Truncated power series with complex coefficients for PHCv2.4.87

Similar to Taylor series approximations for general functions,
we can approximate roots of polynomials in a parameter by series.

The library is divided in three parts:
(1) the basic arithmetic with truncated power series
(2) vectors, matrices, and linear system solving
(3) polynomials with coefficients as truncated power series

In the first design, series are represented by a coefficient vector
of fixed length, a length that is determined at compile time,
and a variable which represents the degree of the series.
While this design allows to treat series just as numbers,
the degree of a series is limited to what was determined at compile time,
which turns out to be too inflexible.
In the second design, a type Link_to_Series was added with which the
series vectors are instantiated.  The third design applies generics
and defines series over any ring extended with division.

In v2.4.80, series in triple, penta, octo, and deca double precision
were added.  Support for hexa double precision was added in v2.4.87.

Run "gprbuild series.gpr" to make all test programs.
On windows, type "gprbuild series.gpr -Xos=windows"
at the PowerShell prompt.
The "gprclean series.gpr" removes all files created by gprbuild.

------------------------------------------------------------------------------
file name                          : short description
------------------------------------------------------------------------------
standard_truncated_series          : defines basic operations on power series
ts_pstrunc                         : tests proof-of-concept power series
binomial_coefficients              : export binomial() function
ts_bincff                          : test on binomial coefficients
------------------------------------------------------------------------------
generic_dense_series               : series over any ring with division
standard_complex_series            : series with standard complex coefficients
dobldobl_complex_series            : series with dobldobl complex coefficients
tripdobl_complex_series            : series with tripdobl complex coefficients
quaddobl_complex_series            : series with quaddobl complex coefficients
pentdobl_complex_series            : series with pentdobl complex coefficients
octodobl_complex_series            : series with octodobl complex coefficients
decadobl_complex_series            : series with decadobl complex coefficients
hexadobl_complex_series            : series with hexadobl complex coefficients
standard_complex_series_io         : i/o for standard complex series
dobldobl_complex_series_io         : i/o for double double complex series
tripdobl_complex_series_io         : i/o for triple double complex series
quaddobl_complex_series_io         : i/o for quad double complex series
pentdobl_complex_series_io         : i/o for penta double complex series
octodobl_complex_series_io         : i/o for octo double complex series
decadobl_complex_series_io         : i/o for deca double complex series
hexadobl_complex_series_io         : i/o for hexa double complex series
standard_complex_random_series     : generators for random standard series
dobldobl_complex_random_series     : generators for random dobldobl series
tripdobl_complex_random_series     : generators for random tripdobl series
quaddobl_complex_random_series     : generators for random quaddobl series
pentdobl_complex_random_series     : generators for random pentdobl series
octodobl_complex_random_series     : generators for random octodobl series
decadobl_complex_random_series     : generators for random decadobl series
hexadobl_complex_random_series     : generators for random hexadobl series
standard_complex_algebraic_series  : sqrt and n-th root of standard series
dobldobl_complex_algebraic_series  : sqrt and n-th root of dobldobl series
tripdobl_complex_algebraic_series  : sqrt and n-th root of tripdobl series
quaddobl_complex_algebraic_series  : sqrt and n-th root of quaddobl series
pentdobl_complex_algebraic_series  : sqrt and n-th root of pentdobl series
octodobl_complex_algebraic_series  : sqrt and n-th root of octodobl series
decadobl_complex_algebraic_series  : sqrt and n-th root of decadobl series
hexadobl_complex_algebraic_series  : sqrt and n-th root of hexadobl series
standard_complex_series_norms      : conjugates and norms of standard series
dobldobl_complex_series_norms      : conjugates and norms of dobldobl series
tripdobl_complex_series_norms      : conjugates and norms of tripdobl series
