atlas::kltest Namespace Reference

Functions
bool	checkBasePoint (const kgb::KGB &kgb)
	Checks whether the conjectural basepoint in each R-packet is independent of the choice of reduced expression.
void	dualityPermutation (setutils::Permutation &a, const kl::KLContext &klc)
bool	dualityVerify (const kl::KLContext &klc, const kl::KLContext &dual_klc)

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Function Documentation

bool atlas::kltest::checkBasePoint (  const kgb::KGB &  kgb  )

Checks whether the conjectural basepoint in each R-packet is independent of the choice of reduced expression. Explanation: let w be a twisted involution, written as an involution-reduced expression w = s_1 ... s_p (here s_j means either conjugation or commuting multiplication). Then the conjecture is that if x is fundamental, the element s_1 ... s_p.x, where the action is cross-action for a conjugation, cayley transform for a commuting multiplication, is independent of the choice of the reduced expression. Algorithm: denote x_w the conjectural element defined for w. Then the conjecture amounts to saying that for any descent s for w, s.x_{sw} is independent of the choice of s. Definition at line 72 of file kltest.cpp. References atlas::kgb::KGB::cayley(), atlas::kgb::KGB::cross(), atlas::weyl::WeylGroup::hasDescent(), atlas::weyl::WeylGroup::hasTwistedCommutation(), atlas::involutionList(), atlas::weyl::WeylGroup::involutionOut(), atlas::weyl::WeylGroup::leftMult(), atlas::kgb::KGB::length(), atlas::printBasePts(), atlas::kgb::KGB::rank(), atlas::kgb::KGB::size(), atlas::kgb::KGB::status(), atlas::weyl::WeylGroup::twistedConjugate(), atlas::weyl::TwistedInvolution, atlas::weyl::TwistedInvolutionList, atlas::weyl::WeylElt::w(), atlas::kgb::KGB::weylGroup(), and atlas::weyl::WeylWord.

void atlas::kltest::dualityPermutation (  setutils::Permutation &  a, const kl::KLContext &  klc )

Definition at line 170 of file kltest.cpp.

bool atlas::kltest::dualityVerify (  const kl::KLContext &  klc, const kl::KLContext &  dual_klc )

Definition at line 174 of file kltest.cpp. References atlas::kl::KLContext::block(), atlas::blocks::dual_map(), atlas::polynomials::Polynomial< C >::isZero(), atlas::kl::KLContext::klPol(), atlas::kl::KLPol, atlas::kl::KLContext::length(), atlas::kl::KLContext::lengthLess(), atlas::prettyprint::printPol(), atlas::kl::KLContext::size(), and atlas::polynomials::Polynomial< C >::subtract_from(). Referenced by atlas::test_f().

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