Index

A

A (ajpastor.misc.linear_solver.LinearSystemSolver attribute) add() (ajpastor.dd_functions.ddFunction.DDFunction method) AiryD() (in module ajpastor.dd_functions.ddExamples) ajpastor.dd_functions.ddExamples module ajpastor.dd_functions.ddFunction module ajpastor.dd_functions.exceptions module ajpastor.dd_functions.symbolic module ajpastor.dd_functions.toDiffAlgebraic module ajpastor.misc.bareiss module

ajpastor.misc.dynamic_string module ajpastor.misc.hermite module ajpastor.misc.linear_solver module ajpastor.misc.matrix module Arccos() (in module ajpastor.dd_functions.ddExamples) Arccosh() (in module ajpastor.dd_functions.ddExamples) Arcsin() (in module ajpastor.dd_functions.ddExamples) Arcsinh() (in module ajpastor.dd_functions.ddExamples) Arctan() (in module ajpastor.dd_functions.ddExamples) Arctanh() (in module ajpastor.dd_functions.ddExamples)

B

b (ajpastor.misc.linear_solver.LinearSystemSolver attribute) BareissAlgorithm (class in ajpastor.misc.bareiss) base_ddRing() (ajpastor.dd_functions.ddFunction.ParametrizedDDRing method) base_derivation (ajpastor.dd_functions.ddFunction.DDRing attribute) base_ring() (ajpastor.dd_functions.ddFunction.DDRing method) BellD() (in module ajpastor.dd_functions.ddExamples)

BernoulliD() (in module ajpastor.dd_functions.ddExamples) BesselD() (in module ajpastor.dd_functions.ddExamples) block_matrix() (in module ajpastor.misc.matrix) build_derivation_matrix() (in module ajpastor.dd_functions.toDiffAlgebraic) build_vector() (in module ajpastor.dd_functions.toDiffAlgebraic) built (ajpastor.dd_functions.ddFunction.DDFunction attribute)

C

CatalanD() (in module ajpastor.dd_functions.ddExamples) change_argument() (ajpastor.misc.dynamic_string.DynamicString method) change_init_values() (ajpastor.dd_functions.ddFunction.DDFunction method) change_variable() (in module ajpastor.dd_functions.toDiffAlgebraic) characteristic() (ajpastor.dd_functions.ddFunction.DDRing method) ChebyshevD() (in module ajpastor.dd_functions.ddExamples) clean() (ajpastor.misc.dynamic_string.DynamicString method) coeff_field (ajpastor.dd_functions.ddFunction.DDRing attribute) command() (in module ajpastor.dd_functions.ddFunction)

compose() (ajpastor.dd_functions.ddFunction.DDFunction method) compose_algebraic() (ajpastor.dd_functions.ddFunction.DDFunction method) computed (ajpastor.dd_functions.ddFunction.DDFunction attribute) construction() (ajpastor.dd_functions.ddFunction.DDRing method) (ajpastor.dd_functions.ddFunction.ParametrizedDDRing method) contraction() (ajpastor.dd_functions.ddFunction.DDFunction method) Cos() (in module ajpastor.dd_functions.ddExamples) Cosh() (in module ajpastor.dd_functions.ddExamples) CoulombSpheroidalFunctionD() (in module ajpastor.dd_functions.ddExamples)

D

DAlgebraic() (in module ajpastor.dd_functions.ddExamples) DDFinite (in module ajpastor.dd_functions.ddFunction) DDFunction (class in ajpastor.dd_functions.ddFunction) DDFunctionError DDRing (class in ajpastor.dd_functions.ddFunction) default_operator() (ajpastor.dd_functions.ddFunction.DDRing method) depth() (ajpastor.dd_functions.ddFunction.DDRing method) derivation_on_base() (ajpastor.dd_functions.ddFunction.DDRing method) derivative() (ajpastor.dd_functions.ddFunction.DDFunction method) DFinite (in module ajpastor.dd_functions.ddFunction)

DFiniteI (in module ajpastor.dd_functions.ddFunction) DFiniteP (in module ajpastor.dd_functions.ddFunction) DFiniteWP() (in module ajpastor.dd_functions.ddExamples) diagonal_matrix() (in module ajpastor.misc.matrix) diff_to_diffalg() (in module ajpastor.dd_functions.toDiffAlgebraic) diffalg_reduction() (in module ajpastor.dd_functions.toDiffAlgebraic) direct_sum() (in module ajpastor.misc.matrix) divide() (ajpastor.dd_functions.ddFunction.DDFunction method) dreplace() (in module ajpastor.misc.dynamic_string) DynamicString (class in ajpastor.misc.dynamic_string)