quaddobl_complex_series_norms      : conjugates and norms of quaddobl series
pentdobl_complex_series_norms      : conjugates and norms of pentdobl series
octodobl_complex_series_norms      : conjugates and norms of octodobl series
decadobl_complex_series_norms      : conjugates and norms of decadobl series
hexadobl_complex_series_norms      : conjugates and norms of hexadobl series
standard_complex_series_functions  : evaluate and shift standard series
dobldobl_complex_series_functions  : evaluate and shift dobldobl series
tripdobl_complex_series_functions  : evaluate and shift tripdobl series
quaddobl_complex_series_functions  : evaluate and shift quaddobl series
pentdobl_complex_series_functions  : evaluate and shift pentdobl series
octodobl_complex_series_functions  : evaluate and shift octodobl series
decadobl_complex_series_functions  : evaluate and shift decadobl series
hexadobl_complex_series_functions  : evaluate and shift hexadobl series
standard_complex_series_transforms : coefficient modulus transformations
dobldobl_complex_series_transforms : dd coefficient modulus transformations
quaddobl_complex_series_transforms : qd coefficient modulus transformations
test_standard_complex_series       : tests series with double complex coeffs
test_dobldobl_complex_series       : tests series in double double precision
test_tripdobl_complex_series       : tests series in triple double precision
test_quaddobl_complex_series       : tests series in quad double precision
test_pentdobl_complex_series       : tests series in penta double precision
test_octodobl_complex_series       : tests series in octo double precision
test_decadobl_complex_series       : tests series in deca double precision
test_hexadobl_complex_series       : tests series in hexa double precision
ts_cseries                         : main test on 3rd version of series
------------------------------------------------------------------------------
standard_complex_series_ring       : ring of series in double precision
standard_complex_series_ring_io    : i/o for standard series in the ring
dobldobl_complex_series_ring       : ring of series in double double precision
dobldobl_complex_series_ring_io    : i/o for dobldobl series in the ring
tripdobl_complex_series_ring       : ring of series in triple double precision
tripdobl_complex_series_ring_io    : i/o for tripdobl series in the ring
quaddobl_complex_series_ring       : ring of series in quad double precision
quaddobl_complex_series_ring_io    : i/o for quaddobl series in the ring
pentdobl_complex_series_ring       : ring of series in penta double precision
pentdobl_complex_series_ring_io    : i/o for pentdobl series in the ring
octodobl_complex_series_ring       : ring of series in octo double precision
octodobl_complex_series_ring_io    : i/o for octodobl series in the ring
decadobl_complex_series_ring       : ring of series in deca double precision
decadobl_complex_series_ring_io    : i/o for decadobl series in the ring
hexadobl_complex_series_ring       : ring of series in hexa double precision
hexadobl_complex_series_ring_io    : i/o for hexadobl series in the ring
standard_complex_series_vectors    : vectors of standard series
standard_complex_series_vectors_io : i/o for vectors of standard series
dobldobl_complex_series_vectors    : vectors of dobldobl series
dobldobl_complex_series_vectors_io : i/o for vectors of dobldobl series
tripdobl_complex_series_vectors    : vectors of tripdobl series
tripdobl_complex_series_vectors_io : i/o for vectors of tripdobl series
quaddobl_complex_series_vectors    : vectors of quaddobl series
quaddobl_complex_series_vectors_io : i/o for vectors of quaddobl series
pentdobl_complex_series_vectors    : vectors of pentdobl series
pentdobl_complex_series_vectors_io : i/o for vectors of pentdobl series
octodobl_complex_series_vectors    : vectors of octodobl series
octodobl_complex_series_vectors_io : i/o for vectors of octodobl series
decadobl_complex_series_vectors    : vectors of decadobl series
decadobl_complex_series_vectors_io : i/o for vectors of decadobl series
hexadobl_complex_series_vectors    : vectors of hexadobl series
hexadobl_complex_series_vectors_io : i/o for vectors of hexadobl series
standard_complex_series_vecvecs    : vectors of vectors of standard series
dobldobl_complex_series_vecvecs    : vectors of vectors of dobldobl series
tripdobl_complex_series_vecvecs    : vectors of vectors of tripdobl series
quaddobl_complex_series_vecvecs    : vectors of vectors of quaddobl series
