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Annotation of OpenXM_contrib/PHC/Ada/Math_Lib/Polynomials/READ_ME, Revision 1.1.1.1

1.1       maekawa     1: Multivariate polynomials and polynomial systems over rings/fields in PHCv2.
                      2:
                      3: New in this release is the availability of multi-precision numbers.
                      4: The data structures are entirely redefined using Ada 95 concepts.
                      5:
                      6: This library is organized in three parts:
                      7: 1) generic packages: polynomials and systems
                      8: 2) instantiations
                      9: 3) utilities
                     10:
                     11: --------------------------------------------------------------------------------
                     12: file name                         : short description
                     13: --------------------------------------------------------------------------------
                     14: generic_lists                     : lists of items
                     15: graded_lexicographic_order        : defines the order of monomials
                     16: generic_polynomials               : generic polynomials in several variables
                     17: generic_laurent_polynomials       : generic polynomials with integer exponents
                     18: generic_polynomial_functions      : evaluation of polynomials
                     19: generic_laur_poly_functions       : evaluation of Laurent polynomials
                     20: generic_polynomial_systems        : systems of polynomials
                     21: generic_laur_poly_systems         : systems of Laurent polynomials
                     22: generic_poly_system_functions     : evaluation of systems of polynomials
                     23: generic_laur_system_functions     : evaluation of Laurent polynomial systems
                     24: generic_jacobian_matrices         : Jacobian matrices of polynomial systems
                     25: generic_laur_jaco_matrices        : Jacobian matrices of Laurent systems
                     26: symbol_table                      : management of table of symbols
                     27: symbol_table_io                   : input/output of symbols
                     28: --------------------------------------------------------------------------------
                     29: standard_complex_polynomials      : polynomials over standard complex numbers
                     30: standard_complex_polynomials_io   : input/output of complex polynomials
                     31: standard_complex_laur_polys       : Laurent polynomials with standard complex
                     32: standard_complex_poly_ring        : abstract_ring(standard complex poly)
                     33: standard_complex_poly_ring_io     : abstract_ring_io(standard complex poly)
                     34: standard_complex_poly_vectors     : generic_vectors(standard complex poly)
                     35: standard_complex_poly_vectors_io  : generic_vectors_io(standard complex poly)
                     36: standard_complex_poly_matrices    : generic_matrices(standard complex poly)
                     37: standard_complex_poly_matrices_io : generic_matrices_io(standard complex poly)
                     38: standard_complex_poly_functions   : generic_polynomial_functions instantiated
                     39: standard_complex_laur_functions   : generic_laur_poly_functions instantiated
                     40: standard_complex_poly_systems     : generic_polynomial_systems instantiated
                     41: standard_complex_poly_systems_io  : input/output for complex polynomial systems
                     42: standard_complex_laur_systems     : generic_laur_poly_systems instantiated
                     43: standard_complex_poly_sysfun      : generic_poly_system_function instantiated
                     44: standard_complex_jaco_matrices    : generic_jacobian_matrices instantiated
                     45: standard_complex_poly_randomizers : randomize coefficients of polynomials
                     46: standard_complex_laur_randomizers : randomize coefficients of polynomials
                     47: standard_complex_substitutors     : substitute equations into polynomials
                     48: standard_poly_laur_convertors     : convert polynomials to Laurent polynomials
                     49: standard_laur_poly_convertors     : convert Laurent polynomials to polynomials
                     50: multprec_complex_polynomials      : polynomials over multiprec complex numbers
                     51: multprec_complex_laur_polys       : Laurent polynomials over multprec complex
                     52: multprec_complex_poly_functions   : evaluating multprec complex polynomials
                     53: multprec_complex_poly_systems     : systems of multiprec complex polynomials
                     54: multprec_complex_poly_sysfun      : evaluating multprec complex poly systems
                     55: multprec_complex_jaco_matrices    : Jacobian matrices of multiprec systems
                     56: multprec_complex_laur_systems     : multi-precision Laurent systems
                     57: exponent_vectors                  : management of exponents of a system
                     58: standard_evaluator_packages       : create package to evaluate systems
                     59: matrix_indeterminates             : manipulate symbols for xij
                     60: --------------------------------------------------------------------------------
                     61: ts_poly                           : test on polynomials and polynomial systems
                     62: ts_jaco                           : test on Jacobian matrices
                     63: ts_evaline                        : calls the evaluator package
                     64: --------------------------------------------------------------------------------
                     65: Three different representations of polynomials are implemented:
                     66: as a list of terms, a nested Horner scheme with fixed coefficients
                     67: and with parametric coefficients.
                     68: The latter provides an efficient way to evaluate coefficient homotopies.
                     69:
                     70: The i/o-routines provide readable formats in symbolic form.
                     71:
                     72: We can take advantage of the way vectors and matrices have been created:
                     73: a polynomial system is an instance of a polynomial vector and
                     74: a matrix with all partial derivatives is an instance of a polynomial matrix.
                     75:
                     76: The package generic_polynomials allow to define polynomial rings.
                     77: The package generic_polynomial_functions is used to evaluate polynomials.
                     78: In version one of PHC both the ring operations and evaluation routines
                     79: were united in one large package.  The current organization has the benefit
                     80: of separating evaluation from the definitions of vectors and matrices.
                     81: The evaluation by means of a function is also supported.
                     82:
                     83: Since functions need separate data structures, separate packages are used,
                     84: instead of working with child units that could also have been used to create
                     85: a different view on the same data structure.
                     86:
                     87: Also the polynomial systems have been implemented separately.
                     88:
                     89: Jacobian matrices are implemented by means of generics.  Their main usage
                     90: is towards evaluation.  Therefore, the type to represent a Jacobian matrix
                     91: is just a two-dimensional array of polynomials.  To perform algebraic
                     92: manipulations, one should convert to the matrix type of the package matrices
                     93: instantiated with the polynomial ring.
                     94:
                     95: Since the different ways to evaluate polynomials use different orders of
                     96: computation, the results may differ when mixed-precision arithmetic is used.
                     97:
                     98: The Laurent polynomials only differ from the usual polynomials by the
                     99: type definition of the exponents and require the instantiation of a field
                    100: for evaluation.
                    101:
                    102: wc *adb counts 7032 lines of Ada code