dedekind::algebra::Monomial< N > Struct Template Reference

A monomial in N variables: its exponents, one per slot (π is the slot 0; π_1, π_2, π_3 the slots 1, 2, 3). The free commutative monoid on N generators, written multiplicatively (the exponents add, as natural numbers: leaving the word raises), and a chain under the graded lexicographic order: by total degree, then by exponents. More...

Collaboration diagram for dedekind::algebra::Monomial< N >:

Public Member Functions
constexpr unsigned long long	degree () const
	The total degree, in a wider word than the exponents.
constexpr unsigned	exponent (std::size_t slot) const
	The exponent of slot.
constexpr Monomial	without (std::size_t slot) const
	This monomial with one factor of slot removed; defined where exponent(slot) is positive (the derivative's use).

Static Public Member Functions
static constexpr Monomial	one ()
	The empty product, the monoid's unit.
static constexpr Monomial	variable (std::size_t slot)
	The variable of slot.

Public Attributes
std::array< unsigned, N >	e {}

Friends
constexpr Monomial	operator* (const Monomial &a, const Monomial &b)
	The product: exponents add.
constexpr bool	operator== (const Monomial &, const Monomial &)=default
constexpr std::strong_ordering	operator<=> (const Monomial &a, const Monomial &b)
	The graded lexicographic order.

Detailed Description

template<std::size_t N>
struct dedekind::algebra::Monomial< N >

A monomial in N variables: its exponents, one per slot (π is the slot 0; π_1, π_2, π_3 the slots 1, 2, 3). The free commutative monoid on N generators, written multiplicatively (the exponents add, as natural numbers: leaving the word raises), and a chain under the graded lexicographic order: by total degree, then by exponents.

Template Parameters

N	the number of variables.

Member Function Documentation

exponent()

template<std::size_t N>

unsigned dedekind::algebra::Monomial< N >::exponent ( std::size_t slot ) const

inlineconstexpr

The exponent of slot.

Exceptions

std::out_of_range

beyond N.

variable()

template<std::size_t N>

constexpr Monomial dedekind::algebra::Monomial< N >::variable ( std::size_t slot )

inlinestaticconstexpr

The variable of slot.

Exceptions

std::out_of_range

beyond N.

Friends And Related Symbol Documentation

operator*

template<std::size_t N>

Monomial operator* ( const Monomial< N > & a, const Monomial< N > & b )

friend

The product: exponents add.

Exceptions

std::overflow_error

where an exponent would leave the word.

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The documentation for this struct was generated from the following file:

• src/main/modules/dedekind/algebra/polynomial.cppm