E

echelon_form() (ajpastor.misc.linear_solver.LinearSystemSolver method) Element (ajpastor.dd_functions.ddFunction.DDRing attribute) element() (ajpastor.dd_functions.ddFunction.DDRing method) EllipticLegendreD() (in module ajpastor.dd_functions.ddExamples) equals() (ajpastor.dd_functions.ddFunction.DDFunction method) equation (ajpastor.dd_functions.ddFunction.DDFunction attribute)

euler_coefficient() (ajpastor.dd_functions.ddFunction.DDFunction static method) eval() (ajpastor.dd_functions.ddFunction.DDRing method) Exp() (in module ajpastor.dd_functions.ddExamples) Exponential_polynomials() (in module ajpastor.dd_functions.toDiffAlgebraic) extend_base_field() (ajpastor.dd_functions.ddFunction.DDRing method) (ajpastor.dd_functions.ddFunction.ParametrizedDDRing method) extend_sequence() (ajpastor.dd_functions.ddFunction.DDFunction method)

F

F00() (in module ajpastor.dd_functions.ddExamples) F01() (in module ajpastor.dd_functions.ddExamples) F10() (in module ajpastor.dd_functions.ddExamples) F11() (in module ajpastor.dd_functions.ddExamples) F21() (in module ajpastor.dd_functions.ddExamples) FaaDiBruno_polynomials() (in module ajpastor.dd_functions.toDiffAlgebraic) FactorialD() (in module ajpastor.dd_functions.ddExamples)

FCoulombD() (in module ajpastor.dd_functions.ddExamples) FibonacciD() (in module ajpastor.dd_functions.ddExamples) find_linear_relation() (in module ajpastor.dd_functions.toDiffAlgebraic) find_relation() (in module ajpastor.dd_functions.toDiffAlgebraic) Fpq() (in module ajpastor.dd_functions.ddExamples) from_symbolic() (in module ajpastor.dd_functions.symbolic) FuchsianD() (in module ajpastor.dd_functions.ddExamples) func_inverse_DA() (in module ajpastor.dd_functions.toDiffAlgebraic)

G

gcd() (ajpastor.dd_functions.ddFunction.DDFunction method) GenericHypergeometricFunction() (in module ajpastor.dd_functions.ddExamples) gens() (ajpastor.dd_functions.ddFunction.DDRing method) (ajpastor.dd_functions.ddFunction.ParametrizedDDRing method)

get_InfinitePolynomialRingGen() (in module ajpastor.dd_functions.toDiffAlgebraic) guess_DA_DDfinite() (in module ajpastor.dd_functions.toDiffAlgebraic) guess_homogeneous_DNfinite() (in module ajpastor.dd_functions.toDiffAlgebraic)

H

H (ajpastor.misc.linear_solver.LinearSystemSolver attribute) has_name() (ajpastor.dd_functions.ddFunction.DDFunction method) have_ideal() (ajpastor.misc.linear_solver.LinearSystemSolver method)

HermiteSolver (class in ajpastor.misc.hermite) HeunD() (in module ajpastor.dd_functions.ddExamples) HillD() (in module ajpastor.dd_functions.ddExamples) HypergeometricFunction() (in module ajpastor.dd_functions.ddExamples)

I

infinite_derivative() (in module ajpastor.dd_functions.toDiffAlgebraic) inhomogeneous() (ajpastor.misc.linear_solver.LinearSystemSolver method) init() (ajpastor.dd_functions.ddFunction.DDFunction method) InitValueError integrate() (ajpastor.dd_functions.ddFunction.DDFunction method) interlace() (ajpastor.dd_functions.ddFunction.DDFunction method) interlace_sequences() (ajpastor.dd_functions.ddFunction.DDRing method) inverse (ajpastor.dd_functions.ddFunction.DDFunction attribute) inverse_DA() (in module ajpastor.dd_functions.toDiffAlgebraic) is_constant() (ajpastor.dd_functions.ddFunction.DDFunction method) is_DDFunction() (in module ajpastor.dd_functions.ddFunction) is_DDRing() (in module ajpastor.dd_functions.ddFunction) is_field() (ajpastor.dd_functions.ddFunction.DDRing method)

