#include <AlgebraicTraits.h>
Inheritance diagram for AlgebraicTraits< T >:
Public Types | |
| enum | |
| enum | |
| enum | |
| typedef T | number_type |
| typedef T | norm_type |
| typedef T | scalar_type |
Static Public Member Functions | |
| static const char * | name () |
| static number_type | zero () |
| static number_type | one () |
| static number_type | zero (const number_type &hint) |
| static number_type | one (const number_type &hint) |
| static bool | is_zero (const number_type &val) |
| static bool | equals (const number_type &first, const number_type &second) |
| static int | valuation (const number_type &arg) |
Public Attributes | |
| enum AlgebraicTraits:: { ... } | AlgebraicType |
Definition at line 122 of file AlgebraicTraits.h.
| typedef T AlgebraicTraits< T >::number_type |
represents the type T of elements of this algebraic structure
Definition at line 130 of file AlgebraicTraits.h.
| typedef T AlgebraicTraits< T >::norm_type |
represents the norm type for elements of this algebraic structure (usually a real number)
Definition at line 134 of file AlgebraicTraits.h.
| typedef T AlgebraicTraits< T >::scalar_type |
For vectorial types (e.g. vector fields) this type represents the scalar type e.g. For Ploynomial<float> scalar_type is float.
Definition at line 138 of file AlgebraicTraits.h.
| anonymous enum |
Is Plain Old Data type must be true for basic types. For types that have a meaningful default constructor or destructor set this constant to false. One should override this in specializations of AlgebraicTraits.
Definition at line 144 of file AlgebraicTraits.h.
| anonymous enum |
true if the algebraic structure T has the commutative property and false otherwise.
Definition at line 148 of file AlgebraicTraits.h.
| static const char* AlgebraicTraits< T >::name | ( | ) | [inline, static] |
This method from the AlgebricTraits<T> class should return a symbolic name for the type "T" (e.g. AlgebraicTraits<Polynomial>::name() could return the string "Polynomial" ). This method is used when we want to serialize an object to an XML file and we need to know the name of the type it represents.
Reimplemented from AlgebraicTraitsBase.
Definition at line 151 of file AlgebraicTraits.h.
| static number_type AlgebraicTraits< T >::zero | ( | ) | [inline, static] |
return the identity element of T with regard to the + (additive) operation
Definition at line 159 of file AlgebraicTraits.h.
Referenced by AlgebraicTraits< LongInt< BITS, MAY_OVERFLOW > >::abs(), AlgebraicTraits< LongInt< BITS, MAY_OVERFLOW > >::degree(), derivative(), AlgebraicTraits< Rational< IntType > >::epsilon(), AlgebraicTraits< LongInt< BITS, MAY_OVERFLOW > >::epsilon(), AlgebraicTraits< T >::equals(), gcdOfMinors(), Matrix< T, NumberTraits >::inverse(), AlgebraicTraits< LongInt< BITS, MAY_OVERFLOW > >::norm(), RationalFunction< T, NumberTraits >::operator/=(), partialDerivative(), recursiveSmithNormalForm1(), recursiveSmithNormalForm3(), Polynomial< T, NumberTraits >::roots(), smithMcMillanForm1(), smithMcMillanForm2(), smithNormalForm1(), smithNormalForm2(), smithNormalForm3(), AlgebraicTraits< RationalFunction< ScalarType, AlgebraicTraits< ScalarType > > >::zero(), AlgebraicTraits< Polynomial< ScalarType, AlgebraicTraits< ScalarType > > >::zero(), AlgebraicTraits< Rational< IntType > >::zero(), AlgebraicTraits< LongInt< BITS, MAY_OVERFLOW > >::zero(), and AlgebraicTraits< Complex< T, AlgebraicTraits< T > > >::zero().
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| static number_type AlgebraicTraits< T >::one | ( | ) | [inline, static] |
return the identity element of T with regard to the * (multiplicative) operation
Definition at line 167 of file AlgebraicTraits.h.