pentdobl_complex_series_vecvecs    : vectors of vectors of pentdobl series
octodobl_complex_series_vecvecs    : vectors of vectors of octodobl series
decadobl_complex_series_vecvecs    : vectors of vectors of decadobl series
hexadobl_complex_series_vecvecs    : vectors of vectors of hexadobl series
standard_complex_series_norms      : norms of vectors of standard series
dobldobl_complex_series_norms      : norms of vectors of dobldobl series
tripdbol_complex_series_norms      : norms of vectors of tripdobl series
quaddobl_complex_series_norms      : norms of vectors of dobldobl series
pentdobl_complex_series_norms      : norms of vectors of pentdobl series
octodobl_complex_series_norms      : norms of vectors of octodobl series
decadobl_complex_series_norms      : norms of vectors of decadobl series
hexadobl_complex_series_norms      : norms of vectors of hexadobl series
standard_complex_vector_series     : series with standard vector coefficients
standard_complex_vector_series_io  : basic output of standard vector series
dobldobl_complex_vector_series     : series with dobldobl vector coefficients
dobldobl_complex_vector_series_io  : basic output of dobldobl vector series
tripdobl_complex_vector_series     : series with tripdobl vector coefficients
tripdobl_complex_vector_series_io  : basic output of tripdobl vector series
quaddobl_complex_vector_series     : series with quaddobl vector coefficients
quaddobl_complex_vector_series_io  : basic output of quaddobl vector series
pentdobl_complex_vector_series     : series with pentdobl vector coefficients
pentdobl_complex_vector_series_io  : basic output of pentdobl vector series
octodobl_complex_vector_series     : series with octodobl vector coefficients
octodobl_complex_vector_series_io  : basic output of octodobl vector series
decadobl_complex_vector_series     : series with decadobl vector coefficients
decadobl_complex_vector_series_io  : basic output of decadobl vector series
hexadobl_complex_vector_series     : series with hexadobl vector coefficients
hexadobl_complex_vector_series_io  : basic output of hexadobl vector series
standard_cseries_vector_norms      : norms of vectors of standard series
dobldobl_cseries_vector_norms      : norms of vectors of dobldobl series
tripdobl_cseries_vector_norms      : norms of vectors of tripdobl series
quaddobl_cseries_vector_norms      : norms of vectors of quaddobl series
pentdobl_cseries_vector_norms      : norms of vectors of pentdobl series
octodobl_cseries_vector_norms      : norms of vectors of octodobl series
decadobl_cseries_vector_norms      : norms of vectors of decadobl series
hexadobl_cseries_vector_norms      : norms of vectors of hexadobl series
standard_random_series_vectors     : random vectors of standard series
dobldobl_random_series_vectors     : random vectors of dobldobl series
tripdobl_random_series_vectors     : random vectors of tripdobl series
quaddobl_random_series_vectors     : random vectors of quaddobl series
pentdobl_random_series_vectors     : random vectors of pentdobl series
octodobl_random_series_vectors     : random vectors of octodobl series
decadobl_random_series_vectors     : random vectors of decadobl series
hexadobl_random_series_vectors     : random vectors of hexadobl series
test_standard_vector_series        : tests vector series in double precision
test_dobldobl_vector_series        : tests vector series in dobldobl precision
test_tripdobl_vector_series        : tests vector series in tripdobl precision
test_quaddobl_vector_series        : tests vector series in quaddobl precision
test_pentdobl_vector_series        : tests vector series in pentdobl precision
test_octodobl_vector_series        : tests vector series in octodobl precision
test_decadobl_vector_series        : tests vector series in decadobl precision
test_hexadobl_vector_series        : tests vector series in hexadobl precision
ts_cservec                         : test on 3rd version of vector series
standard_cseries_vector_functions  : evaluating vectors of standard series
dobldobl_cseries_vector_functions  : evaluating vectors of dobldobl series
tripdobl_cseries_vector_functions  : evaluating vectors of tripdobl series
quaddobl_cseries_vector_functions  : evaluating vectors of quaddobl series
pentdobl_cseries_vector_functions  : evaluating vectors of pentdobl series
octodobl_cseries_vector_functions  : evaluating vectors of octodobl series
decadobl_cseries_vector_functions  : evaluating vectors of decadobl series
