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Classes |
class | BlackboxBlockContainerBase |
| A base class for BlackboxBlockContainer. The primary member function is begin(). More...
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class | BlackboxContainerBase |
| A base class for BlackboxContainer. The primary member function is begin(). More...
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class | BlackboxContainerSymmetric |
| See base class for doc. More...
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class | BlackboxContainerSymmetrize |
| Symmetrizing iterator (for rank computations). More...
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class | BlackboxContainer |
| Limited doc so far. More...
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class | BlasMatrixDomainMulAdd |
class | BlockLanczosSolver |
| Block Lanczos iteration. More...
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class | BlockMasseyDomain |
| Compute the linear generator of a sequence of matrices. More...
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class | DenseContainer |
| Limited doc so far. More...
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class | DiophantineSolver |
| DiophantineSolver<QSolver> creates a diophantine solver using a QSolver to generate rational solutions. More...
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class | Eliminator |
class | GaussDomain |
| Repository of functions for rank by elimination on sparse matrices. More...
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class | LABlockLanczosSolver |
class | LanczosSolver |
| Solve a linear system using the conjugate Lanczos iteration. More...
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class | LastInvariantFactor |
| This is used in a Smith Form algorithm. More...
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class | MasseyDomain |
| Berlekamp/Massey algorithm. More...
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class | MatrixRank |
class | MGBlockLanczosSolver |
| Block Lanczos iteration. More...
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class | OneInvariantFactor |
| Limited doc so far. More...
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struct | RationalRemainder |
| Chinese remainder of rationals. More...
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class | RationalReconstruction |
| Limited doc so far. Used, for instance, after LiftingContainer. More...
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class | RationalSolver |
| interface for the different specialization of p-adic lifting based solvers. More...
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class | RationalSolver< Ring, Field, RandomPrime, WiedemannTraits > |
| partial specialization of p-adic based solver with Wiedemann algorithm More...
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class | RationalSolver< Ring, Field, RandomPrime, BlockWiedemannTraits > |
| partial specialization of p-adic based solver with block Wiedemann algorithm More...
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class | RationalSolver< Ring, Field, RandomPrime, DixonTraits > |
| partial specialization of p-adic based solver with Dixon algorithm More...
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class | RationalSolver< Ring, Field, RandomPrime, NumericalTraits > |
| partial specialization of p-adic based solver with a hybrid Numeric/Symbolic computation More...
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class | SmithFormBinary |
| Compute Smith form. More...
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class | SmithFormIliopoulos |
| This is Iliopoulos' algorithm do diagonalize. More...
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class | SmithFormLocal |
| Smith normal form (invariant factors) of a matrix over a local ring. More...
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class | PowerGaussDomain |
| Repository of functions for rank modulo a prime power by elimination on sparse matrices. More...
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class | VectorFraction |
| VectorFraction<Domain> is a vector of rational elements with common reduced denominator. Here Domain is a ring supporting the gcd, eg NTL_ZZ or PID_integer For compatability with the return type of rationalSolver, it allows conversion from/to std::vector<std::pair<Domain::Element> >. All functions will return the fraction in reduced form, calling reduce() if necessary. More...
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class | WiedemannSolver |
| Linear system solvers based on Wiedemann's method. More...
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class | BlackboxArchetype |
| showing the member functions provided by all blackbox matrix classes. More...
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class | BlackboxInterface |
| This blackbox base class exists solely to aid documentation organization. More...
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class | BlasBlackbox |
| dense matrix representation for BLAS based elimination. More...
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class | Butterfly |
| Switching Network based BlackBox Matrix. A good preconditioner. More...
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struct | Companion |
| Companion matrix of a monic polynomial. More...
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class | Compose |
| General case. More...
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class | Compose< _Blackbox, _Blackbox > |
| specialization for _Blackbox1 = _Blackbox2 More...
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class | ComposeTraits |
| used in ..., for example More...
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class | ComposeTraits< DenseMatrix< Field > > |
| used in smith-binary, for example More...
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class | DenseMatrix |
| Blackbox interface to dense matrix representation. More...
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class | DenseMatrixFactory |
class | Diagonal |
| Random diagonal matrices are used heavily as preconditioners. More...
