Package edu.jas.poly

Class TermOrderByName


  • public class TermOrderByName
    extends java.lang.Object
    Term order names for ordered polynomials. Defines names for the most used term orders: graded and lexicographical orders. For the definitions see for example the articles Kredel, Admissible term orderings used in computer algebra systems and Sit, Some comments on term-ordering in Gröbner basis computations. Not all algorithms may work with all term orders since not all are well-founded, so watch your step. Note: Variables in printed JAS polynomial (low, ..., medium, ..., high) Variables in other CAS polynomial (high, ..., medium, ..., low) with low < medium < high. Example: for variables x1, ..., xr it is assumed in JAS that x1 < ... < xr in other CAS it means x1 > ... > xr.
    • Field Detail

      • logger

        private static final org.apache.logging.log4j.Logger logger
      • LEX

        public static final TermOrder LEX
        TermOrder named LEX.
      • INVLEX

        public static final TermOrder INVLEX
        TermOrder named INVLEX.
      • GRLEX

        public static final TermOrder GRLEX
        TermOrder named GRLEX.
      • IGRLEX

        public static final TermOrder IGRLEX
        TermOrder named IGRLEX.
      • REVLEX

        public static final TermOrder REVLEX
        TermOrder named REVLEX.
      • REVILEX

        public static final TermOrder REVILEX
        TermOrder named REVILEX.
      • REVTDEG

        public static final TermOrder REVTDEG
        TermOrder named REVTDEG.
      • REVITDG

        public static final TermOrder REVITDG
        TermOrder named REVITDG.
      • ITDEGLEX

        public static final TermOrder ITDEGLEX
        TermOrder named ITDEGLEX.
      • REVITDEG

        public static final TermOrder REVITDEG
        TermOrder named REVITDEG.
      • DEFAULT

        public static final TermOrder DEFAULT
        Default TermOrder.
      • Lexicographic

        public static final TermOrder Lexicographic
        TermOrder name Lexicographic of Math like CAS.
      • NegativeLexicographic

        public static final TermOrder NegativeLexicographic
        TermOrder name NegativeLexicographic of Math like CAS.
      • DegreeLexicographic

        public static final TermOrder DegreeLexicographic
        TermOrder name DegreeLexicographic of Math like CAS.
      • NegativeDegreeLexicographic

        public static final TermOrder NegativeDegreeLexicographic
        TermOrder name NegativeDegreeLexicographic of Math like CAS.
      • ReverseLexicographic

        public static final TermOrder ReverseLexicographic
        TermOrder name ReverseLexicographic of Math like CAS.
      • DegreeReverseLexicographic

        public static final TermOrder DegreeReverseLexicographic
        TermOrder name DegreeReverseLexicographic of Math like CAS.
      • NegativeReverseLexicographic

        public static final TermOrder NegativeReverseLexicographic
        TermOrder name NegativeReverseLexicographic of Math like CAS.
      • NegativeDegreeReverseLexicographic

        public static final TermOrder NegativeDegreeReverseLexicographic
        TermOrder name NegativeDegreeReverseLexicographic of Math like CAS.
      • lex

        public static final TermOrder lex
        TermOrder name lex of Sage.
      • degrevlex

        public static final TermOrder degrevlex
        TermOrder name degrevlex of Sage.
      • deglex

        public static final TermOrder deglex
        TermOrder name deglex of Sage.
      • invlex

        public static final TermOrder invlex
        TermOrder name invlex of Sage.
      • neglex

        public static final TermOrder neglex
        TermOrder name neglex of Sage.
      • negdegrevlex

        public static final TermOrder negdegrevlex
        TermOrder name negdegrevlex of Sage.
      • negdeglex

        public static final TermOrder negdeglex
        TermOrder name negdeglex of Sage.
      • negrevlex

        public static final TermOrder negrevlex
        TermOrder name negrevlex of Sage.
      • lp

        public static final TermOrder lp
        TermOrder name lp of Singular.
      • dp

        public static final TermOrder dp
        TermOrder name dp of Singular.
      • Dp

        public static final TermOrder Dp
        TermOrder name Dp of Singular.
      • rp

        public static final TermOrder rp
        TermOrder name rp of Singular.
      • ls

        public static final TermOrder ls
        TermOrder name ls of Singular.
      • ds

        public static final TermOrder ds
        TermOrder name ds of Singular.
      • Ds

        public static final TermOrder Ds
        TermOrder name Ds of Singular.
    • Constructor Detail

      • TermOrderByName

        public TermOrderByName()
    • Method Detail

      • blockOrder

        public static final TermOrder blockOrder​(TermOrder t1,
                                                 int s)
        Construct elimination block TermOrder. Variables {x1, ..., x s-1} < {xs, ..., xr}
        Parameters:
        t1 - term order for both blocks
        s - split index
        Returns:
        constructed term order
      • blockOrder

        public static final TermOrder blockOrder​(TermOrder t1,
                                                 ExpVector e,
                                                 int s)
        Construct elimination block TermOrder. Variables {x1, ..., x s-1} < {xs, ..., xr}
        Parameters:
        t1 - term order for both blocks
        e - exponent vector of desired length, r = length(e)
        s - split index
        Returns:
        constructed term order
      • blockOrder

        public static final TermOrder blockOrder​(TermOrder t1,
                                                 TermOrder t2,
                                                 int s)
        Construct elimination block TermOrder. Variables {x1, ..., x s-1} < {xs, ..., xr}
        Parameters:
        t1 - term order for lower valiables
        t2 - term order for higher variables
        s - split index
        Returns:
        constructed term order
      • blockOrder

        public static final TermOrder blockOrder​(TermOrder t1,
                                                 TermOrder t2,
                                                 ExpVector e,
                                                 int s)
        Construct elimination block TermOrder. Variables {x1, ..., x s-1} < {xs, ..., xr}
        Parameters:
        t1 - term order for lower valiables
        t2 - term order for higher variables
        e - exponent vector of desired length, r = length(e)
        s - split index
        Returns:
        constructed term order
      • weightOrder

        public static final TermOrder weightOrder​(long[] v)
        Construct weight TermOrder.
        Parameters:
        v - weight vector
        Returns:
        constructed term order
      • weightOrder

        public static final TermOrder weightOrder​(long[][] w)
        Construct weight TermOrder.
        Parameters:
        w - weight matrix
        Returns:
        constructed term order
      • weightOrder

        public static final TermOrder weightOrder​(java.util.List<java.util.List<java.lang.Long>> wa)
        Construct weight TermOrder.
        Parameters:
        wa - weight matrix as List
        Returns:
        constructed term order
      • weightForOrder

        public static final long[][] weightForOrder​(TermOrder to,
                                                    int n)
        Construct weight for term order.
        Parameters:
        to - term order
        n - exponent vector size
        Returns:
        weight matrix
      • weightForOrder

        static final long[][] weightForOrder​(int to,
                                             int n)
        Construct weight for term order.
        Parameters:
        to - term order indicator
        n - exponent vector size
        Returns:
        weight matrix
      • weightForSplitOrder

        static final long[][] weightForSplitOrder​(int to,
                                                  int to2,
                                                  int n,
                                                  int s)
        Construct weight for split term order.
        Parameters:
        to - first term order indicator
        to2 - second term order indicator
        n - exponent vector size
        s - slpit index
        Returns:
        weight matrix