hexadobl_cseries_vector_functions  : evaluating vectors of hexadobl series
------------------------------------------------------------------------------
standard_complex_series_matrices   : matrices of standard series
dobldobl_complex_series_matrices   : matrices of dobldobl series
tripdobl_complex_series_matrices   : matrices of tripdobl series
quaddobl_complex_series_matrices   : matrices of quaddobl series
pentdobl_complex_series_matrices   : matrices of pentdobl series
octodobl_complex_series_matrices   : matrices of octodobl series
decadobl_complex_series_matrices   : matrices of decadobl series
hexadobl_complex_series_matrices   : matrices of hexadobl series
standard_complex_matrix_series     : series with standard matrix coefficients
dobldobl_complex_matrix_series     : series with dobldobl matrix coefficients
tripdobl_complex_matrix_series     : series with tripdobl matrix coefficients
quaddobl_complex_matrix_series     : series with quaddobl matrix coefficients
pentdobl_complex_matrix_series     : series with pentdobl matrix coefficients
octodobl_complex_matrix_series     : series with octodobl matrix coefficients
decadobl_complex_matrix_series     : series with decadobl matrix coefficients
hexadobl_complex_matrix_series     : series with hexadobl matrix coefficients
standard_complex_matrix_series_io  : basic output of standard matrix series
dobldobl_complex_matrix_series_io  : basic output of dobldobl matrix series
tripdobl_complex_matrix_series_io  : basic output of tripdobl matrix series
quaddobl_complex_matrix_series_io  : basic output of quaddobl matrix series
pentdobl_complex_matrix_series_io  : basic output of pentdobl matrix series
octodobl_complex_matrix_series_io  : basic output of octodobl matrix series
decadobl_complex_matrix_series_io  : basic output of decadobl matrix series
hexadobl_complex_matrix_series_io  : basic output of hexadobl matrix series
standard_random_series_matrices    : standard random matrices of series
dobldobl_random_series_matrices    : dobldobl random matrices of series
tripdobl_random_series_matrices    : tripdobl random matrices of series
quaddobl_random_series_matrices    : quaddobl random matrices of series
pentdobl_random_series_matrices    : pentdobl random matrices of series
octodobl_random_series_matrices    : octodobl random matrices of series
decadobl_random_series_matrices    : decadobl random matrices of series
hexadobl_random_series_matrices    : hexadobl random matrices of series
standard_series_linear_solvers     : standard LU solver on matrices of series
dobldobl_series_linear_solvers     : dobldobl LU solver on matrices of series
tripdobl_series_linear_solvers     : tripdobl LU solver on matrices of series
quaddobl_series_linear_solvers     : quaddobl LU solver on matrices of series
pentdobl_series_linear_solvers     : pentdobl LU solver on matrices of series
octodobl_series_linear_solvers     : octodobl LU solver on matrices of series
decadobl_series_linear_solvers     : decadobl LU solver on matrices of series
hexadobl_series_linear_solvers     : hexadobl LU solver on matrices of series
standard_series_least_squares      : standard QR solver on matrices of series
dobldobl_series_least_squares      : dobldobl QR solver on matrices of series
tripdobl_series_least_squares      : tripdobl QR solver on matrices of series
quaddobl_series_least_squares      : quaddobl QR solver on matrices of series
pentdobl_series_least_squares      : pentdobl QR solver on matrices of series
octodobl_series_least_squares      : octodobl QR solver on matrices of series
decadobl_series_least_squares      : decadobl QR solver on matrices of series
hexadobl_series_least_squares      : hexadobl QR solver on matrices of series
test_standard_matrix_series        : tests matrix series in double precision
test_dobldobl_matrix_series        : tests matrix series in dobldobl precision
test_tripdobl_matrix_series        : tests matrix series in tripdobl precision
test_quaddobl_matrix_series        : tests matrix series in quaddobl precision
test_pentdobl_matrix_series        : tests matrix series in pentdobl precision
test_octodobl_matrix_series        : tests matrix series in octodobl precision
test_decadobl_matrix_series        : tests matrix series in decadobl precision
ts_csermat                         : test on 3rd version of matrices of series
------------------------------------------------------------------------------
standard_interpolating_series      : interpolation for standard series systems
dobldobl_interpolating_series      : interpolation for dobldobl series systems
