Index

A

A (pseries_basis.polynomial.factorial.DivisionCondition attribute) (pseries_basis.psbasis.Compatibility attribute) add() (pseries_basis.psbasis.Compatibility method) ak (pseries_basis.polynomial.factorial.FactorialBasis attribute) (pseries_basis.polynomial.orthogonal.OrthogonalBasis attribute) almost_equals() (pseries_basis.sequences.base.Sequence method) almost_zero() (pseries_basis.sequences.base.Sequence method) apply_operator_to_seq() (in module pseries_basis.misc.ore) args_to_self() (pseries_basis.polynomial.factorial.FactorialBasis method) (pseries_basis.polynomial.orthogonal.OrthogonalBasis method) (pseries_basis.psbasis.PSBasis method) (pseries_basis.sequences.base.ConstantSequence method) (pseries_basis.sequences.base.Sequence method) (pseries_basis.sequences.element.ExpressionSequence method)

as_2dim() (pseries_basis.psbasis.PSBasis method) as_constant() (pseries_basis.sequences.base.Sequence method) as_polynomial() (pseries_basis.sequences.base.Sequence method) (pseries_basis.sequences.element.ExpressionSequence method) (pseries_basis.sequences.element.RationalSequence method) as_rational() (pseries_basis.sequences.base.Sequence method) (pseries_basis.sequences.element.ExpressionSequence method) (pseries_basis.sequences.element.RationalSequence method)

B

B (pseries_basis.psbasis.Compatibility attribute) base (pseries_basis.psbasis.PSBasis attribute) base() (pseries_basis.polynomial.factorial.DivisionCondition method) (pseries_basis.psbasis.Compatibility method)

basic_compatibilities() (pseries_basis.psbasis.PSBasis method) basis_matrix() (in module pseries_basis.psbasis) BinomialTypeBasis() (in module pseries_basis.polynomial.factorial) bk (pseries_basis.polynomial.factorial.FactorialBasis attribute) (pseries_basis.polynomial.orthogonal.OrthogonalBasis attribute)

C

change_base() (pseries_basis.polynomial.factorial.DivisionCondition method) (pseries_basis.psbasis.Compatibility method) (pseries_basis.psbasis.PSBasis method) change_class() (pseries_basis.sequences.base.Sequence method) change_dimension() (pseries_basis.sequences.base.Sequence method) change_universe() (pseries_basis.sequences.base.Sequence method) check_compatibility() (in module pseries_basis.psbasis) check_consistency() (pseries_basis.misc.io.EnhOEISSequence method) check_division_condition() (in module pseries_basis.polynomial.factorial) ck (pseries_basis.polynomial.orthogonal.OrthogonalBasis attribute)

coefficient() (pseries_basis.polynomial.factorial.DivisionCondition method) Compatibility (class in pseries_basis.psbasis) compatibility() (pseries_basis.psbasis.PSBasis method) compatibility_type() (pseries_basis.psbasis.PSBasis method) compatible_derivations() (pseries_basis.psbasis.PSBasis method) compatible_division() (pseries_basis.polynomial.factorial.FactorialBasis method) compatible_endomorphisms() (pseries_basis.psbasis.PSBasis method) composition() (pseries_basis.sequences.base.Sequence method) ConstantSequence (class in pseries_basis.sequences.base) counts() (pseries_basis.polynomial.factorial.ShuffledBasis method) cycle (pseries_basis.polynomial.factorial.ShuffledBasis attribute)

D

data() (pseries_basis.psbasis.Compatibility method) DefiniteSumSolutions() (in module pseries_basis.polynomial.factorial) derivation_compatibility() (pseries_basis.polynomial.orthogonal.OrthogonalBasis method) derivation_factor (pseries_basis.polynomial.orthogonal.OrthogonalBasis attribute) dfinite_recurrence() (pseries_basis.misc.io.EnhOEISSequence method) diagonal() (pseries_basis.sequences.base.Sequence method)

differential_equation() (pseries_basis.polynomial.orthogonal.OrthogonalBasis method) dim() (pseries_basis.sequences.base.Sequence method) division_decomposition() (pseries_basis.polynomial.factorial.ShuffledBasis method) DivisionCondition (class in pseries_basis.polynomial.factorial) double_algebra() (pseries_basis.psbasis.PSBasis method) double_gens() (pseries_basis.psbasis.PSBasis method) double_var() (pseries_basis.psbasis.PSBasis method)

E

element() (pseries_basis.sequences.base.Sequence method) EnhOEISSequence (class in pseries_basis.misc.io) equiv() (pseries_basis.psbasis.Compatibility method) equiv_CtD() (pseries_basis.polynomial.factorial.FactorialBasis method) equiv_DtC() (pseries_basis.polynomial.factorial.FactorialBasis method)

