {
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std::cout << "For now you can only check periodicity for primes up to 31..." << "\n";
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exit(EXIT_FAILURE);
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}
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std::ofstream out(out_file);
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std::ofstream out(out_file, std::ios_base::app);
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if(periodicity_test == "all") {
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std::cout << "I will perform both test..." << "\n";
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}
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else if(periodicity_test == "Przytycki") {
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switch(period) {
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case 5: {
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Przytycki_periodicity_checker<5> pcc;
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if(out_file.size() != 0)
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out << pcc(compute_jones(kd)) << std::endl;
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else
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std::cout << pcc(compute_jones(kd)) << std::endl;
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break;
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}
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case 7: {
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Przytycki_periodicity_checker<7> pcc;
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if(out_file.size() != 0)
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out << pcc(compute_jones(kd)) << std::endl;
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else
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std::cout << pcc(compute_jones(kd)) << std::endl;
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break;
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}
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case 11: {
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Przytycki_periodicity_checker<11> pcc;
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if(out_file.size() != 0)
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out << pcc(compute_jones(kd)) << std::endl;
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else
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std::cout << pcc(compute_jones(kd)) << std::endl;
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break;
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}
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case 13: {
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Przytycki_periodicity_checker<13> pcc;
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if(out_file.size() != 0)
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out << pcc(compute_jones(kd)) << std::endl;
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else
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std::cout << pcc(compute_jones(kd)) << std::endl;
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break;
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}
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case 17: {
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Przytycki_periodicity_checker<17> pcc;
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if(out_file.size() != 0)
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out << pcc(compute_jones(kd)) << std::endl;
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else
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std::cout << pcc(compute_jones(kd)) << std::endl;
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break;
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}
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case 19: {
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Przytycki_periodicity_checker<19> pcc;
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if(out_file.size() != 0)
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out << pcc(compute_jones(kd)) << std::endl;
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else
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std::cout << pcc(compute_jones(kd)) << std::endl;
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break;
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}
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}
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if(periodicity_test == "Przytycki") {
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Przytycki_periodicity_checker P_pc(compute_jones(kd));
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if(out_file.size() != 0)
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out << P_pc(period) << std::endl;
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else
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std::cout << P_pc(period) << std::endl;
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}
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else if(periodicity_test == "Kh") {
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Kh_periodicity_checker pc(kd);
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Kh_periodicity_checker Kh_pc(kd);
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if(out_file.size() != 0)
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out << pc(period) << std::endl;
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out << Kh_pc(period) << std::endl;
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else
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std::cout << pc(period) << std::endl;
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std::cout << Kh_pc(period) << std::endl;
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}
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else {
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std::cout << "Sorry, I don't recognize this option..." << "\n";
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exit(EXIT_FAILURE);
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std::cout << "Sorry, I don't recognize this option..." << "\n";
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exit(EXIT_FAILURE);
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}
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}
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}