tripdobl_interpolating_series      : interpolation for tripdobl series systems
quaddobl_interpolating_series      : interpolation for quaddobl series systems
pentdobl_interpolating_series      : interpolation for pentdobl series systems
octodobl_interpolating_series      : interpolation for octodobl series systems
decadobl_interpolating_series      : interpolation for decadobl series systems
hexadobl_interpolating_series      : interpolation for hexadobl series systems
ts_cseritp                         : test on linear series interpolation
------------------------------------------------------------------------------
standard_echelon_forms             : echelon standard Hermite-Laurent systems
dobldobl_echelon_forms             : echelon dobldobl Hermite-Laurent systems
tripdobl_echelon_forms             : echelon tripdobl Hermite-Laurent systems
quaddobl_echelon_forms             : echelon quaddobl Hermite-Laurent systems
pentdobl_echelon_forms             : echelon pentdobl Hermite-Laurent systems
octodobl_echelon_forms             : echelon octodobl Hermite-Laurent systems
decadobl_echelon_forms             : echelon decadobl Hermite-Laurent systems
hexadobl_echelon_forms             : echelon hexadobl Hermite-Laurent systems
ts_csersin                         : test on solving singular linear systems
------------------------------------------------------------------------------
standard_series_matrix_solvers     : linearization for standard series systems
dobldobl_series_matrix_solvers     : linearization for dobldobl series systems
tripdobl_series_matrix_solvers     : linearization for tripdobl series systems
quaddobl_series_matrix_solvers     : linearization for quaddobl series systems
pentdobl_series_matrix_solvers     : linearization for pentdobl series systems
octodobl_series_matrix_solvers     : linearization for octodobl series systems
decadobl_series_matrix_solvers     : linearization for decadobl series systems
hexadobl_series_matrix_solvers     : linearization for hexadobl series systems
series_coefficient_vectors         : flatten data structure
test_standard_linearization        : tests linearization in double precision
test_dobldobl_linearization        : tests linearization in dobldobl precision
test_tripdobl_linearization        : tests linearization in tripdobl precision
test_quaddobl_linearization        : tests linearization in quaddobl precision
test_pentdobl_linearization        : tests linearization in pentdobl precision
test_octodobl_linearization        : tests linearization in octodobl precision
test_decadobl_linearization        : tests linearization in decadobl precision
test_hexadobl_linearization        : tests linearization in hexadobl precision
ts_cserlin                         : test on linearization
ts_cserinv                         : test on inverting singular problems
------------------------------------------------------------------------------
standard_cseries_polynomials       : polynomials with standard cseries coeffs
standard_cseries_polynomials_io    : output of standard cseries polynomials
standard_cseries_poly_functions    : evaluating standard cseries polynomials
standard_cseries_poly_systems      : systems of standard cseries polynomials
standard_cseries_poly_systems_io   : output of standard cseries poly systems
standard_cseries_poly_sysfun       : evaluating standard series poly systems
standard_cseries_jaco_matrices     : differentiating standard series systems
dobldobl_cseries_polynomials       : polynomials with dobldobl cseries coeffs
dobldobl_cseries_polynomials_io    : output of dobldobl cseries polynomials
dobldobl_cseries_poly_functions    : evaluating dobldobl cseries polynomials
dobldobl_cseries_poly_systems      : systems of dobldobl cseries polynomials
dobldobl_cseries_poly_systems_io   : output of dobldobl cseries poly systems
dobldobl_cseries_poly_sysfun       : evaluating dobldobl series poly systems
dobldobl_cseries_jaco_matrices     : differentiating dobldobl series systems
tripdobl_cseries_polynomials       : polynomials with tripdobl cseries coeffs
tripdobl_cseries_polynomials_io    : output of tripdobl cseries polynomials
tripdobl_cseries_poly_functions    : evaluating tripdobl cseries polynomials
tripdobl_cseries_poly_systems      : systems of tripdobl cseries polynomials
tripdobl_cseries_poly_systems_io   : output of tripdobl cseries poly systems
tripdobl_cseries_poly_sysfun       : evaluating tripdobl series poly systems
tripdobl_cseries_jaco_matrices     : differentiating tripdobl series systems