Referenced by derivative(), Rational< IntType >::display(), fastDerivative(), Polynomial< T, NumberTraits >::fromRoots(), gcdOfMinors(), RationalFunction< T, NumberTraits >::normalize(), AlgebraicTraits< RationalFunction< ScalarType, AlgebraicTraits< ScalarType > > >::one(), AlgebraicTraits< Polynomial< ScalarType, AlgebraicTraits< ScalarType > > >::one(), AlgebraicTraits< Rational< IntType > >::one(), AlgebraicTraits< LongInt< BITS, MAY_OVERFLOW > >::one(), AlgebraicTraits< Complex< T, AlgebraicTraits< T > > >::one(), partialDerivative(), RationalFunction< T, NumberTraits >::RationalFunction(), recursiveSmithNormalForm1(), recursiveSmithNormalForm3(), smithMcMillanForm1(), smithMcMillanForm2(), smithNormalForm1(), smithNormalForm2(), smithNormalForm3(), AlgebraicTraits< T >::valuation(), and AlgebraicTraits< RationalFunction< ScalarType, AlgebraicTraits< ScalarType > > >::zero().
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| static number_type AlgebraicTraits< T >::zero | ( | const number_type & | hint | ) | [inline, static] |
return the zero value for the type "T". The parameter "hint" is a number used to synthesize the zero value. Not all types contain at compile time all the necessary information needed to generate a zero of that particular type, thus we need a "model", supplied at runtime, of the same exact type to do this. Consider, for example, that we need to generate the null matrix but the number of rows and the number of columns of that matrix is not (in this implementation) a compile time constant so in order to know the number of rows and the number of columns of the null matrix we want to create we need another matrix of the same type to find out the sizes of our null matrix.
Definition at line 183 of file AlgebraicTraits.h.
| static number_type AlgebraicTraits< T >::one | ( | const number_type & | hint | ) | [inline, static] |
return the multiplicative identity value for the type "T". The parameter "hint" is a number used to synthesize the zero value. Not all types contain at compile time all the necessary information needed to generate a zero of that particular type, thus we need a "model", supplied at runtime, of the same exact type to do this. Consider, for example, that we need to generate the identity matrix but the number of rows and the number of columns of that matrix is not (in this implementation) a compile time constant so in order to know the number of rows and the number of columns of the null matrix we want to create we need another matrix of the same type to find out the sizes of our null matrix.
Definition at line 200 of file AlgebraicTraits.h.
| static bool AlgebraicTraits< T >::is_zero | ( | const number_type & | val | ) | [inline, static] |
Return true if the parameter supplied to it is zero and false otherwise. This method should use some tolerance to determine if a floating point value is zero.
Definition at line 209 of file AlgebraicTraits.h.
Referenced by AlgebraicTraits< Rational< IntType > >::is_zero(), and AlgebraicTraits< Complex< T, AlgebraicTraits< T > > >::is_zero().
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| static bool AlgebraicTraits< T >::equals | ( | const number_type & | first, | |
| const number_type & | second | |||
| ) | [inline, static] |
return true if the first parameter equals to the second parameter. In the implementation of this function one should also consider a tolerance if comparing two floating point values
Definition at line 219 of file AlgebraicTraits.h.
References AlgebraicTraits< T >::zero().
Referenced by AlgebraicTraits< Rational< IntType > >::equals(), and AlgebraicTraits< Complex< T, AlgebraicTraits< T > > >::equals().
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| static int AlgebraicTraits< T >::valuation | ( | const number_type & | arg | ) | [inline, static] |
Compute the valuation for an element of an Euclidean domain
Definition at line 229 of file AlgebraicTraits.h.
References AlgebraicTraits< T >::one().
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| enum { ... } AlgebraicTraits< T >::AlgebraicType |
This constant from the AlgebricTraits<T> class should represent the type of the algebraic structure formed by the elements that have the type "T". (e.g. AlgebraicTraits<int>::type should return the value AlgebraicTraitsBase::integral_domain and AlgebraicTraits<double>::type should return the value AlgebraicTraitsBase::field)
Reimplemented from AlgebraicTraitsBase.