203477c3a8
Verification of Przytycki's congruence works fine, however there are some small modifications that could be made. The, naive, approach to the verification of periodicity congruence for the Khovanov polynomial didn't work. There are just too many cases to check. Generation of all of them can exhaust the memory.
80 lines
1.7 KiB
C++
80 lines
1.7 KiB
C++
#ifndef _KNOTKIT_ALGEBRA_H
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#define _KNOTKIT_ALGEBRA_H
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#include <lib/lib.h>
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#ifdef DEBUG_ALGEBRA
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#define DEBUG_Z
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#define DEBUG_Q
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#endif
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inline int recip (int x)
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{
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assert (x == 1 || x == -1);
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return x;
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}
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template<class T> inline T recip (const T &x) { return x.recip (); }
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template<class T> inline T
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pow (const T &x, int d)
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{
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if (d == 0)
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return 1;
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else if (d == 1)
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return x;
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else if (d < 0)
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return pow (recip (x), -d);
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else
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{
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T x2 = x * x;
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if (d & 1)
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return x * pow (x2, (d - 1) / 2);
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else
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return pow (x2, d / 2);
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}
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}
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unsigned unsigned_gcd (unsigned a, unsigned b);
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uint64 uint64_gcd (uint64 a, uint64 b);
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unsigned int_gcd (int a, int b);
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uint64 int64_gcd (int64 a, int64 b);
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unsigned unsigned_lcm (unsigned a, unsigned b);
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uint64 uint64_lcm (uint64 a, uint64 b);
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unsigned int_lcm (int a, int b);
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uint64 int64_lcm (int64 a, int64 b);
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// (d, x, y) = gcd (a, b) where x*a + y*b = d
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tuple<unsigned, int, int> extended_gcd (int a, int b);
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tuple<unsigned, int, int> unsigned_extended_gcd (unsigned a, unsigned b);
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template<class R> class linear_combination;
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template<class R> class linear_combination_const_iter;
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template<class R> class module;
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/* constructor tag for multivariate_polynomial,
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multivariate_laurentpoly. */
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enum variable { VARIABLE };
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#include <algebra/grading.h>
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#include <algebra/Z2.h>
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#include <algebra/multivariate_polynomial.h>
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#include <algebra/multivariate_laurentpoly.h>
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#include <algebra/Z.h>
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#include <algebra/Zp.h>
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#include <algebra/Q.h>
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#include <algebra/polynomial.h>
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#include <algebra/fraction_field.h>
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#include <algebra/module.h>
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#include <algebra/linear_combination.h>
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#endif // _KNOTKIT_ALGEBRA_H
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