quaddobl_cseries_polynomials       : polynomials with quaddobl cseries coeffs
quaddobl_cseries_polynomials_io    : output of quaddobl cseries polynomials
quaddobl_cseries_poly_functions    : evaluating quaddobl cseries polynomials
quaddobl_cseries_poly_systems      : systems of quaddobl cseries polynomials
quaddobl_cseries_poly_systems_io   : output of quaddobl cseries poly systems
quaddobl_cseries_poly_sysfun       : evaluating quaddobl series poly systems
quaddobl_cseries_jaco_matrices     : differentiating quaddobl series systems
pentdobl_cseries_polynomials       : polynomials with pentdobl cseries coeffs
pentdobl_cseries_polynomials_io    : output of pentdobl cseries polynomials
pentdobl_cseries_poly_functions    : evaluating pentdobl cseries polynomials
pentdobl_cseries_poly_systems      : systems of pentdobl cseries polynomials
pentdobl_cseries_poly_systems_io   : output of pentdobl cseries poly systems
pentdobl_cseries_poly_sysfun       : evaluating pentdobl series poly systems
pentdobl_cseries_jaco_matrices     : differentiating pentdobl series systems
octodobl_cseries_polynomials       : polynomials with octodobl cseries coeffs
octodobl_cseries_polynomials_io    : output of octodobl cseries polynomials
octodobl_cseries_poly_functions    : evaluating octodobl cseries polynomials
octodobl_cseries_poly_systems      : systems of octodobl cseries polynomials
octodobl_cseries_poly_systems_io   : output of octodobl cseries poly systems
octodobl_cseries_poly_sysfun       : evaluating octodobl series poly systems
octodobl_cseries_jaco_matrices     : differentiating octodobl series systems
decadobl_cseries_polynomials       : polynomials with decadobl cseries coeffs
decadobl_cseries_polynomials_io    : output of decadobl cseries polynomials
decadobl_cseries_poly_functions    : evaluating decadobl cseries polynomials
decadobl_cseries_poly_systems      : systems of decadobl cseries polynomials
decadobl_cseries_poly_systems_io   : output of decadobl cseries poly systems
decadobl_cseries_poly_sysfun       : evaluating decadobl series poly systems
decadobl_cseries_jaco_matrices     : differentiating decadobl series systems
hexadobl_cseries_polynomials       : polynomials with hexadobl cseries coeffs
hexadobl_cseries_polynomials_io    : output of hexadobl cseries polynomials
hexadobl_cseries_poly_functions    : evaluating hexadobl cseries polynomials
hexadobl_cseries_poly_systems      : systems of hexadobl cseries polynomials
hexadobl_cseries_poly_systems_io   : output of hexadobl cseries poly systems
hexadobl_cseries_poly_sysfun       : evaluating hexadobl series poly systems
hexadobl_cseries_jaco_matrices     : differentiating hexadobl series systems
complex_series_and_polynomials     : convertor functions
complex_series_and_polynomials_io  : symbolic i/o of series
standard_polynomial_cseries        : standard polynomial series
dobldobl_polynomial_cseries        : dobldobl polynomial series
tripdobl_polynomial_cseries        : tripdobl polynomial series
quaddobl_polynomial_cseries        : quaddobl polynomial series
pentdobl_polynomial_cseries        : pentdobl polynomial series
octodobl_polynomial_cseries        : octodobl polynomial series
decadobl_polynomial_cseries        : decadobl polynomial series
hexadobl_polynomial_cseries        : hexadobl polynomial series
test_standard_cseries_polynomials  : tests standard cseries polynomials
test_dobldobl_cseries_polynomials  : tests dobldobl cseries polynomials
test_tripdobl_cseries_polynomials  : tests tripdobl cseries polynomials
test_quaddobl_cseries_polynomials  : tests quaddobl cseries polynomials
test_pentdobl_cseries_polynomials  : tests pentdobl cseries polynomials
test_octodobl_cseries_polynomials  : tests octodobl cseries polynomials
test_decadobl_cseries_polynomials  : tests decadobl cseries polynomials
ts_cserpol                         : test on series polynomials
test_standard_cseries_systems      : tests standard cseries systems
test_dobldobl_cseries_systems      : tests dobldobl cseries systems
test_quaddobl_cseries_systems      : tests quaddobl cseries systems
ts_csersys                         : test systems of series polynomials
random_series_polynomials          : random polynomials with series coeff
ts_sercffpol                       : test series coefficient-parameter eval
------------------------------------------------------------------------------

Below are the descriptions of the original design,
with fixed maximal degree power series, written without generics.