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class | Diagonal< _Field, VectorCategories::DenseVectorTag > |
| Specialization of Diagonal for application to dense vectors. More...
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class | Diagonal< Field, VectorCategories::SparseSequenceVectorTag > |
| Specialization of Diagonal for application to sparse sequence vectors. More...
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class | Diagonal< Field, VectorCategories::SparseAssociativeVectorTag > |
| Specialization of Diagonal for application to sparse associative vectors. More...
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class | Dif |
| Blackbox of a difference: C := A - B, i.e. Cx = Ax - Bx. More...
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class | DirectSum |
| If C = DirectSum(A, B) and y = xA and z = wB, then (y,z) = (x,w)C. More...
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class | BlackboxFactory |
| A tool for computations with integer and rational matrices. More...
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class | Frobenius |
| template More...
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class | Hilbert |
| Example of a blackbox that is space efficient, though not time efficient. More...
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class | Inverse |
| A Blackbox for the inverse. Not efficient if many applications are used. More...
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class | MoorePenrose |
| Generalized inverse of a blackbox. Efficiency concerns when many applications are used. More...
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class | Hankel |
| template More...
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class | Sylvester |
| template More...
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class | NullMatrix |
| This is a representation of the 0 by 0 empty matrix which does not occupy memory. It has it's uses! More...
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class | Permutation |
| size is n. More...
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class | PolynomialBB |
| represent the matrix P(A) where A is a blackbox and P a polynomial More...
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class | ScalarMatrix |
| Blackbox for aI . Use particularly for representing 0 and I . More...
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class | SparseMatrix |
| vector of sparse rows. More...
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class | SparseMatrixFactory |
class | Submatrix |
class | Submatrix< Blackbox, VectorCategories::DenseVectorTag > |
class | Submatrix< DenseMatrix< _Field >, VectorCategories::DenseVectorTag > |
class | Sum |
| blackbox of a matrix sum without copying. More...
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class | Toeplitz |
| This is the blackbox representation of a Toeplitz matrix. More...
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class | Toeplitz< typename _PField::CoeffField, _PField > |
class | Transpose |
| transpose matrix without copying. More...
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class | TriplesBB |
| wrapper for NAG Sparse Matrix format. More...
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class | ZeroOne |
| Time and space efficient representation of sparse {0,1}-matrices. More...
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class | ElementAbstract |
| Abstract element base class, a technicality. More...
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class | ElementArchetype |
| Field and Ring element interface specification and archetypical instance class. More...
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class | ElementEnvelope |
| Adaptor from archetypical interface to abstract interface, a technicality. More...
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class | GivPolynomial |
| Polynomials over a domain. More...
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class | GMPRationalElement |
| elements of GMP_Rationals. More...
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class | FFLAS |
| BLAS for matrices over finite fields. More...
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class | FFPACK |
| Set of elimination based routines for dense linear algebra with matrices over finite prime field of characteristic less than 2^26. More...
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class | FieldAbstract |
| field base class. More...
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class | FieldArchetype |
| field specification and archetypical instance. More...
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class | FieldEnvelope |
| Derived class used to implement the field archetype. More...
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class | FieldInterface |
| This field base class exists solely to aid documentation organization. More...
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struct | GivaroField |
| give LinBox fields an allure of Givaro Fields More...
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class | GivaroExtension |
class | GivaroExtension< GivaroGfq > |
class | GivaroGfq |
class | GivaroMontg |
| wrapper of Givaro's Montgomery<Std32>. More...
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class | GivaroZpz |
| wrapper of Givaro's ZpzDom. More...
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class | NoHomError |
| Error object for attempt to establish a Hom that cannot exist. More...
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class | Hom |
| map element of source ring(field) to target ring More...
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class | LidiaGfq |
| defines the Galois Field GF(pk). More...
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struct | Local2_32 |
| Fast arithmetic mod 2^32, including gcd. More...
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class | ModularBalance< int > |
| template <> More...
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class | Modular< int32 > |
| template <> More...
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class | Modular< int8 > |
| Specialization of Modular to signed 8 bit element type with efficient dot product. More...
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class | Modular< double > |
| template <> More...
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class | Modular< int16 > |
| Specialization of Modular to short element type with efficient dot product. More...
