Monomial
Monomials are ordered products of algebra generators. Even though monomials stored as parts of a polynomial expression are always canonically ordered, that need not be true in general.
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template<typename ...IndexTypes>
class monomial Monomial, an ordered product of zero or more algebra generators \(g_{i_1}, g_{i_2}, \ldots, g_{i_n}\),
\[M^{(n)}_{i_1, i_2, \ldots, i_n} = g_{i_1} g_{i_2} \ldots g_{i_n}.\]IndexTypes- types of indices carried by the algebra generators.Member type aliases
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using index_types = std::tuple<IndexTypes...>
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using generator_type = generator<IndexTypes...>
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using gen_ptr_type = std::unique_ptr<generator_type>
Constructors
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monomial() = default
Construct an empty (zero-length) monomial \(M^{(0)} = 1\).
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template<typename ...GenTypes>
explicit monomial(GenTypes&&... generators) Construct a non-empty monomial from a list of generators.
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monomial(std::initializer_list<generator_type*> generators)
Construct a monomial from a list of pointers to generators using the list initialization syntax. This constructor creates copies of the generators by calling
generator::clone().
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monomial(std::vector<generator_type*> generators)
Construct a monomial from a vector of pointers to generators. This constructor creates copies of the generators by calling
generator::clone().
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monomial(std::initializer_list<gen_ptr_type> generators)
Construct a monomial from a list of smart pointers to generators using the list initialization syntax. This constructor creates copies of the generators by calling
generator::clone().
Copy/move-constructors and assignments
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class const_iterator
Random access constant iterator to the list of algebra generators. The dereference type is
generator_type.
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const_iterator begin() const noexcept
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const_iterator cbegin() const noexcept
Constant iterator to the first algebra generator.
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const_iterator end() const noexcept
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const_iterator cend() const noexcept
Constant past-the-end iterator.
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using const_reverse_iterator = std::reverse_iterator<const_iterator>
Reverse iteration version of
const_iterator.
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const_reverse_iterator rbegin() const noexcept
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const_reverse_iterator crbegin() const noexcept
Reverse constant iterator to last algebra generator.
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const_reverse_iterator rend() const noexcept
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const_reverse_iterator crend() const noexcept
Reverse constant past-the-end iterator.
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generator_type const &operator[](std::size_t n) const
Access an algebra generator by its position n in the monomial.
Other methods and friend functions
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std::size_t size() const
Number of algebra generators in the monomial.
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bool empty() const
Is this a zero-length monomial?
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friend bool operator==(monomial const &m1, monomial const &m2)
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friend bool operator!=(monomial const &m1, monomial const &m2)
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friend bool operator<(monomial const &m1, monomial const &m2)
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friend bool operator>(monomial const &m1, monomial const &m2)
Compare two monomials. The lesser and greater comparisons check monomials’ lengths first, and in the case of equal lengths perform the lexicographical comparison of the
generatorlists.
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bool is_ordered() const
Is this monomial canonically ordered? In other words, does its algebra generator list satisfy \(g_{i_1} < g_{i_2} < \ldots < g_{i_n}\)?
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void swap_generators(std::size_t n1, std::size_t n2)
Swap algebra generators at positions n1 and n2 within the list.
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void append(generator_type const &g)
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void append(monomial const &m)
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void append(std::pair<const_iterator, const_iterator> const &r)
Append a generator, a monomial or a range of generators specified by a begin-end iterator pair std::pair<const_iterator, const_iterator> to this monomial.
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template<typename ...PartTypes>
friend monomial concatenate(PartTypes&&... parts) Concatenate a number of parts to build a new monomial. The parts can be monomials, algebra generators and ranges within monomials. The ranges should be passed as begin-end iterator pairs std::pair<const_iterator, const_iterator>.
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using index_types = std::tuple<IndexTypes...>