ExpressionSequence (class in pseries_basis.sequences.element) extra() (pseries_basis.polynomial.factorial.ShuffledBasis method) extra_info() (pseries_basis.sequences.base.Sequence method) (pseries_basis.sequences.element.ExpressionSequence method) (pseries_basis.sequences.element.RationalSequence method)

F

F (pseries_basis.polynomial.factorial.ShuffledBasis attribute) FactorialBasis (class in pseries_basis.polynomial.factorial) factors (pseries_basis.polynomial.factorial.ShuffledBasis attribute)

FallingBasis() (in module pseries_basis.polynomial.factorial) Fibonacci() (in module pseries_basis.sequences.examples) from_compatibility() (pseries_basis.polynomial.factorial.DivisionCondition static method)

G

GegenbauerBasis() (in module pseries_basis.polynomial.orthogonal) gen() (pseries_basis.polynomial.factorial.FactorialBasis method) (pseries_basis.polynomial.orthogonal.OrthogonalBasis method) generic() (pseries_basis.psbasis.PSBasis method) (pseries_basis.sequences.base.Sequence method) (pseries_basis.sequences.element.ExpressionSequence method) gens_double_qshift_algebra() (in module pseries_basis.misc.ore)

gens_double_recurrence_algebra() (in module pseries_basis.misc.ore) gens_qshift_algebra() (in module pseries_basis.misc.ore) gens_recurrence_algebra() (in module pseries_basis.misc.ore) get_differential_algebra() (in module pseries_basis.misc.ore) get_double_qshift_algebra() (in module pseries_basis.misc.ore) get_double_recurrence_algebra() (in module pseries_basis.misc.ore) get_qshift_algebra() (in module pseries_basis.misc.ore) get_recurrence_algebra() (in module pseries_basis.misc.ore)

H

HermiteBasis() (in module pseries_basis.polynomial.orthogonal)

HermitePBasis() (in module pseries_basis.polynomial.orthogonal)

I

IdentitySequence() (in module pseries_basis.sequences.base) in_sections() (pseries_basis.polynomial.factorial.DivisionCondition method) (pseries_basis.psbasis.Compatibility method) increasing_basis() (pseries_basis.polynomial.factorial.FactorialBasis method) indices() (pseries_basis.polynomial.factorial.ShuffledBasis method) inner_init_values() (pseries_basis.psbasis.PSBasis method) interlace() (pseries_basis.sequences.base.Sequence method) is_compatible() (pseries_basis.psbasis.PSBasis method) is_constant() (pseries_basis.sequences.base.Sequence method) is_dfinite() (pseries_basis.misc.io.EnhOEISSequence method) is_differential_algebra() (in module pseries_basis.misc.ore) is_double_qshift_algebra() (in module pseries_basis.misc.ore)

is_double_recurrence_algebra() (in module pseries_basis.misc.ore) is_hypergeometric() (pseries_basis.sequences.base.Sequence method) is_polynomial() (pseries_basis.sequences.base.Sequence method) (pseries_basis.sequences.element.ExpressionSequence method) (pseries_basis.sequences.element.RationalSequence method) is_QSequence() (in module pseries_basis.sequences.qsequences) is_qshift_algebra() (in module pseries_basis.misc.ore) is_quasi_triangular() (pseries_basis.psbasis.PSBasis method) is_rational() (pseries_basis.sequences.base.Sequence method) (pseries_basis.sequences.element.ExpressionSequence method) (pseries_basis.sequences.element.RationalSequence method) is_recurrence_algebra() (in module pseries_basis.misc.ore)

J

JacobiBasis() (in module pseries_basis.polynomial.orthogonal)

L

LaguerreBasis() (in module pseries_basis.polynomial.orthogonal) lc (pseries_basis.polynomial.factorial.FactorialBasis attribute) LegendreBasis() (in module pseries_basis.polynomial.orthogonal)

linear_subsequence() (pseries_basis.sequences.base.Sequence method) lower (pseries_basis.psbasis.Compatibility attribute) lower_bound (pseries_basis.polynomial.factorial.DivisionCondition attribute)

M

m (pseries_basis.polynomial.factorial.ShuffledBasis attribute) matrix_ItP() (pseries_basis.polynomial.factorial.FactorialBasis method) matrix_PtI() (pseries_basis.polynomial.factorial.FactorialBasis method) meanings() (pseries_basis.sequences.element.ExpressionSequence method) MinimalCommonClass() (pseries_basis.sequences.base.Sequence static method) mixed_equation() (pseries_basis.polynomial.orthogonal.OrthogonalBasis method) module pseries_basis pseries_basis.misc pseries_basis.misc.io pseries_basis.misc.ore pseries_basis.order pseries_basis.order.fun_basis pseries_basis.polynomial pseries_basis.polynomial.factorial pseries_basis.polynomial.orthogonal pseries_basis.psbasis pseries_basis.qbasis pseries_basis.qbasis.qbasis pseries_basis.sequences pseries_basis.sequences.base pseries_basis.sequences.element pseries_basis.sequences.examples pseries_basis.sequences.qsequences

mul() (pseries_basis.psbasis.Compatibility method)