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class | Modular |
| Prime fields of positive characteristic implemented directly in LinBox. More...
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class | Modular< uint8 > |
| Allows compact storage when the modulus is less than 2^8. More...
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class | Modular< uint16 > |
| Specialization of class Modular for uint16 element type. More...
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class | Modular< uint32 > |
| Specialization of class Modular for uint32 element type. More...
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class | UnparametricRandIter< NTL::GF2E > |
| template<> More...
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struct | NTL_zz_p |
| long ints modulo a positive integer. More...
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class | NTL_zz_pX |
struct | NTL_PID_zz_p |
| extend Wrapper of zz_p from NTL. Add PID functions More...
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class | NTL_ZZ_pX |
class | ParamFuzzy |
class | PIRModular< int > |
| template <> More...
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class | PIRModular< int32 > |
| template <> More...
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class | PIR_ntl_ZZ_p |
| extend Wrapper of ZZ_p from NTL. Add PIR functions More...
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struct | Rebind |
| used in support of Hom, MatrixHom More...
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class | MatrixArchetype |
| Directly-represented matrix archetype. More...
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class | indexDomain |
class | DenseRowsMatrix |
class | DenseSubmatrix |
class | DenseMatrixBase |
struct | MatrixCategories |
| For specializing matrix arithmetic. More...
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class | MVProductDomain |
| Helper class to allow specializations of certain matrix-vector products. More...
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class | MatrixDomain |
| Class of matrix arithmetic functions. More...
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class | InvalidMatrixInput |
class | FieldIO |
| Dummy field for conceptually unclear io. More...
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class | SparseMatrixBase |
class | TransposeMatrix |
class | RandIterAbstract |
class | RandIterArchetype |
| Random field element generator archetype. More...
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class | RandIterEnvelope |
class | GF2RandIter |
class | GmpRandomPrime |
| generating random prime integers, using the gmp library. More...
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class | ModularBalanceRandIter |
class | ModularRandIter |
class | NonzeroRandIter |
class | ParamFuzzyRandIter |
class | UnparametricRandIter |
class | RingAbstract |
| Abstract ring base class. More...
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class | RingArchetype |
| specification and archetypic instance for the ring interface More...
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class | RingEnvelope |
| implement the ring archetype to minimize code bloat. More...
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class | GivPolynomialRing |
| polynomials with coefficients modulo some power of two More...
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class | PowerOfTwoModular |
| Ring of elements modulo some power of two. More...
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struct | PowerOfTwoModular::RandIter |
class | RingInterface |
| This ring base class exists solely to aid documentation organization. More...
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struct | Method |
| Method specifiers for controlling algorithm choice. More...
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struct | SolverTraits |
class | SolveFailed |
class | InconsistentSystem |
class | BooleanSwitch |
class | BooleanSwitchFactory |
class | CekstvSwitch |
class | CekstvSwitchFactory |
class | ActivityState |
| used by commentator More...
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class | Commentator |
| give information to user during runtime More...
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class | MessageClass |
class | LinboxError |
class | FieldAXPY |
class | MatrixStreamReader |
class | PrimeStream |
class | BaseTimer |
| base for class RealTimer; class SysTimer; class UserTimer; More...
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class | BitVector |
class | ReverseVector |
class | Sparse_Vector |
| vector< Pair<T> > and actualsize More...
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class | VectorStream |
| Vector factory. More...
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class | ConstantVectorStream |
class | RandomDenseStream |
class | RandomSparseStream |
class | StandardBasisStream |
class | Subiterator |
| Subvector iterator class provides striding iterators. More...
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class | Subvector |
| Dense subvector. More...
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struct | VectorCategories |
| List of vector categories. More...
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struct | VectorTraits |
class | RawVector |
Butterfly |
Butterfly preconditioner and supporting function
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std::vector< bool > | setButterfly (const std::vector< bool > &x, size_t j=0) |
class RR. |
Rational number field. This field is provided as a convenience in a few places. Use with caution because expression swell.
This specialization allows the UnparametricField} template class to be used to wrap NTL's RR class as a LinBox field.