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@ -726,7 +686,7 @@ main (int argc, char **argv)
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else if(!strcmp (argv[i], "-p")) {
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i++;
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if(i == argc) {
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fprintf (stderr, "error: missing argument to option `-o'\n");
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fprintf (stderr, "error: missing argument to option `-p'\n");
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exit (EXIT_FAILURE);
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}
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period = std::stoi(argv[i]);
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@ -734,7 +694,7 @@ main (int argc, char **argv)
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else if (!strcmp(argv[i], "-t")) {
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i++;
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if(i == argc) {
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fprintf (stderr, "error: missing argument to option `-o'\n");
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fprintf (stderr, "error: missing argument to option `-t'\n");
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exit (EXIT_FAILURE);
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}
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periodicity_test = argv[i];
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@ -844,25 +804,6 @@ main (int argc, char **argv)
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<< ") of " << knot << " = " << std::endl
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<< khp << std::endl;
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}
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else if(!strcmp(invariant, "periodicity_congruence")) {
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if(!strcmp(field, "Z2")) {
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// first we check whether period is a prime
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if(period == 2 || period == 3) {
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std::cerr << "The criterion does not work for period = " << period << "\n";
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exit(EXIT_FAILURE);
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}
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auto result = find(primes.begin(), primes.end(), period);
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if(result == primes.end()) {
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std::cerr << "For now it is possible to check periodicity for primes up to 31" << "\n";
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exit(EXIT_FAILURE);
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}
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check_periodicity_criterion<Z2>(kd,period);
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}
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else {
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std::cerr << "error: for now this function is only defined for Z2 coefficients..." << "\n";
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exit(EXIT_FAILURE);
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}
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}
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else
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{
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if (!strcmp (field, "Z2"))
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@ -64,7 +64,7 @@ class map_wrapper
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/* returns the pair associated to the largest key */
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pair<K, V> tail () const
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{
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typename M::const_reverse_iterator i = impl->t.rbegin ();
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typename M::const_reverse_iterator i = impl->t.rbegin();
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assert (i != impl->t.rend ());
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return pair<K, V> (i->first, i->second);
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}
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223
periodicity.cpp
223
periodicity.cpp
@ -1,6 +1,150 @@
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#include <periodicity.h>
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#include <simplify_chain_complex.h>
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bool Przytycki_periodicity_checker::check(int period) const {
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switch(period) {
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case 5: {
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periodic_congruence_checker<Zp<5>> pcc(5);
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return pcc(jones_pol);
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}
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case 7: {
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periodic_congruence_checker<Zp<7>> pcc(7);
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return pcc(jones_pol);
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}
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case 11: {
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periodic_congruence_checker<Zp<11>> pcc(11);
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return pcc(jones_pol);
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}
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case 13: {
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periodic_congruence_checker<Zp<13>> pcc(13);
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return pcc(jones_pol);
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}
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case 17: {
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periodic_congruence_checker<Zp<17>> pcc(17);
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return pcc(jones_pol);
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}
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case 19: {
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periodic_congruence_checker<Zp<19>> pcc(19);
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return pcc(jones_pol);