is_finite() (ajpastor.dd_functions.ddFunction.DDRing method) is_fully_defined (ajpastor.dd_functions.ddFunction.DDFunction attribute) is_homogeneous() (ajpastor.misc.linear_solver.LinearSystemSolver method) is_InfinitePolynomialRing() (in module ajpastor.dd_functions.toDiffAlgebraic) is_inverse() (ajpastor.dd_functions.ddFunction.DDFunction method) is_invertible() (ajpastor.dd_functions.ddFunction.DDRing method) is_noetherian() (ajpastor.dd_functions.ddFunction.DDRing method) is_null (ajpastor.dd_functions.ddFunction.DDFunction attribute) is_one (ajpastor.dd_functions.ddFunction.DDFunction attribute) is_ParametrizedDDRing() (in module ajpastor.dd_functions.ddFunction) is_Riccati() (in module ajpastor.dd_functions.toDiffAlgebraic) is_string() (in module ajpastor.misc.dynamic_string) is_zero() (ajpastor.misc.linear_solver.LinearSystemSolver method) isequence() (ajpastor.dd_functions.ddFunction.DDFunction method)

K

kappa_v() (in module ajpastor.misc.matrix)

kronecker_sum() (in module ajpastor.misc.matrix)

L

LegendreD() (in module ajpastor.dd_functions.ddExamples) LinearSystemSolver (class in ajpastor.misc.linear_solver) load_init() (ajpastor.dd_functions.ddFunction.DDFunction method)

Log() (in module ajpastor.dd_functions.ddExamples) Log1() (in module ajpastor.dd_functions.ddExamples) Logarithmic_polynomials() (in module ajpastor.dd_functions.toDiffAlgebraic)

M

m_dreplace() (in module ajpastor.misc.dynamic_string) m_replace() (ajpastor.misc.dynamic_string.DynamicString method) MathieuCos() (in module ajpastor.dd_functions.ddExamples) MathieuCosh() (in module ajpastor.dd_functions.ddExamples) MathieuD() (in module ajpastor.dd_functions.ddExamples) MathieuH() (in module ajpastor.dd_functions.ddExamples) MathieuSin() (in module ajpastor.dd_functions.ddExamples) MathieuSinh() (in module ajpastor.dd_functions.ddExamples) matrix_of_dMovement() (in module ajpastor.misc.matrix) min_coefficient() (ajpastor.dd_functions.ddFunction.DDFunction method) module ajpastor.dd_functions.ddExamples ajpastor.dd_functions.ddFunction ajpastor.dd_functions.exceptions ajpastor.dd_functions.symbolic ajpastor.dd_functions.toDiffAlgebraic ajpastor.misc.bareiss ajpastor.misc.dynamic_string ajpastor.misc.hermite ajpastor.misc.linear_solver ajpastor.misc.matrix

mult() (ajpastor.dd_functions.ddFunction.DDFunction method)

N

name (ajpastor.dd_functions.ddFunction.DDFunction attribute) nargs() (ajpastor.misc.dynamic_string.DynamicString method) ngens() (ajpastor.dd_functions.ddFunction.DDRing method) noetherian_ring() (ajpastor.dd_functions.ddFunction.DDFunction method)

NoSolutionError NoValueError numeric_coefficient_comparison_asymptotics() (ajpastor.dd_functions.ddFunction.DDFunction method) numerical_solution() (ajpastor.dd_functions.ddFunction.DDFunction method)

O

op_cols() (in module ajpastor.misc.matrix) op_rows() (in module ajpastor.misc.matrix)

operator_class (ajpastor.dd_functions.ddFunction.DDRing attribute) order() (ajpastor.dd_functions.ddFunction.DDFunction method) original_ring() (ajpastor.dd_functions.ddFunction.DDRing method)

P

ParabolicCylinderD() (in module ajpastor.dd_functions.ddExamples) parameter() (ajpastor.dd_functions.ddFunction.DDRing method) parameters() (ajpastor.dd_functions.ddFunction.DDRing method) (ajpastor.dd_functions.ddFunction.ParametrizedDDRing method)

ParametrizedDDRing (class in ajpastor.dd_functions.ddFunction) parent() (ajpastor.misc.linear_solver.LinearSystemSolver method) PolylogarithmD() (in module ajpastor.dd_functions.ddExamples) polynomial_inverse() (in module ajpastor.dd_functions.ddExamples) ps_order (ajpastor.dd_functions.ddFunction.DDFunction attribute)

Q

quick_equals() (ajpastor.dd_functions.ddFunction.DDFunction method)