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template<> NTL::RR & | UnparametricField< NTL::RR >::init (NTL::RR &x, const integer &y) const |
template<> integer & | UnparametricField< NTL::RR >::convert (integer &x, const NTL::RR &y) const |
template<> NTL::RR & | UnparametricField< NTL::RR >::inv (NTL::RR &x, const NTL::RR &y) const |
template<> bool | UnparametricField< NTL::RR >::isZero (const NTL::RR &x) const |
template<> bool | UnparametricField< NTL::RR >::isOne (const NTL::RR &x) const |
template<> NTL::RR & | UnparametricField< NTL::RR >::invin (NTL::RR &x) const |
template<> std::ostream & | UnparametricField< NTL::RR >::write (std::ostream &os) const |
template<> NTL::RR & | UnparametricRandIter< NTL::RR >::random (NTL::RR &elt) const |
NTL_ZZ_p |
Arbitrary precision integers modulus a positive integer.
While NTL allows any integer to serve as the modulus, only prime moduli yield fields. Therefore, while arthmetic operations may be valid for any modulus, only prime moduli are supported in this implementation. The primality of the modulus will not be checked, so it is the programmer's responsibility to supply a prime modulus. These specializations allow the UnparametricField} template class to be used to wrap NTL's { ZZ} class as a LinBox field.
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template<> | UnparametricField< NTL::ZZ_p >::UnparametricField (integer q, size_t e) |
template<> NTL::ZZ_p & | UnparametricField< NTL::ZZ_p >::init (NTL::ZZ_p &x, const integer &y) const |
| Initialization of field element from an integer. Behaves like C++ allocator construct. This function assumes the output field element x has already been constructed, but that it is not already initialized. This done by converting to a std::string : inefficient but correct.
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[NOHEADER] |
template<> integer & | UnparametricField< NTL::ZZ_p >::convert (integer &x, const NTL::ZZ_p &y) const |
template<> integer & | UnparametricField< NTL::ZZ_p >::cardinality (integer &c) const |
template<> integer & | UnparametricField< NTL::ZZ_p >::characteristic (integer &c) const |
template<> NTL::ZZ_p & | UnparametricField< NTL::ZZ_p >::inv (NTL::ZZ_p &x, const NTL::ZZ_p &y) const |
template<> bool | UnparametricField< NTL::ZZ_p >::isZero (const NTL::ZZ_p &x) const |
template<> bool | UnparametricField< NTL::ZZ_p >::isOne (const NTL::ZZ_p &x) const |
template<> NTL::ZZ_p & | UnparametricField< NTL::ZZ_p >::invin (NTL::ZZ_p &x) const |
template<> std::ostream & | UnparametricField< NTL::ZZ_p >::write (std::ostream &os) const |
template<> | UnparametricRandIter< NTL::ZZ_p >::UnparametricRandIter (const UnparametricField< NTL::ZZ_p > &F, const integer &size, const integer &seed) |
| Constructor for random field element generator.
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template<> NTL::ZZ_p & | UnparametricRandIter< NTL::ZZ_p >::random (NTL::ZZ_p &x) const |
| Random field element creator.
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Typedefs |
typedef UnparametricField<
integer > | GMP_Integers |
typedef NTL_ZZRandIter | RandIter |
| the integer ring. class NTL_ZZ {
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typedef Integer | integer |
| This is a representation of arbitrary integers.
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typedef signed __LINBOX_INT32 | int32 |
typedef unsigned __LINBOX_INT32 | uint32 |
Enumerations |
enum | SolverReturnStatus |
| define the different return status of the p-adic based solver's computation. More...
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enum | SolverLevel |
| define the different strategy which can be used in the p-adic based solver. More...
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enum | FileFormatTag |
| tags for SparseMatrixBase::read() and write()
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Functions |
template<class Blackbox, class MyMethod> Blackbox::Field::Element & | lif_cra_det (typename Blackbox::Field::Element &d, const Blackbox &A, const RingCategories::IntegerTag &tag, const MyMethod &M) |
| Compute the determinant of A over the integers.
