Tests a group given by generators for being an Alternating Group or a Symmetric Group. More...
#include <giant_test.h>
Public Member Functions | |
| template<typename ForwardIterator , typename TRANS > | |
| GiantGroupType | determineGiantType (double eps, unsigned int n, ForwardIterator begin, ForwardIterator end, BSGS< PERM, TRANS > &bsgs, bool isKnownPrimitive=false) const |
| tests whether group given by generators is an Alternating or a Symmetric Group More... | |
| template<typename ForwardIterator > | |
| GiantGroupType | determineGiantType (double eps, unsigned int n, ForwardIterator begin, ForwardIterator end, bool isKnownPrimitive=false) const |
| tests whether group given by generators is an Alternating or a Symmetric Group More... | |
| template<typename T > | |
| GiantTestBase::GiantGroupType | giantTypeByOrder (const T &order, const T &symOrder) |
| template<typename ForwardIterator , typename TRANS > | |
| GiantTestBase::GiantGroupType | determineGiantType (double eps, unsigned int n, ForwardIterator begin, ForwardIterator end, BSGS< PERM, TRANS > &bsgs, bool isKnownPrimitive) const |
Static Public Member Functions | |
| template<typename ForwardIterator > | |
| static bool | isSubgroupOfAlternatingGroup (ForwardIterator begin, ForwardIterator end) |
| tests whether group given by generators is a subgroup of an Alternating Group More... | |
Additional Inherited Members | |
 Public Types inherited from permlib::GiantTestBase | |
| enum | GiantGroupType { None , Alternating , Symmetric } |
| Enumeration of "giant" groups, i.e. Alternating and Symmetric group. | |
Detailed Description
template<typename PERM>
class permlib::GiantTest< PERM >
Tests a group given by generators for being an Alternating Group or a Symmetric Group.
This an implementation of the algorithm given in Holt, Eick, O'Brien: Handbook of Computational Group Theory, 2005. Chapter 4.2
Member Function Documentation
◆ determineGiantType() [1/2]
|
inline |
tests whether group given by generators is an Alternating or a Symmetric Group
The test is deterministic for n < 8 and randomized for n >= 8. The randomized test assumes that n is smaller than
- Parameters
-
eps If randomized, 1-eps is the probability that the decision "None" is wrong n Degree of the group begin iterator of Permutation::ptr, group generators end iterator of Permutation::ptr, group generators isKnownPrimitive true if group is known to be primitive
- Returns
- Result "None" may be wrong if n >= 8 with probability eps
◆ determineGiantType() [2/2]
| GiantGroupType permlib::GiantTest< PERM >::determineGiantType | ( | double | eps, |
| unsigned int | n, | ||
| ForwardIterator | begin, | ||
| ForwardIterator | end, | ||
| BSGS< PERM, TRANS > & | bsgs, | ||
| bool | isKnownPrimitive = false |
||
| ) | const |
tests whether group given by generators is an Alternating or a Symmetric Group
The test is deterministic for n < 8 and randomized for n >= 8. The randomized test assumes that n is smaller than
- Parameters
-
eps If randomized, 1-eps is the probability that the decision "None" is wrong n Degree of the group begin iterator of Permutation::ptr, group generators end iterator of Permutation::ptr, group generators bsgs if for the test a BSGS is computed, it is stored into this variable isKnownPrimitive true if group is known to be primitive
- Returns
- Result "None" may be wrong if n >= 8 with probability eps
◆ isSubgroupOfAlternatingGroup()
|
static |
tests whether group given by generators is a subgroup of an Alternating Group
Tests subgroup property by computing parity of all generators.
- Parameters
-
begin iterator of Permutation::ptr, group generators end iterator of Permutation::ptr, group generators
- Returns
- true if the group is a subgroup of an alternating group
The documentation for this class was generated from the following file:
- include/permlib/test/giant_test.h
