This class implements the semiring consisting of \(\{0, 1, ..., t, t + 1, ..., t + p - 1\}\) for some threshold \(t\) and period \(p\) with operations addition and multiplication modulo the congruence \(t = t + p\). More...
#include <semiring.h>
Public Member Functions | |
| NaturalSemiring (int64_t t, int64_t p) | |
| Construct from threshold and period. More... | |
| int64_t | one () const override |
| Return the integer 1. More... | |
| int64_t | period () const |
| Returns the period of the semiring. More... | |
| int64_t | plus (int64_t x, int64_t y) const override |
Returns x + y modulo the congruence \(t = t + p\) where \(t\) and \(p\) are the threshold and period of the semiring, respectively. More... | |
| int64_t | prod (int64_t x, int64_t y) const override |
Returns x * y modulo the congruence \(t = t + p\) where \(t\) and \(p\) are the threshold and period of the semiring, respectively. More... | |
| int64_t | zero () const override |
| Return the integer 0. More... | |
 Public Member Functions inherited from libsemigroups::SemiringWithThreshold | |
| SemiringWithThreshold (int64_t threshold) | |
| A class for semirings with a threshold. More... | |
| int64_t | threshold () const |
| Returns the threshold of a semiring with threshold. More... | |
| Public Member Functions inherited from libsemigroups::Semiring< int64_t > | |
| virtual | ~Semiring () |
| A default destructor. More... | |
Additional Inherited Members | |
| Static Public Attributes inherited from libsemigroups::Semiring< int64_t > | |
| static const int64_t | INFTY |
| Value representing \(\infty\). More... | |
| static const int64_t | MINUS_INFTY |
| Value representing \(-\infty\). More... | |
| static const int64_t | UNDEFINED |
| Value representing an undefined quantity. More... | |
Detailed Description
This class implements the semiring consisting of \(\{0, 1, ..., t, t + 1, ..., t + p - 1\}\) for some threshold \(t\) and period \(p\) with operations addition and multiplication modulo the congruence \(t = t + p\).
Constructor & Destructor Documentation
◆ NaturalSemiring()
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inline |
Construct from threshold and period.
This method constructs a semiring whose elements are \(\{0, 1, ..., t, t + 1, ..., t + p - 1\}\) with operations addition and multiplication modulo the congruence \(t = t + p\).
The parameter t should be greater than or equal to 0, and the parameter p must be strictly greater than 0, both which are asserted in the constructor.
Member Function Documentation
◆ one()
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inlineoverridevirtual |
Return the integer 1.
Implements libsemigroups::Semiring< int64_t >.
◆ period()
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inline |
Returns the period of the semiring.
◆ plus()
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inlineoverridevirtual |
Returns x + y modulo the congruence \(t = t + p\) where \(t\) and \(p\) are the threshold and period of the semiring, respectively.
Implements libsemigroups::Semiring< int64_t >.
◆ prod()
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inlineoverridevirtual |
Returns x * y modulo the congruence \(t = t + p\) where \(t\) and \(p\) are the threshold and period of the semiring, respectively.
Implements libsemigroups::Semiring< int64_t >.
◆ zero()
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inlineoverridevirtual |
Return the integer 0.
Implements libsemigroups::Semiring< int64_t >.
The documentation for this class was generated from the following file:
- src/semiring.h