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template<class Ring, class ItMatrix> void | SpecialBound (const Ring &R, typename Ring::Element &H_col_sqr, typename Ring::Element &short_col_sqr, const ItMatrix &A) |
template<class Ring, class ItMatrix> void | ApplyBound (const Ring &R, typename Ring::Element &bound_A, const ItMatrix &A) |
template<class Domain> void | reduceIn (Domain &D, std::pair< typename Domain::Element, typename Domain::Element > &frac) |
template<class Domain, class Vector> void | vectorGcdIn (typename Domain::Element &result, Domain &D, Vector &v) |
template<class Domain, class Vector> Domain::Element | vectorGcd (Domain &D, Vector &v) |
template<class Domain, class IMatrix> void | create_MatrixQadic (const Domain &D, const IMatrix &M, double *chunks, size_t num_chunks, const integer &shift=0) |
| split an integer matrix into a padic chunk representation
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template<class Domain, class Vector> void | create_VectorQadic (const Domain &D, const Vector &V, double *chunks, size_t num_chunks) |
| split an integer vector into a padic chunk representation
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template<class Domain, class Vector> void | create_VectorQadic_32 (const Domain &D, const Vector &V, double *chunks, size_t num_chunks) |
| split an integer vector into a padic chunk representation
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template<> NTL::zz_p & | UnparametricField< NTL::zz_p >::init (NTL::zz_p &x, const integer &y) const |
template<> integer & | UnparametricField< NTL::zz_p >::convert (integer &x, const NTL::zz_p &y) const |
template<> integer & | UnparametricField< NTL::zz_p >::cardinality (integer &c) const |
template<> integer & | UnparametricField< NTL::zz_p >::characteristic (integer &c) const |
template<> NTL::zz_p & | UnparametricField< NTL::zz_p >::inv (NTL::zz_p &x, const NTL::zz_p &y) const |
template<> bool | UnparametricField< NTL::zz_p >::isZero (const NTL::zz_p &x) const |
template<> bool | UnparametricField< NTL::zz_p >::isOne (const NTL::zz_p &x) const |
template<> NTL::zz_p & | UnparametricField< NTL::zz_p >::invin (NTL::zz_p &x) const |
template<> std::ostream & | UnparametricField< NTL::zz_p >::write (std::ostream &os) const |
template<> | UnparametricRandIter< NTL::zz_p >::UnparametricRandIter (const UnparametricField< NTL::zz_p > &F, const integer &size, const integer &seed) |
| Constructor for random field element generator.
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template<> NTL::zz_p & | UnparametricRandIter< NTL::zz_p >::random (NTL::zz_p &x) const |
| Random field element creator.
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template<> std::ostream & | UnparametricField< NTL::zz_pX >::write (std::ostream &os) const |
template<class Element2> Element & | init (Element &x, const Element2 &y) const |
| Init x from y.
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Element & | init (Element &x, const Element &y) const |
| Init from a NTL::ZZ.
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Element & | init (Element &x, const int64 &y) const |
| Init from an int64.
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Element & | init (Element &x, const uint64 &y) const |
| Init from a uint64.
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Element & | init (Element &x, const integer &y) const |
| I don't know how to init from integer efficiently.
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Element & | assign (Element &x, const Element &y) const |
| x = y.
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bool | areEqual (const Element &x,const Element &y) const |
| Test if x == y.
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bool | isZero (const Element &x) const |
| Test if x == 0.
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bool | isOne (const Element &x) const |
| Test if x == 1.
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Element & | add (Element &x, const Element &y, const Element &z) const |
| return x = y + z
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Element & | sub (Element &x, const Element &y, const Element &z) const |
| return x = y - z
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template<class Int> Element & | mul (Element &x, const Element &y, const Int &z) const |
| return x = y * z
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Element & | div (Element &x, const Element &y, const Element &z) const |
| If z divides y, return x = y / z, otherwise, throw an exception.
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Element & | inv (Element &x, const Element &y) const |
| If y is a unit, return x = 1 / y, otherwsie, throw an exception.
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Element & | neg (Element &x, const Element &y) const |
| return x = -y;
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template<class Int> Element & | axpy (Element &r, const Element &a, const Int &x, const Element &y) const |
| return r = a x + y
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Element & | addin (Element &x, const Element &y) const |
| return x += y;
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Element & | subin (Element &x, const Element &y) const |
| return x -= y;
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template<class Int> Element & | mulin (Element &x, const Int &y) const |
| return x *= y;
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Element & | divin (Element &x, const Element &y) const |
| If y divides x, return x /= y, otherwise throw an exception.
