atlas::arithmetic Namespace Reference

Functions
unsigned long	gcd (unsigned long a, unsigned long b)
unsigned long	lcm (unsigned long a, unsigned long b)
unsigned long &	modProd (unsigned long &a, unsigned long b, unsigned long n)
unsigned long &	modAdd (unsigned long &, unsigned long, unsigned long)
template<typename C>
unsigned long	remainder (C, unsigned long)
unsigned long	gcd (long a, unsigned long b)

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Function Documentation

unsigned long gcd (  long  a, unsigned long  b )  [inline]

Definition at line 39 of file arithmetic.h. Referenced by atlas::interpreter::annihilator_modulo(), atlas::abelian::cycGenerators(), gcd(), lcm(), atlas::makeOrthogonal(), atlas::abelian::FiniteAbelianGroup::order(), atlas::filekl::scan_polynomials(), atlas::abelian::transpose(), and atlas::updateCycGenerator().

unsigned long atlas::arithmetic::gcd (  unsigned long  a, unsigned long  b )

Synopsis: the classic Euclidian algorithm. It is assumed that Precondition: b > 0; Definition at line 30 of file arithmetic.cpp. References gcd().

unsigned long atlas::arithmetic::lcm (  unsigned long  a, unsigned long  b )

Synopsis: returns the lowest common multiple of a and b. Precondition: b > 0; Definition at line 57 of file arithmetic.cpp. References gcd(). Referenced by atlas::checkGenerator(), do_work(), atlas::abelian::Homomorphism::Homomorphism(), atlas::abelian::FiniteAbelianGroup::order(), atlas::interpreter::quotient_basis_wrapper(), and atlas::lattice::toCommonDenominator().

unsigned long & atlas::arithmetic::modAdd (  unsigned long &  , unsigned  long, unsigned  long )  [inline]

Definition at line 46 of file arithmetic.h. Referenced by atlas::abelian::FiniteAbelianGroup::leftApply().

unsigned long & atlas::arithmetic::modProd (  unsigned long &  a, unsigned long  b, unsigned long  n )

Synopsis: a *= b mod n. Precondition: a < n; b < n. NOTE: preliminary implementation. It assumes that n <= 2^^(longBits/2). Will exit brutally if this is not fulfilled. Definition at line 70 of file arithmetic.cpp. Referenced by atlas::abelian::FiniteAbelianGroup::leftApply().

template<typename C> unsigned long atlas::arithmetic::remainder (  C  a, unsigned long  m )

Synopsis: returns the remainder of the division of c modulo m. The point is to always return the unique number r in [0,m[ such that a = q.m + r for a (unique) q. The difficulty arises when C is a signed type; if we are not careful the sign conversions will mess things up big time. NOTE: this looks rather clumsy but I didn't see a better way. It is not always true that for a < 0 one should return m - (-a m); this fails iff a is divisible by m. Definition at line 16 of file arithmetic_def.h. Referenced by test(), atlas::abelian::toArray(), and atlas::abelian::toEndomorphism().

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