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}
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}
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}
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std::string Przytycki_periodicity_checker::operator () (int period) const {
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std::ostringstream res;
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res << knot << ": period = " << period << ": "
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<< (check(period) ? "Maybe" : "No");
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return res.str();
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}
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template<class T>
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polynomial_iterator<T>::polynomial_iterator(const multivariate_laurentpoly<T>& pol,
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start_pos sp) {
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for(typename map<monomial, T>::const_iter i = pol.coeffs; i; ++i) {
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monomials.push_back(i.key());
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bounds.push_back(i.val());
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current_pos.push_back(Z(0));
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}
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if(sp == start_pos::begin) {
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level = 0;
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}
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else {
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level = bounds.size();
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}
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#ifndef NDEBUG
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check_current_pos();
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#endif
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}
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#ifndef NDEBUG
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template<class T>
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void polynomial_iterator<T>::check_current_pos() {
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assert(bounds.size() == monomials.size());
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assert(bounds.size() == current_pos.size());
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assert(level <= current_pos.size());
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for(unsigned i = 0; i < current_pos.size(); i++) {
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if(i < level) {
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assert((current_pos[i] <= bounds[i]) &&
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Z(0) <= (current_pos[i]));
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}
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else if(i == level) {
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if(level > 0)
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assert(current_pos[i] <= bounds[i] && Z(0) < current_pos[i]);
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else
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assert((current_pos[i] <= bounds[i]) && Z(0) <= (current_pos[i]));
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}
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else
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assert(current_pos[i] == Z(0));
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}
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}
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#endif // NDEBUG
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template<class T>
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polynomial_iterator<T>&
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polynomial_iterator<T>::operator ++ () {
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#ifndef NDEBUG
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check_current_pos();
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#endif
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if(level == monomials.size())
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return *this;
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unsigned i = 0;
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while(i <= level) {
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#ifndef NDEBUG
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check_current_pos();
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#endif
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if(current_pos[i] < bounds[i]) {
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current_pos[i] += 1;
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break;
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}
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else {
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if(i == level) {
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if(level < monomials.size() - 1) {
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current_pos[i] = 0;
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current_pos[i+1] += 1;
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level++;
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break;
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}
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else {
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level++;
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break;
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}
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}
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else {
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current_pos[i] = 0;
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}
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}
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i++;
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}
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return *this;
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}
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template<class T>
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multivariate_laurentpoly<T> polynomial_iterator<T>::operator *() const {
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polynomial res;