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Element & | invin (Element &x) |
| If x is a unit, x = 1 / x, otherwise, throw an exception.
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Element & | negin (Element &x) const |
| return x = -x;
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template<class Int> Element & | axpyin (Element &r, const Element &a, const Int &x) const |
| return r += a x
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std::ostream & | write (std::ostream &out, const Element &y) const |
| out << y;
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std::istream & | read (std::istream &in, Element &x) const |
| read x from istream in
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bool | isUnit (const Element &x) const |
| Test if x is a unit.
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Element & | gcd (Element &g, const Element &a, const Element &b) const |
| return g = gcd (a, b)
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Element & | gcdin (Element &g, const Element &b) const |
| return g = gcd (g, b)
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Element & | xgcd (Element &g, Element &s, Element &t, const Element &a, const Element &b) const |
| g = gcd(a, b) = a*s + b*t. The coefficients s and t are defined according to the standard Euclidean algorithm applied to |a| and |b|, with the signs then adjusted according to the signs of a and b.
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Element & | lcm (Element &c, const Element &a, const Element &b) const |
| c = lcm (a, b)
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Element & | lcmin (Element &l, const Element &b) const |
| l = lcm (l, b)
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Element & | sqrt (Element &x, const Element &y) const |
| x = floor ( sqrt(y)).
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long | reconstructRational (Element &a, Element &b, const Element &x, const Element &m, const Element &a_bound, const Element &b_bound) const |
| Requires 0 <= x < m, m > 2 * a_bound * b_bound, a_bound >= 0, b_bound > 0 This routine either returns 0, leaving a and b unchanged, or returns 1 and sets a and b so that (1) a = b x (mod m), (2) |a| <= a_bound, 0 < b <= b_bound, and (3) gcd(m, b) = gcd(a, b).
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Element & | quo (Element &q, const Element &a, const Element &b) const |
| q = floor (x/y);
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Element & | rem (Element &r, const Element &a, const Element &b) const |
| r = remindar of a / b
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Element & | quoin (Element &a, const Element &b) const |
| a = quotient (a, b)
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Element & | remin (Element &x, const Element &y) const |
| a = quotient (a, b)
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void | quoRem (Element &q, Element &r, const Element &a, const Element &b) const |
| q = [a/b], r = a - b*q |r| < |b|, and if r != 0, sign(r) = sign(b)
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bool | isDivisor (const Element &a, const Element &b) const |
| Test if b | a.
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long | compare (const Element &a, const Element &b) const |
Element & | abs (Element &x, const Element &a) const |
template<> std::ostream & | UnparametricField< NTL::ZZ_pX >::write (std::ostream &os) const |
template<class Blackbox, class Polynomial, class MyMethod> Polynomial & | charpoly (Polynomial &P, const Blackbox &A, const MyMethod &M) |
| ...using an optional Method parameter
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template<class Blackbox, class Polynomial> Polynomial & | charpoly (Polynomial &P, const Blackbox &A) |
| ...using default method
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template<class Polynomial, class Blackbox> Polynomial & | charpoly (Polynomial &P, const Blackbox &A, const RingCategories::ModularTag &tag, const Method::BlasElimination &M) |
| Compute the characteristic polynomial over Zp.
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template<class Polynomial, class Blackbox> Polynomial & | charpoly (Polynomial &P, const Blackbox &A, const RingCategories::ModularTag &tag, const Method::Blackbox &M) |
template<class Blackbox, class MyMethod> Blackbox::Field::Element & | det (typename Blackbox::Field::Element &d, const Blackbox &A, const MyMethod &M) |
| Compute the determinant of A.
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template<class Field> Field::Element & | detin (typename Field::Element &d, BlasBlackbox< Field > &A) |
| A will be modified.
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template<class BB> BB::Field::Element & | getEntry (typename BB::Field::Element &x, const BB &A, const size_t i, const size_t j) |
| Getting the i,j entry of the blackbox.