R

random_element() (ajpastor.dd_functions.ddFunction.DDRing method) random_matrix() (in module ajpastor.misc.matrix) rank() (ajpastor.misc.linear_solver.LinearSystemSolver method)

real() (ajpastor.misc.dynamic_string.DynamicString method) relations() (ajpastor.misc.linear_solver.LinearSystemSolver method) replace() (ajpastor.misc.dynamic_string.DynamicString method) RiccatiD() (in module ajpastor.dd_functions.ddExamples)

S

SageSolver (class in ajpastor.misc.linear_solver) save_init() (ajpastor.dd_functions.ddFunction.DDFunction method) scal_col() (in module ajpastor.misc.matrix) scal_row() (in module ajpastor.misc.matrix) scalar() (ajpastor.dd_functions.ddFunction.DDFunction method) scale_operator() (ajpastor.dd_functions.ddFunction.DDFunction method) sequence() (ajpastor.dd_functions.ddFunction.DDFunction method) serialize() (ajpastor.dd_functions.ddFunction.DDFunction method) simple_add() (ajpastor.dd_functions.ddFunction.DDFunction method) simple_derivative() (ajpastor.dd_functions.ddFunction.DDFunction method) simple_mult() (ajpastor.dd_functions.ddFunction.DDFunction method) simplify() (ajpastor.misc.linear_solver.LinearSystemSolver method) simplify_coefficients() (in module ajpastor.dd_functions.toDiffAlgebraic) simplify_derivatives() (in module ajpastor.dd_functions.toDiffAlgebraic) simplify_matrix() (in module ajpastor.misc.matrix) Sin() (in module ajpastor.dd_functions.ddExamples)

singularities() (ajpastor.dd_functions.ddFunction.DDFunction method) Sinh() (in module ajpastor.dd_functions.ddExamples) size() (ajpastor.dd_functions.ddFunction.DDFunction method) solution() (ajpastor.misc.linear_solver.LinearSystemSolver method) solution_parent() (ajpastor.misc.linear_solver.LinearSystemSolver method) SpheroidalWaveFunctionD() (in module ajpastor.dd_functions.ddExamples) split_sequence() (ajpastor.dd_functions.ddFunction.DDFunction method) StruveD() (in module ajpastor.dd_functions.ddExamples) sub() (ajpastor.dd_functions.ddFunction.DDFunction method) swap_cols() (in module ajpastor.misc.matrix) swap_rows() (in module ajpastor.misc.matrix) symbolic() (in module ajpastor.dd_functions.symbolic) symbolic_simplify() (in module ajpastor.dd_functions.symbolic) symbolic_simplify_coefficients() (in module ajpastor.dd_functions.symbolic) system_matrix() (ajpastor.misc.linear_solver.LinearSystemSolver method) syzygy() (ajpastor.misc.linear_solver.LinearSystemSolver method)

T

Tan() (in module ajpastor.dd_functions.ddExamples) Tanh() (in module ajpastor.dd_functions.ddExamples) taylor (ajpastor.dd_functions.ddFunction.DDFunction attribute) to_depth() (ajpastor.dd_functions.ddFunction.DDRing method) (ajpastor.dd_functions.ddFunction.ParametrizedDDRing method) to_poly() (ajpastor.dd_functions.ddFunction.DDFunction method)

to_simpler() (ajpastor.dd_functions.ddFunction.DDFunction method) to_symbolic() (ajpastor.dd_functions.ddFunction.DDFunction method) toDifferentiallyAlgebraic_Below() (in module ajpastor.dd_functions.toDiffAlgebraic) transformation_matrix() (ajpastor.misc.linear_solver.LinearSystemSolver method) truncation() (ajpastor.dd_functions.ddFunction.DDFunction method) turn_matrix() (in module ajpastor.misc.matrix)

U

U (ajpastor.misc.linear_solver.LinearSystemSolver attribute)

V

valuation (ajpastor.dd_functions.ddFunction.DDFunction attribute) vandermonde_matrix() (in module ajpastor.misc.matrix)

variable() (ajpastor.dd_functions.ddFunction.DDRing method) variables() (ajpastor.dd_functions.ddFunction.DDRing method) vector_derivative() (in module ajpastor.misc.matrix)

Z

zero_extraction (ajpastor.dd_functions.ddFunction.DDFunction attribute) zero_extraction() (in module ajpastor.dd_functions.ddFunction)

zeros() (ajpastor.dd_functions.ddFunction.DDFunction method) ZeroValueRequired