Template class for partial permutations. More...
#include <elements.h>
Public Member Functions | |
| PartialPerm (std::vector< T > const &dom, std::vector< T > const &ran, size_t deg) | |
| A constructor. More... | |
| size_t | crank () const |
| Returns the rank of a partial permutation. More... | |
| bool | operator< (const Element &that) const override |
Returns true if this is less than that. More... | |
| Element * | really_copy (size_t increase_deg_by=0) const override |
Returns a pointer to a copy of this. More... | |
| void | redefine (Element const *x, Element const *y) override |
Multiply x and y and stores the result in this. More... | |
 Public Member Functions inherited from libsemigroups::PartialTransformation< T, PartialPerm< T > > | |
| size_t | complexity () const override |
| Returns the approximate time complexity of multiplying two partial transformations. More... | |
| size_t | crank () const |
| Returns the rank of a partial transformation. More... | |
| size_t | degree () const override |
| Returns the degree of a partial transformation. More... | |
| Element * | identity () const override |
Returns the identity transformation with degrees of this. More... | |
| Public Member Functions inherited from libsemigroups::ElementWithVectorData< T, PartialPerm< T > > | |
| ElementWithVectorData () | |
| A constructor. More... | |
| ElementWithVectorData (std::vector< T > *vector) | |
| A constructor. More... | |
| ElementWithVectorData (std::vector< T > const &vector) | |
| A constructor. More... | |
| T | at (size_t pos) const |
Returns the pos entry in the vector containing the defining data. More... | |
| std::vector< T >::iterator | begin () const |
| Returns an iterator. More... | |
| std::vector< T >::iterator | cbegin () const |
| Returns a const iterator. More... | |
| std::vector< T >::iterator | cend () const |
| Returns a const iterator. More... | |
| void | copy (Element const *x) override |
Copy another Element into this. More... | |
| std::vector< T >::iterator | end () const |
| Returns an iterator. More... | |
| bool | operator< (Element const &that) const override |
Returns true if this is less than that. More... | |
| bool | operator== (Element const &that) const override |
Returns true if this equals that. More... | |
| T | operator[] (size_t pos) const |
Returns the pos entry in the vector containing the defining data. More... | |
| Element * | really_copy (size_t increase_deg_by=0) const override |
Returns a pointer to a copy of this. More... | |
| void | really_delete () override |
| Deletes the defining data of an ElementWithVectorData. More... | |
| void | swap (Element *x) override |
Swap another Element with this. More... | |
| Public Member Functions inherited from libsemigroups::Element | |
| Element (elm_t type=Element::elm_t::NOT_RWSE) | |
| A constructor. More... | |
| virtual | ~Element () |
| A default destructor. More... | |
| elm_t | get_type () const |
| Returns the type libsemigroups::Element::elm_t of an Element object. More... | |
| size_t | hash_value () const |
| Return the hash value of an Element. More... | |
| virtual void | redefine (Element const *x, Element const *y, size_t const &thread_id) |
Multiplies x and y and stores the result in this. More... | |
Additional Inherited Members | |
| Public Types inherited from libsemigroups::Element | |
| enum | elm_t { RWSE = 0, NOT_RWSE = 1 } |
| This enum contains some different types of Element. More... | |
| Static Public Attributes inherited from libsemigroups::PartialTransformation< T, PartialPerm< T > > | |
| static T const | UNDEFINED |
| Undefined image value. More... | |
| Protected Member Functions inherited from libsemigroups::ElementWithVectorDataDefaultHash< T, PartialPerm< T > > | |
| void | cache_hash_value () const override |
This method implements the default hash function for an ElementWithVectorData, which uses ElementWithVectorData::vector_hash. Derive from this class if you are defining a class derived from ElementWithVectorData and there is a specialization of std::hash for the template parameter TValueType, and you do not want to define a hash function explicitly in your derived class. More... | |
| Protected Member Functions inherited from libsemigroups::Element | |
| void | reset_hash_value () const |
| Reset the cached value used by Element::hash_value. More... | |
| Static Protected Member Functions inherited from libsemigroups::ElementWithVectorData< T, PartialPerm< T > > | |
| static size_t | vector_hash (std::vector< T > const *vec) |
Returns a hash value for a vector provided there is a specialization of std::hash for the template type T. More... | |
| Protected Attributes inherited from libsemigroups::ElementWithVectorData< T, PartialPerm< T > > | |
| std::vector< T > * | _vector |
The vector containing the defining data of this. More... | |
| Protected Attributes inherited from libsemigroups::Element | |
| size_t | _hash_value |
| This data member holds a cached version of the hash value of an Element. It is stored here if it is ever computed. It is invalidated by libsemigroups::Element::redefine and sometimes by libsemigroups::Element::really_copy, and potentially any other non-const data member of Element or any of its subclasses. More... | |
| Static Protected Attributes inherited from libsemigroups::Element | |
| static size_t const | UNDEFINED = std::numeric_limits<size_t>::max() |
| UNDEFINED value. More... | |
Detailed Description
template<typename T>
class libsemigroups::PartialPerm< T >
Template class for partial permutations.
The value of the template parameter T can be used to reduce the ! amount ! of memory required by instances of this class; see PartialTransformation ! and ElementWithVectorData for more details.
A partial permutation \(f\) is just an injective partial transformation, which is stored as a vector of the images of \(\{0, 1, \ldots, n - 1\}\), i.e. i.e. \(\{(0)f, (1)f, \ldots, (n - 1)f\}\) where the value PartialTransformation::UNDEFINED is used to indicate that \((i)f\) is undefined (i.e. not among the points where \(f\) is defined).
Constructor & Destructor Documentation
◆ PartialPerm()
|
inlineexplicit |
A constructor.
Constructs a partial perm of degree deg such that
for all i and which is undefined on every other value in the range 0 to (strictly less than deg). This method asserts that dom and ran have equal size and that deg is greater than or equal to the maximum value in dom or ran.
Member Function Documentation
◆ crank()
|
inline |
Returns the rank of a partial permutation.
The rank of a partial permutation is the number of its distinct image values, not including PartialTransformation::UNDEFINED. This method involves slightly less work than PartialTransformation::crank since a partial permutation is injective, and so every image value occurs precisely once. This method recomputes the return value every time it is called.
◆ operator<()
|
inlineoverridevirtual |
Returns true if this is less than that.
This defines a total order on partial permutations that is equivalent to that used by GAP. It is not short-lex on the list of images.
Returns true if something complicated is true and false if it is not.
Implements libsemigroups::Element.
◆ really_copy()
|
inlineoverridevirtual |
Returns a pointer to a copy of this.
See Element::really_copy for more details about this method.
The copy returned by this method is undefined on all the values between the PartialPerm::degree of this and increase_deg_by.
Implements libsemigroups::Element.
◆ redefine()
|
inlineoverridevirtual |
Multiply x and y and stores the result in this.
See Element::redefine for more details about this method.
This method asserts that the degrees of x, y, and this, are all equal, and that neither x nor y equals this.
Reimplemented from libsemigroups::Element.
The documentation for this class was generated from the following file:
- src/elements.h