The second design allows for variable degree series,
but available only in standard double precision, without generics.
The code below will become obsolete at some later stage.

------------------------------------------------------------------------------
file name                         : short description
------------------------------------------------------------------------------
standard_dense_series2            : dense power series, standard coefficients
standard_dense_series2_io         : basic input/output of standard series
standard_algebraic_series2        : sqrt and n-th root of standard series
standard_dense_series_norms2      : norms, normalization of standard series
random_series_generators          : generators for random series
ts_series2                        : test on 2nd design of series
------------------------------------------------------------------------------
standard_dense_series2_ring       : the ring of standard power series
standard_dense_series2_ring_io    : i/o operations for ring elements
standard_dense_series2_vectors    : vectors of standard power series
standard_dense_series2_vectors_io : i/o of vectors of standard power series
standard_dense_series2_vecvecs    : vector of vectors of standard series
standard_dense_vector_series2     : series with standard vector coefficients
standard_dense_vector_series2_io  : basic output of vector series
random_series_vectors             : generators for vectors of random series
standard_series_vector_norms2     : norms of vectors of standard series
ts_servec2                        : test on vectors of standard series
------------------------------------------------------------------------------
standard_dense_series2_matrices   : matrices of standard double power series
standard_dense_matrix_series2     : series with matrix coefficients
standard_dense_matrix_series2_io  : i/o of standard matrix series
standard_linear_series2_solvers   : LU factorization to solve linear system
standard_least_squares_series2    : QR factorization to solve linear system
random_dense_matrices             : random matrices of series
ts_sermat2                        : test on matrices of standard series
------------------------------------------------------------------------------
standard_interpolating_series2    : interpolation for linear series systems
ts_seritp2                        : test on linear series interpolation
------------------------------------------------------------------------------
standard_echelon_forms            : echelon form for Hermite-Laurent systems
ts_sersin2                        : test on solving singular linear systems
------------------------------------------------------------------------------
standard_matrix_series2_solvers   : linearization for matrix series systems
ts_serlin2                        : test on linearization
standard_inlined_linearization    : linearization with inlined solvers
ts_perfserlin                     : a better performing solver
------------------------------------------------------------------------------
standard_dense_series            : dense power series, standard coefficients
dobldobl_dense_series            : dense series in double double precision
quaddobl_dense_series            : dense series in quad double precision
standard_dense_series_io         : basic output of standard series
dobldobl_dense_series_io         : basic output of dobldobl series
quaddobl_dense_series_io         : basic output of quaddobl series
standard_random_series           : series with standard random coefficients
dobldobl_random_series           : series with dobldobl random coefficients
quaddobl_random_series           : series with quaddobl random coefficients
standard_algebraic_series        : sqrt and n-th root of standard series
dobldobl_algebraic_series        : sqrt and n-th root of dobldobl series
quaddobl_algebraic_series        : sqrt and n-th root of quaddobl series
standard_dense_series_norms      : norms and normalizations of standard series
dobldobl_dense_series_norms      : norms and normalizations of dobldobl series
quaddobl_dense_series_norms      : norms and normalizations of quaddobl series
standard_dense_series_ring       : the ring of standard power series
standard_dense_series_ring_io    : i/o operations for ring elements
dobldobl_dense_series_ring       : the ring of double double power series
dobldobl_dense_series_ring_io    : i/o operations for ring elements
quaddobl_dense_series_ring       : the ring of quad double power series
quaddobl_dense_series_ring_io    : i/o operations for ring elements
ts_series                        : basic test on truncated dense series
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standard_dense_series_vectors    : vectors of double power series
standard_dense_series_vectors_io : i/o for double power series vectors
standard_dense_vector_series     : series with double vectors coefficients
standard_dense_vector_series_io  : output for double vector series
dobldobl_dense_series_vectors    : vectors of double double power series
dobldobl_dense_series_vectors_io : i/o for double double power series vectors