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for(unsigned i = 0; i <= level; i++) {
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res += polynomial(current_pos[i], monomials[i]);
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}
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return res;
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}
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template<class T>
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std::string polynomial_iterator<T>::write_self() const {
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std::ostringstream res;
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res << "level = " << level << std::endl
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<< "monomials:" << std::endl;
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for(auto& mon : monomials)
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res << mon << std::endl;
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res << "bounds: " << std::endl;
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for(auto& b : bounds)
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res << b << std::endl;
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res << "current_pos: " << std::endl;
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for(auto& pos : current_pos)
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res << pos << std::endl;
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return res.str();
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}
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void Kh_periodicity_checker::compute_knot_polynomials(knot_diagram& kd) {
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unsigned m = kd.num_components ();
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@ -57,8 +201,14 @@ void Kh_periodicity_checker::compute_quot() {
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quot += polynomial(m1.second, m1.first);
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polynomial p = polynomial(m1.second, m1.first) * mul;
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diff -= p;
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m1 = diff.tail();
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if(diff != 0)
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m1 = diff.tail();
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else break;
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}
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if(diff != 0)
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m = diff.head();
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else
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break;
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}
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quot += polynomial(m.second, m.first);
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polynomial p = polynomial(m.second, m.first) * mul;
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@ -91,33 +241,6 @@ Kh_periodicity_checker::compute_quotient_and_remainder(const polynomial& quot,
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return std::make_pair(quotient, remainder);
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}
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std::list<multivariate_laurentpoly<Z>>
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Kh_periodicity_checker::generate_candidates(const polynomial &q) const {
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std::list<polynomial> result;
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Z size = 0;
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map<monomial, Z>::const_iter i = q.coeffs;
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for(int j = 0; Z(j) <= i.val(); j++) {
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result.push_back(polynomial(Z(j), i.key()));
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size += 1;
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}
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i++;
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for( ; i; i++) {
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for(int j = 1; Z(j) <= i.val(); j++) {
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std::list<polynomial> temp_list;
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for_each(result.begin(), result.end(),
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[&result, &temp_list, j, i](const polynomial& p){
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temp_list.push_back(p + polynomial(Z(j), i.key()));
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});
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result.splice(result.end(), temp_list);
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size += 1;
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}
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}
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return result;
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}
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bool Kh_periodicity_checker::check(const polynomial& q,
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const polynomial& r,
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int period) const {
|
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@ -126,26 +249,34 @@ bool Kh_periodicity_checker::check(const polynomial& q,
|
||||
if(q == 0) {
|
||||
return pcc(t.evaluate(-1,1));
|
||||
}
|
||||
else {
|
||||
// generate all polynomials
|
||||
if(verbose) {
|
||||
std::cout << "Generating all candidates..." << std::endl;
|
||||
if(verbose)
|
||||
std::cout << "Checking congruences...";
|
||||
polynomial_iterator<Z> pi(q);
|
||||
polynomial_iterator<Z> pi_end(q, polynomial_iterator<Z>::start_pos::end);
|
||||
Z count = pi.get_count();
|
||||
if(verbose)
|
||||
std::cout << count << " candidates..." << std::endl;
|
||||
Z step = 1;
|
||||
if(count >= 32)
|
||||
step = count / 32;
|
||||
Z c = 0;
|
||||
while(pi != pi_end) {
|
||||
//std::cout << "pi: " << std::endl << pi;
|
||||
polynomial temp = t + polynomial(period - 1) * mul * (*pi);
|
||||
if(pcc(temp.evaluate(-1,1))) {
|
||||
std::cout << "Candidates:" << std::endl
|
||||
<< "EKhP_1 = " << temp << std::endl
|
||||
<< "EKhP_" << (period - 1) << " = "
|
||||
<< (polynomial(period - 1) * mul *(r - *pi))
|
||||
<< std::endl;
|
||||
return true;
|
||||
}
|
||||
