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/*****************************************************************************\
* Computer Algebra System SINGULAR
\*****************************************************************************/
/** @file ExtensionInfo.h
*
* This file provides a class to store information about finite fields and
* extensions thereof.
*
*
* @author Martin Lee
*
**/
/*****************************************************************************/
#ifndef EXTENSION_INFO_H
#define EXTENSION_INFO_H
// #include "config.h"
#include "canonicalform.h"
/** @class ExtensionInfo ExtensionInfo.h "factory/ExtensionInfo.h"
* ExtensionInfo contains information about extension.
* If @a m_extension is true we are in an extension of some initial field.
* If the initial field is \f$ F_p \f$ and we pass to \f$ F_p (\alpha) \f$
* then @a m_alpha is an algebraic variable, @a m_beta= Variable(1),
* @a m_gamma= @a m_delta= 1, @a m_GFDegree= 0, @a m_GFName= 'Z'. If we pass
* to some GF (p^k) then @a m_alpha= Variable (1), @a m_beta= Variable(1),
* @a m_gamma= @a m_delta= 1, @a m_GFDegree= 1, @a m_GFName= 'Z'.
* @n If the initial field is \f$ F_p (\epsilon) \f$, then @a m_beta=
* \f$ \epsilon \f$, @a m_alpha an algebraic variable defining an extension of
* \f$ F_p (\epsilon) \f$, @a m_gamma is a primitive element of
* \f$ F_p (\alpha) \f$, @a m_delta is a primitive element of
* \f$ F_p (\beta) \f$, @a m_GFDegree= 0, @a m_GFName= 'Z'.
* @n If the initial field is GF(p^k), then @a m_alpha= Variable (1),
* @a m_beta= Variable (1), @a m_gamma= 1, @a m_delta= 1, @a m_GFDegree()= k,
* @a m_GFName= gf_name of the initial field.
* @n If @a m_extension is false and the current field is \f$ F_p \f$ then
* @a m_alpha= Variable (1), @a m_beta= Variable (1), @a m_gamma= 1,
* @a m_delta= 1, @a m_GFDegree= 1, @a m_GFName= 'Z'.
* @n If the current field is \f$ F_p (\alpha) \f$ then
* @a m_alpha is some algebraic variable, @a m_beta= Variable (1),
* @a m_gamma= 1, @a m_delta= 1, @a m_GFDegree= 0, @a m_GFName= 'Z'.
* @n If the current field is GF then @a m_alpha= Variable (1),
* @a m_beta= Variable (1), @a m_gamma= 1, @a m_delta= 1,
* @a m_GFDegree= getGFDegree(), @a m_GFName= gf_name.
*
* @sa facFqBivar.h, facFqFactorize.h
*/
class ExtensionInfo
{
private:
/// an algebraic variable or Variable (1)
Variable m_alpha;
/// an algebraic variable or Variable (1)
Variable m_beta;
/// a primitive element of \f$ F_p (\alpha) \f$ or 1
CanonicalForm m_gamma;
/// a primitive element of \f$ F_p (\beta) \f$ or 1
CanonicalForm m_delta;
/// GF degree or 1
int m_GFDegree;
/// name of GF variable
char m_GFName;
/// indicates if we are in an extension of some initial field
bool m_extension;
public:
/// \f$ F_p \f$ as initial field, if @a extension is true we are in some GF
ExtensionInfo (const bool extension ///< [in] some bool
);
/// Construct an @a ExtensionInfo
ExtensionInfo (const Variable& alpha, ///< [in] some algebraic variable
const Variable& beta, ///< [in] some algebraic variable
const CanonicalForm& gamma, ///< [in] some primitive element
///< of \f$ F_p (\alpha) \f$
const CanonicalForm& delta, ///< [in] some primitive element
///< of \f$ F_p (\beta) \f$
const int nGFDegree, ///< [in] GFDegree of initial field
const char cGFName, ///< [in] name of GF variable of
///< initial field
const bool extension ///< [in] some bool
);
/// \f$ F_p (\beta) \f$ as initial field and switch to an extension given by
/// @a alpha, needs primitive elements @a gamma and @a delta for maps
/// between \f$ F_p (\alpha) \subset F_p (\beta) \f$
ExtensionInfo (const Variable& alpha, ///< [in] some algebraic variable
const Variable& beta, ///< [in] some algebraic variable
const CanonicalForm& gamma, ///< [in] some primitive element
///< of \f$ F_p (\alpha) \f$
const CanonicalForm& delta ///< [in] some primitive element
///< of \f$ F_p (\beta) \f$
);
/// \f$ F_p (\alpha) \f$ as initial field, if @a extension is false.
/// Else initial field is \f$ F_p \f$
ExtensionInfo (const Variable& alpha, ///< [in] some algebraic variable
const bool extension ///< [in] some bool
);
ExtensionInfo (const Variable& alpha ///< [in] some algebraic variable
);
/// GF as initial field
ExtensionInfo (const int nGFDegree, ///< [in] GF degree of initial field
const char cGFName, ///< [in] name of GF variable
const bool extension ///< [in] some bool
);
/// getter
///
/// @return @a getAlpha() returns @a m_alpha
Variable getAlpha () const
{
return m_alpha;
}
/// getter
///
/// @return @a getBeta() returns @a m_beta
Variable getBeta () const
{
return m_beta;
}
/// getter
///
/// @return @a getGamma() returns @a m_gamma
CanonicalForm getGamma() const
{
return m_gamma;
}
/// getter
///
/// @return @a getDelta() returns @a m_delta
CanonicalForm getDelta() const
{
return m_delta;
}
/// getter
///
/// @return @a getGFDegree() returns @a m_GFDegree
int getGFDegree() const
{
return m_GFDegree;
}
/// getter
///
/// @return @a getGFName() returns @a m_GFName
char getGFName() const
{
return m_GFName;
}
/// getter
///
/// @return @a isInextension() returns @a m_extension
bool isInExtension() const
{
return m_extension;
}
};
#endif
/* EXTENSION_INFO_H */
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