dobldobl_dense_vector_series     : series with double double vector coeffs
dobldobl_dense_vector_series_io  : output for double double vector series
quaddobl_dense_series_vectors    : vectors of quad double power series
quaddobl_dense_series_vectors_io : i/o for quad double power series vectors
quaddobl_dense_vector_series     : series with quad double vector coefficients
quaddobl_dense_vector_series_io  : output for quad double vector series
standard_dense_series_vecvecs    : vectors of vectors of standard power series
dobldobl_dense_series_vecvecs    : vectors of vectors of dobldobl power series
quaddobl_dense_series_vecvecs    : vectors of vectors of quaddobl power series
standard_series_vector_norms     : standard double inner products and norms
dobldobl_series_vector_norms     : double double inner products and norms
quaddobl_series_vector_norms     : quad double inner products and norms
standard_series_vector_functions : evaluating vectors of standard power series
dobldobl_series_vector_functions : evaluating vectors of dobldobl power series
quaddobl_series_vector_functions : evaluating vectors of quaddobl power series
ts_servec                        : test on vectors of dense power series
standard_dense_series_matrices   : matrices of standard double power series
standard_dense_matrix_series     : series with double matrices as coefficients
standard_dense_matrix_series_io  : basic output for double matrix series
dobldobl_dense_series_matrices   : matrices of double double power series
dobldobl_dense_matrix_series     : series with dobldobl matrices as coeffs
dobldobl_dense_matrix_series_io  : basic output for double double matrix series
quaddobl_dense_series_matrices   : matrices of quad double power series
dobldobl_dense_matrix_series     : series with quaddobl matrices as coeffs
dobldobl_dense_matrix_series_io  : basic output for quad double matrix series
standard_linear_series_solvers   : lu factorization for standard linear systems
dobldobl_linear_series_solvers   : lu factorization for dobldobl linear systems
quaddobl_linear_series_solvers   : lu factorization for quaddobl linear systems
standard_least_squares_series    : standard qr decomposition and least squares
dobldobl_least_squares_series    : dobldobl qr decomposition and least squares
quaddobl_least_squares_series    : quaddobl qr decomposition and least squares
ts_sermat                        : test on matrices of dense power series
standard_matrix_series_solvers   : linearization to solve a system of series
dobldobl_matrix_series_solvers   : linearization in double double precision
quaddobl_matrix_series_solvers   : linearization in quad double precision
ts_serlin                        : test on matrix series solver
standard_interpolating_series    : interpolation for linear series systems
dobldobl_interpolating_series    : interpolating series with double doubles
quaddobl_interpolating_series    : interpolating series with quad doubles
random_matrix_series             : matrix series with random coefficients
ts_seritp                        : test interpolation on linear series systems
standard_echelon_forms           : echelon form for Hermite-Laurent systems
dobldobl_echelon_forms           : double double echelon Hermite-Laurent forms
quaddobl_echelon_forms           : quad double echelon Hermite-Laurent forms
ts_sersin                        : test solving of singular matrix series
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standard_series_polynomials      : polynomials with series as coefficients
standard_series_poly_functions   : evaluating standard series polynomials
standard_series_poly_systems     : systems of standard series polynomials
standard_series_poly_sysfun      : evaluating systems of series polynomials
dobldobl_series_polynomials      : polynomials with series as coefficients
dobldobl_series_poly_functions   : evaluating dobldobl series polynomials
dobldobl_series_poly_systems     : systems of dobldobl series polynomials
dobldobl_series_poly_sysfun      : evaluating systems of series polynomials
quaddobl_series_polynomials      : polynomials with series as coefficients
quaddobl_series_poly_functions   : evaluating quaddobl series polynomials
quaddobl_series_poly_systems     : systems of quaddobl series polynomials
quaddobl_series_poly_sysfun      : evaluating systems of series polynomials
standard_series_jaco_matrices    : differentiating standard series systems
dobldobl_series_jaco_matrices    : differentiating dobldobl series systems
quaddobl_series_jaco_matrices    : differentiating quaddobl series systems
series_and_polynomials           : convertor functions
series_and_polynomials_io        : symbolic i/o of series
standard_polynomial_series       : series with polynomials for coefficients
dobldobl_polynomial_series       : double double precision polynomial series
quaddobl_polynomial_series       : quad double precision polynomial series
ts_serpol                        : test on series polynomials
ts_sersys                        : test systems of series polynomials
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