std::list<polynomial> candidates = generate_candidates(q);
|
||||
// Z i = 0;
|
||||
// for(auto& l : candidates) {
|
||||
// i += 1;
|
||||
// std::cout << i << ": " << l << std::endl;
|
||||
// }
|
||||
// and check each one of them
|
||||
if(verbose)
|
||||
std::cout << "Checking congruences..." << std::endl;
|
||||
polynomial m = mul;
|
||||
return any_of(candidates.begin(), candidates.end(),
|
||||
[&pcc, &t, &m, &period](const polynomial& p){
|
||||
return pcc((t + Z(period - 1) * m * p).evaluate(-1,1));
|
||||
});
|
||||
++pi;
|
||||
c += 1;
|
||||
if(verbose && c % step == 0)
|
||||
std::cout << c << "/" << count << "..." << std::endl;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
std::string Kh_periodicity_checker::operator () (int period) const {
|
||||
|
||||
111
periodicity.h
111
periodicity.h
@ -5,9 +5,6 @@
|
||||
#include <sstream>
|
||||
#include <string>
|
||||
#include <vector>
|
||||
#include <utility>
|
||||
#include <list>
|
||||
#include <algorithm>
|
||||
|
||||
extern bool verbose;
|
||||
extern const char* knot;
|
||||
@ -16,15 +13,12 @@ extern std::string periodicity_test;
|
||||
|
||||
const std::vector<int> primes_list = {5, 7, 11, 13, 17, 19};
|
||||
|
||||
enum class Test_type {
|
||||
Przytycki_criterion,
|
||||
BKP_criterion,
|
||||
all
|
||||
};
|
||||
const unsigned eval_index = 1;
|
||||
const unsigned invert_index = 2;
|
||||
|
||||
template<class T>
|
||||
class periodic_congruence_checker {
|
||||
public:
|
||||
protected:
|
||||
using polynomial = multivariate_laurentpoly<T>;
|
||||
using monomial = multivariate_laurent_monomial;
|
||||
|
||||
@ -32,19 +26,20 @@ public:
|
||||
unsigned index;
|
||||
|
||||
polynomial prepare_polynomial(const polynomial& pol) const {
|
||||
return (pol - invert_variable(pol, index));
|
||||
polynomial inv = invert_variable(pol, index);
|
||||
return pol - inv;
|
||||
}
|
||||
|
||||
bool reduce(const polynomial& pol) const;
|
||||
|
||||
public:
|
||||
periodic_congruence_checker(int pprime = 5,
|
||||
unsigned ind = 2) :
|
||||
unsigned ind = invert_index) :
|
||||
prime(pprime),
|
||||
index(ind)
|
||||
{}
|
||||
|
||||
~periodic_congruence_checker() {};
|
||||
virtual ~periodic_congruence_checker() {};
|
||||
|
||||
bool operator() (const polynomial& pol) const {
|
||||
return reduce(prepare_polynomial(pol));
|
||||
@ -61,32 +56,90 @@ bool periodic_congruence_checker<T>::reduce(const multivariate_laurentpoly<T>& p
|
||||
monomial mon = monomial(VARIABLE, index, c);
|
||||
res += polynomial(i.val(), mon);
|
||||
}
|
||||
if(verbose)
|
||||
std::cout << "reduced = " << res << "\n";
|
||||
// if(verbose)
|
||||
// std::cout << "reduced = " << res << "\n";
|
||||
return res == 0;
|
||||
}
|
||||
|
||||
template<unsigned p>
|
||||
class Przytycki_periodicity_checker {
|
||||
using polynomial = multivariate_laurentpoly<Zp<p>>;
|
||||
using polynomial = multivariate_laurentpoly<Z>;
|
||||
using monomial = multivariate_laurent_monomial;
|
||||
|
||||
periodic_congruence_checker<Zp<p>> cong_checker;
|
||||
polynomial jones_pol;
|
||||
|
||||
bool check(int period) const;
|
||||
|
||||
public:
|
||||
Przytycki_periodicity_checker() : cong_checker(p) {}
|
||||
Przytycki_periodicity_checker(polynomial j) : jones_pol(j) {}
|
||||
|
||||
~Przytycki_periodicity_checker() {}
|
||||
|
||||
std::string operator() (const polynomial& pol) const {
|
||||
std::ostringstream out;
|
||||
out << knot << ": period = " << p
|
||||
<< ": "
|
||||
<< (cong_checker(pol) ? "Maybe" : "No");
|
||||
return out.str();
|
||||
std::string operator() (int period) const;
|
||||
};
|
||||
|
||||
template<class T>
|
||||
class polynomial_iterator {
|
||||
using polynomial = multivariate_laurentpoly<T>;
|
||||
using monomial = multivariate_laurent_monomial;
|
||||
|
||||
std::vector<monomial> monomials;
|
||||
std::vector<T> bounds;
|
||||
std::vector<T> current_pos;
|
||||
unsigned level;
|
||||
|
||||
void check_current_pos();
|
||||
|
||||
public:
|
||||
enum class start_pos { begin, end };
|
||||
|
||||
polynomial_iterator(const polynomial& init,
|
||||
start_pos sp = start_pos::begin);
|
||||
polynomial_iterator(const polynomial_iterator& pi) =default;
|
||||
polynomial_iterator(polynomial_iterator&& pi) =default;
|
||||
|
||||
~polynomial_iterator() {}
|
||||
|
||||
polynomial_iterator& operator = (const polynomial_iterator& pi) =default;
|
||||
polynomial_iterator& operator = (polynomial_iterator&& pi) =default;
|
||||
|
||||
polynomial_iterator& operator ++();
|
||||
|
||||
bool operator == (const polynomial_iterator& pi) const {
|
||||
if(level == monomials.size() || pi.level == pi.monomials.size()) {
|
||||
return level == pi.level &&
|
||||
monomials == pi.monomials &&
|
||||
bounds == pi.bounds;
|
||||
}
|
||||
else {
|
||||
return level == pi.level &&
|
||||
bounds == pi.bounds &&
|
||||
monomials == pi.monomials &&
|
||||
current_pos == pi.current_pos;
|
||||
}
|
||||
}
|
||||
bool operator != (const polynomial_iterator& pi) const {
|
||||
return !(*this == pi);
|
||||
}
|
||||
polynomial operator*() const;
|
||||
|
||||
T get_count() const {
|
||||
Z res = 1;
|
||||
for(auto& v : bounds)
|
||||
res *= (v + 1);
|
||||
return res;
|
||||
}
|
||||
|
||||
std::string write_self() const;
|
||||
friend inline std::ostream& operator << (std::ostream& os, const polynomial_iterator& pi) {
|
||||
return os << pi.write_self();
|
||||
}
|
||||
};
|
||||
|
||||
template<class T>
|
||||
std::ostream& operator << (std::ostream& os, const polynomial_iterator<T>& pi) {
|
||||
return os << *pi;
|
||||
}
|
||||
|
||||
class Kh_periodicity_checker {
|
||||
using polynomial = multivariate_laurentpoly<Z>;
|
||||
using monomial = multivariate_laurent_monomial;
|
||||
@ -101,7 +154,7 @@ class Kh_periodicity_checker {
|
||||
void compute_quot();
|
||||
std::pair<polynomial, polynomial> compute_quotient_and_remainder(const polynomial& p,
|
||||
int period) const;
|
||||
std::list<polynomial> generate_candidates(const polynomial& q) const;
|
||||
// std::list<polynomial> generate_candidates(const polynomial& q) const;
|
||||
bool check(const polynomial& q, const polynomial& r, int period) const;
|
||||
|
||||
public:
|
||||
@ -119,6 +172,14 @@ class Kh_periodicity_checker {
|
||||
~Kh_periodicity_checker() {}
|
||||
|
||||
std::string operator () (int period) const;
|
||||
|
||||
polynomial get_KhP() const {
|
||||
return khp;
|
||||
}
|
||||
|
||||
polynomial get_LeeP() const {
|
||||
return leep;
|
||||
}
|
||||
};
|
||||
|
||||
#endif // _KNOTKIT_PERIODICITY_H
|
||||
|
||||
Loading…
Reference in New Issue
Block a user