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template<class BB> BB::Field::Element & | getEntry (typename BB::Field::Element &x, const BB &A, const size_t i, const size_t j, const Method::Hybrid &m) |
| our best guess
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template<class BB> BB::Field::Element & | getEntry (typename BB::Field::Element &x, const BB &A, const size_t i, const size_t j, const Method::Elimination &m) |
| our elimination (a fake in this case)
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template<class Blackbox> Blackbox::Field::Element & | getEntry (typename Blackbox::Field::Element &res, const Blackbox &A, const size_t i, const size_t j, const Method::Blackbox &m) |
template<class Blackbox, class MyMethod> bool | isPositiveDefinite (const Blackbox &A, const MyMethod &M) |
template<class Blackbox, class MyMethod> bool | isPositiveSemiDefinite (const Blackbox &A, const MyMethod &M) |
template<class Field> void | LU (DenseMatrix< Field > &M) |
template<class Blackbox, class Polynomial, class MyMethod> Polynomial & | minpoly (Polynomial &P, const Blackbox &A, const MyMethod &M) |
| ...using an optional Method parameter
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template<class Polynomial, class Blackbox> Polynomial & | minpoly (Polynomial &P, const Blackbox &A) |
| ...using default Method
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template<class Blackbox, class Method, class DomainCategory> unsigned long & | rank (unsigned long &r, const Blackbox &A, const DomainCategory &tag, const Method &M) |
template<class Blackbox> unsigned long & | rank (unsigned long &r, const Blackbox &A) |
template<class Matrix> unsigned long & | rankin (unsigned long &r, Matrix &A) |
template<class Blackbox, class Method> unsigned long & | rank (unsigned long &r, const Blackbox &A, const Method &M) |
template<class Blackbox> unsigned long & | rank (unsigned long &res, const Blackbox &A, const RingCategories::ModularTag &tag, const Method::Wiedemann &M) |
| M may be Method::Wiedemann() .
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template<class Field> unsigned long & | rank (unsigned long &r, const SparseMatrix< Field, typename LinBox::Vector< Field >::SparseSeq > &A, const RingCategories::ModularTag &tag, const Method::SparseElimination &M) |
| M may be Method::SparseElimination() .
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template<class Field> unsigned long & | rankin (unsigned long &r, BlasBlackbox< Field > &A, const RingCategories::ModularTag &tag, const Method::BlasElimination &M) |
| A is modified.
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template<class Output, class Blackbox, class MyMethod> Output & | smithForm (Output &S, const Blackbox &A, const MyMethod &M) |
template<class Vector, class Blackbox, class SolveMethod> Vector & | solve (Vector &x, const Blackbox &A, const Vector &b, const SolveMethod &M) |
| Solve Ax = b, for x.
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template<class Vector, class Ring> Vector & | solve (Vector &x, typename Ring::Element &d, const BlasBlackbox< Ring > &A, const Vector &b, const RingCategories::IntegerTag tag, Method::Dixon &m) |
| solver specialization with the 2nd API and DixonTraits over integer (no copying)
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template<class Vector, class Ring> Vector & | solve (Vector &x, typename Ring::Element &d, const DenseMatrix< Ring > &A, const Vector &b, const RingCategories::IntegerTag tag, const Method::Dixon &m) |
| solver specialization with the 2nd API and DixonTraits over integer (no copying)
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template<class BB> BB::Field::Element & | trace (typename BB::Field::Element &t, const BB &A) |
| sum of eigenvalues
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template<class BB> BB::Field::Element & | trace (typename BB::Field::Element &t, const BB &A, const Method::Hybrid &m) |
| our best guess
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template<class BB> BB::Field::Element & | trace (typename BB::Field::Element &t, const BB &A, const Method::Elimination &m) |
| our elimination (a fake in this case)
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template<class Blackbox> Blackbox::Field::Element & | trace (typename Blackbox::Field::Element &res, const Blackbox &A, const Method::Blackbox &m) |
template<class Blackbox, class MyMethod> Blackbox::Field::Element & | valence (typename Blackbox::Field::Element &v, const Blackbox &A, const MyMethod &M) |
| Compute the valence of A.
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template<class Field, class Vector> Vector | randomVector (Field &F, size_t n, typename Field::RandIter &r) |