136 lines
3.2 KiB
C++
136 lines
3.2 KiB
C++
#ifndef _KNOTKIT_PERIODICITY_H
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#define _KNOTKIT_PERIODICITY_H
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#include <algebra/algebra.h>
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#include <vector>
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extern bool verbose;
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extern const char* knot;
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int period = 5;
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std::vector<int> primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
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template<class T>
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class congruence_checker {
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using polynomial = multivariate_laurentpoly<T>;
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using monomial = multivariate_laurent_monomial;
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int prime;
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unsigned index;
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unsigend ev_index;
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polynomial prepare_polynomial(const polynomial& pol) const {
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return (pol - invert_variable(pol, index)).evaluate(-1, ev_index);
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}
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bool reduce (const polynomial& pol) const;
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public:
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congruence_checker(int pprime = 5,
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unsigned ind = 2,
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unsigned ev_ind = 1) :
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prime(pprime), index(ind), ev_index(ev_ind) {}
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congruence_checker(const congruence_checker& cc) =default;
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congruence_checker(congruence_checker&& cc) =default;
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~congruence_checker() {};
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congruence_checker& operator= (const congruence_checker&& cc) =default;
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congruence_checker& operator= (congruence_checker&& cc) =default;
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bool operator () (const polynomial& pol) const {
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return reduce(prepare_polynomial(pol));
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}
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};
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enum class Test_type {
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przytycki_criterion,
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BKP_criterion,
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all
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};
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class periodicity_checker {
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using polynomial = multivariate_laurentpoly;
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using monomial = multivariate_laurent_monomial;
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const unsigned ev_index = 1;
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const unsigned index = 2;
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int prime;
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polynomial<Z> khp;
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polynomial<Z> leep;
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polynomial<Z> quotient;
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polynomial<Z> remainder;
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polynomial<Z> mul;
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Test_type type;
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void write_test_result(bool result) const {
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std::cout << knot;
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if(result)
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std::cout << " may be ";
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else
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std::cout << " is not ";
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std::cout << prime << "-periodic.\n";
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}
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polynomial<Z> divide(const polynomial<Z>& kh, const polynomial<Z>& lee) const;
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std::pair<polynomial<Z>, polynomial<Z>>
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divide_p(const polynomial<Z>& q) const;
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public:
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periodicity_checker(polynomial<Z> kh,
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polynomial<Z> lee,
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int p = 5,
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Test_type t = Test_type::all) :
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khp(kh),
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leep(lee),
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prime(p),
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type(t) {
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// check if prime is in primes
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// compute mul
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mul = polynomial(Z(1)) + polynomial(1, VARIABLE, ev_index) * polynomial(1, VARIABLE, index, 2);
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// compute quotient and remainder
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std::pair<polynomial<Z>, polynomial<Z>>
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p = divide_p(divide(khp, leep));
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quotient = std::get<0>(p);
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remainder = std::get<1>(p);
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}
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periodicity_checker(const periodicity_checker& pc) =default;
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periodicity_checker(periodicity_checker&& pc) =default;
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periodicity_checker& operator= (const periodicity_checker& pc) =default;
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periodicity_checker& operator= (periodicity_checker&& pc) =default;
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void operator () () const {
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if(type == Test_type::przytycki_criterion ||
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type == Test_type::all) {
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std::cout << "Przytycki's test: ";
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write_test_result(przytycki_test());
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}
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if(type == Test_type::BKP_criterion ||
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type == Test_type::all) {
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std::cout << "BKP test: ";
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write_test_result(BKP_test);
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}
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}
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bool przytycki_test() const {
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return true;
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}
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bool BKP_test() const {
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return false;
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}
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}
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#endif // _KNOTKIT_PERIODICITY_H
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