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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/READ_ME, Revision 1.1

1.1     ! maekawa     1: The root-counting library in PHCv2 is organized as follows :
        !             2:
        !             3:   Root_Counts          : 4. root counts and homotopy construction
        !             4:      |-- Product       : 4.1. linear-product start systems
        !             5:      |-- Implift       : 4.2. implicit lifting
        !             6:      |-- Stalift       : 4.3. static lifting
        !             7:      |-- Dynlift       : 4.4. dynamic lifting
        !             8:      |-- Symmetry      : 4.5. exploitation of symmetry relations
        !             9:
        !            10: The root counts that are available in the directory Product are
        !            11: based on Bezout's theorem.  The corresponding start systems are
        !            12: in general linear-product systems.
        !            13:
        !            14: Implicit lifting is the name we gave to the algorithm Bernshtein
        !            15: used in his proof that the mixed volume of the Newton polytopes
        !            16: of a polynomial system is a generically exact upper bound on the
        !            17: number of its isolated complex solutions with all components different
        !            18: from zero.
        !            19:
        !            20: Static lifting is the general procedure to compute mixed volumes
        !            21: of polytopes.  Subdivisions induced by an integer-valued or
        !            22: floating-point lifting functions can be computed.
        !            23: In order to deal with non-fine subdivisions induced by a nongeneric
        !            24: integer lifting, recursive algorithms have been implemented.
        !            25:
        !            26: Dynamic lifting allows to have a control of the lifting values to
        !            27: obtain a numerically stable polyhedral continuation.
        !            28: When some or all supports are equal, the Cayley trick is
        !            29: recommended to use.
        !            30:
        !            31: The Symmetry library provides routines to construct start systems
        !            32: that are invariant under a given permutation symmetry.
        !            33: Hereby symmetric homotopies can be constructed, so that only the
        !            34: generating solution paths need to be computed.