N

nfactors (pseries_basis.polynomial.factorial.ShuffledBasis attribute)

nsections (pseries_basis.polynomial.factorial.ShuffledBasis attribute) (pseries_basis.psbasis.Compatibility attribute)

O

operator2file() (in module pseries_basis.misc.io) operator2Mathematica() (in module pseries_basis.misc.io) order() (pseries_basis.misc.io.EnhOEISSequence method)

ore_algebra() (pseries_basis.psbasis.PSBasis method) ore_gen() (pseries_basis.psbasis.PSBasis method) ore_var() (pseries_basis.psbasis.PSBasis method) OrthogonalBasis (class in pseries_basis.polynomial.orthogonal)

P

partial_prod() (pseries_basis.sequences.base.Sequence method) partial_sum() (pseries_basis.sequences.base.Sequence method) poly_ring() (pseries_basis.polynomial.factorial.FactorialBasis method) (pseries_basis.polynomial.orthogonal.OrthogonalBasis method) PowerTypeBasis() (in module pseries_basis.polynomial.factorial) ProductBasis() (in module pseries_basis.polynomial.factorial) PSBasis (class in pseries_basis.psbasis) pseries_bases_version() (in module pseries_basis) pseries_basis module pseries_basis.misc module pseries_basis.misc.io module pseries_basis.misc.ore module pseries_basis.order module pseries_basis.order.fun_basis module pseries_basis.polynomial module

pseries_basis.polynomial.factorial module pseries_basis.polynomial.orthogonal module pseries_basis.psbasis module pseries_basis.qbasis module pseries_basis.qbasis.qbasis module pseries_basis.sequences module pseries_basis.sequences.base module pseries_basis.sequences.element module pseries_basis.sequences.examples module pseries_basis.sequences.qsequences module

Q

Q_binomial_type() (in module pseries_basis.sequences.examples) Q_pochhammer() (in module pseries_basis.sequences.examples) QBasis() (in module pseries_basis.qbasis.qbasis) QBinomialBasis() (in module pseries_basis.qbasis.qbasis) QExpressionSequence() (in module pseries_basis.sequences.qsequences)

QFactorialBasis() (in module pseries_basis.qbasis.qbasis) QPower() (in module pseries_basis.sequences.qsequences) QPowerBasis() (in module pseries_basis.qbasis.qbasis) QRationalSequence() (in module pseries_basis.sequences.qsequences) QSequence() (in module pseries_basis.sequences.qsequences)

R

RationalSequence (class in pseries_basis.sequences.element) recurrence() (pseries_basis.psbasis.PSBasis method) register_class() (pseries_basis.sequences.base.Sequence class method) (pseries_basis.sequences.element.ExpressionSequence class method) (pseries_basis.sequences.element.RationalSequence class method)

required_init() (in module pseries_basis.misc.ore) rho (pseries_basis.polynomial.factorial.FactorialBasis attribute) RootSequenceBasis() (in module pseries_basis.polynomial.factorial)

S

scalar() (pseries_basis.psbasis.PSBasis method) scale() (pseries_basis.psbasis.Compatibility method) scale_basis() (pseries_basis.psbasis.Compatibility method) sections (pseries_basis.polynomial.factorial.DivisionCondition attribute) Sequence (class in pseries_basis.sequences.base) sequence (pseries_basis.misc.io.EnhOEISSequence attribute) set_compatibility() (pseries_basis.psbasis.PSBasis method) set_derivation() (pseries_basis.psbasis.PSBasis method)

set_homomorphism() (pseries_basis.psbasis.PSBasis method) shift() (pseries_basis.sequences.base.Sequence method) ShuffledBasis (class in pseries_basis.polynomial.factorial) size() (pseries_basis.polynomial.factorial.DivisionCondition method) slicing() (pseries_basis.sequences.base.Sequence method) solution() (in module pseries_basis.misc.ore) subsequence() (pseries_basis.sequences.base.Sequence method) swap() (pseries_basis.sequences.base.Sequence method)

T

t (pseries_basis.polynomial.factorial.DivisionCondition attribute) (pseries_basis.psbasis.Compatibility attribute)

TChebyshevBasis() (in module pseries_basis.polynomial.orthogonal) to_compatibility() (pseries_basis.polynomial.factorial.DivisionCondition method)

U

UChebyshevBasis() (in module pseries_basis.polynomial.orthogonal) universe() (pseries_basis.sequences.base.Sequence method)

unroll_matrix() (in module pseries_basis.misc.ore) upper (pseries_basis.psbasis.Compatibility attribute)

V

variables() (pseries_basis.sequences.element.ExpressionSequence method)