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atlas::FiberAction Class Reference

Constructs a function object defining the action of the simple imaginary reflections on a fiber. More...

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Public Member Functions

 FiberAction (const gradings::Grading &gr, const gradings::GradingList &gs, const bitset::RankFlagsList &ma)
bool grading (bitset::RankFlags x, unsigned long s) const
unsigned long operator() (unsigned long s, unsigned long x) const

Private Attributes

gradings::Grading d_baseGrading
bitset::RankFlagsList d_alpha
bitset::RankFlagsList d_mAlpha

Detailed Description

Constructs a function object defining the action of the simple imaginary reflections on a fiber.

The function object this class provides, and that can be used by |partitionmakeOrbits| takes the index |s| of an imaginary root and a number |x| encoding an element of the fiber; it return a number |y| similarly encoding the image of that element under the action of |s|.

In fact the number |x| describes (in binary form) the element of the fiber group that translates the base point to fiber element in question, and the interpretation of |y| is the same. The action is determined by (1) the grading of the simple imaginary roots associated to the chosen base point of the fiber, (2) the grading shifts associated with the generators of the fiber group, and (3) the vectors |d_mAlpha[s]| by which each of the simple imaginary roots $\alpha_s$ translates if it acts act non-trivially (this is the image in the fiber group of the coroot of $\alpha_s$). The action of $\alpha_s$ will translate |x| by |d_mAlpha[s]| if the grading at $\alpha_s$ associated to |x| is odd (noncompact). To facilitate the determination of that grading, the grading shift information is stored as bitsets |d_alpha[s]| for each simple imaginary root. Since in |Fiber|, the grading shifts are organised by generator of the fiber group, the neceesary "transposition" of the information is done by the constructor below.

Definition at line 62 of file cartanclass.cpp.

Constructor & Destructor Documentation

atlas::FiberAction::FiberAction (  const gradings::Grading &  gr,
const gradings::GradingList &  gs,
const bitset::RankFlagsList &  ma
)  [inline]
 

Definition at line 71 of file cartanclass.cpp.

References atlas::gradings::Grading, and atlas::bitset::BitSet< n >::set().

Member Function Documentation

bool atlas::FiberAction::grading (  bitset::RankFlags  x,
unsigned long  s
)  const [inline]
 

Definition at line 84 of file cartanclass.cpp.

References atlas::bitset::RankFlags, and atlas::bitset::BitSet< n >::scalarProduct().

unsigned long atlas::FiberAction::operator() (  unsigned long  s,
unsigned long  x
)  const [inline]
 

Definition at line 87 of file cartanclass.cpp.

References atlas::bitset::RankFlags, and atlas::bitset::BitSet< n >::to_ulong().

Member Data Documentation

bitset::RankFlagsList atlas::FiberAction::d_alpha [private]
 

Definition at line 66 of file cartanclass.cpp.

gradings::Grading atlas::FiberAction::d_baseGrading [private]
 

Definition at line 65 of file cartanclass.cpp.

bitset::RankFlagsList atlas::FiberAction::d_mAlpha [private]
 

Definition at line 67 of file cartanclass.cpp.

The documentation for this class was generated from the following file:
Generated on Wed Mar 26 16:52:17 2008 for atlas by  doxygen 1.3.9.1