mirror of https://github.com/CGAL/cgal
132 lines
3.8 KiB
TeX
132 lines
3.8 KiB
TeX
\begin{ccRefClass}{Exponent_vector}
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\ccDefinition
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For a given monomial the vector of its exponents is called the
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exponent vector. The class \ccClassName\ is meant to represent
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such a vector.
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A vector is considered as valid, in case it represents a valid monomial.
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In particular, it should not contain negative exponents.
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\footnote{We choose value type int, since negative exponents may appear in intermediate results. }
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Note that the set of exponent vectors with element vise
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addition forms an {\em Abelian Group}.
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\footnote{Should we add a scalar multiplication? }
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\ccInclude{CGAL/Exponent_vector.h}
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\ccInheritsFrom
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\ccc{std::vector<int>}
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\ccIsModel
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\ccc{Random Access Container}\\
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\ccc{Back Insertion Sequence}\\
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\ccc{DefaultConstructible}\\
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\ccc{Assignable}\\
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\ccc{CopyConstructible}\\
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\ccc{EqualityComparable}\\
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\ccc{LessThanComparable}\\
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\ccCreation
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\ccCreationVariable{ev}
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%\ccc{DefaultConstructible}\\
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\ccConstructor{Exponent_vector();}
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{introduces an uninitialized variable \ccVar.
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}\ccGlue
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%\ccc{CopyConstructible}\\
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\ccConstructor{Exponent_vector(const Exponent_vector & ev_);}
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{The copy constructor
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}\ccGlue
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\ccConstructor{Exponent_vector(size_type n);}
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{Creates a vector with \ccc{n} elements.
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}\ccGlue
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\ccConstructor{Exponent_vector(size_type n, int i);}
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{Creates a vector with \ccc{n} copies of \ccc{i}.
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}\ccGlue
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\ccConstructor{
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template < class InputIterator >
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Exponent_vector(InputIterator begin, InputIterator end);}{
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Creates a vector with a copy of the given range.
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\ccPrecond \ccc{InputIterator} must allow the value type \ccc{int}. \\
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}\ccGlue
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\ccOperations
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\ccMethod{void swap(const size_type& i, const size_type& j) const;}{
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Swap exponent at position i with exponent at position j.
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\ccPrecond { i <= \ccVar.size()}
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\ccPrecond { j <= \ccVar.size()}
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}
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\ccGlue
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\ccFunction{bool is_valid(const Exponent_vector & ev_);}
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{ Returns true if all entries are not negative. }
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\ccOperations
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Group Operation:
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\ccFunction{Exponent_vector operator+(const Exponent_vector &ev1);}{}\ccGlue
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\ccFunction{Exponent_vector operator-(const Exponent_vector &ev1);}{}\ccGlue
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\ccFunction{Exponent_vector
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operator+(const Exponent_vector &ev1,
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const Exponent_vector &ev2);}{
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\ccPrecond ev1.size() == ev2.size()
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}
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\ccGlue
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\ccFunction{Exponent_vector
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operator-(const Exponent_vector &ev1,
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const Exponent_vector &ev2);}{
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\ccPrecond ev1.size() == ev2.size()
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}
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\ccGlue
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\ccMethod{Exponent_vector
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operator+=(const Exponent_vector &ev2);}{
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\ccPrecond \ccVar.size() == ev2.size()
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}
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\ccGlue
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\ccMethod{Exponent_vector
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operator-=(const Exponent_vector &ev2);}{
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\ccPrecond \ccVar.size() == ev2.size()
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}
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\begin{ccAdvanced}
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TODO: Should we add these functions? what about operator $/$ ?
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\ccMethod{Exponent_vector operator*=(int i);}{}
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\ccGlue
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\ccFunction{Exponent_vector operator*(const Exponent_vector &ev, int i);}{}
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\ccGlue
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\ccFunction{Exponent_vector operator*(int i ,const Exponent_vector &ev);}{}
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\end{ccAdvanced}
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\ccc{EqualityComparable}:
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\ccFunction{bool
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operator==(const Exponent_vector &ev1,
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const Exponent_vector &ev2);}{}
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\ccGlue
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\ccFunction{bool
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operator!=(const Exponent_vector &ev1,
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const Exponent_vector &ev2);}{}
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\ccc{LessThanComparable}:
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\ccFunction{bool
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operator<(const Exponent_vector &ev1,
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const Exponent_vector &ev2);}{
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Lexicographic compare, starting with the {\em last} variable. }
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\ccGlue
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\ccSeeAlso
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\ccRefIdfierPage{Polynomial_d}\\
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\ccRefIdfierPage{PolynomialTraits_d}\\
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\end{ccRefClass} |