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Junaid Alam Khan

  1. Converting Subalgebra Bases with the Sagbi Walk.

    Чт, 11/26/2009 - 16:01 — SomNambul
    Authors: Junaid Alam Khan
    Subjects: Commutative Algebra
    Abstract

    We present an algorithm which converts a given Sagbi basis of a polynomial
    $K$-subalgebra $\mathcal{A}$ to a Sagbi basis of $\mathcal{A}$ in a polynomial
    ring with respect to another term ordering, under the assumption that
    subalgebra $\mathcal{A}$ admits a finite Sagbi basis with respect to all term
    ordering. The Sagbi walk method converts a Sagbi basis by partitioning the
    computations following a path in the Sagbi Fan. The algorithms have been
    implemented as a library for the computer algebra system SINGULAR \cite{GPS1}.

  2. Subalgebra Analogue to Standard Basis for Ideal.

    Чт, 10/01/2009 - 00:35 — SomNambul
    Authors: Junaid Alam Khan
    Subjects: Commutative Algebra
    Abstract

    The theory of "subalgebra basis" analogous to standard basis (the
    generalization of Gr\"{o}bner bases to monomial ordering which are not
    necessarily well ordering \cite{GP1}.) for ideals in polynomial rings over a
    field is developed. We call these bases "SASBI Basis" for "Subalgebra Analogue
    to Standard Basis for Ideals". The case of global orderings, here they are
    called "SAGBI Basis" for "Subalgebra Analogue to Gr\"{o}bner Basis for Ideals",
    is treated in \cite{RS1}. Sasbi bases may be infinite.

  3. Subalgebra Analogue to Standard Basis for Ideal.

    Чт, 10/01/2009 - 00:35 — SomNambul
    Authors: Junaid Alam Khan
    Subjects: Commutative Algebra
    Abstract

    The theory of "subalgebra basis" analogous to standard basis (the
    generalization of Gr\"{o}bner bases to monomial ordering which are not
    necessarily well ordering \cite{GP1}.) for ideals in polynomial rings over a
    field is developed. We call these bases "SASBI Basis" for "Subalgebra Analogue
    to Standard Basis for Ideals". The case of global orderings, here they are
    called "SAGBI Basis" for "Subalgebra Analogue to Gr\"{o}bner Basis for Ideals",
    is treated in \cite{RS1}. Sasbi bases may be infinite.

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