Package edu.jas.poly

Class TermOrderByName

java.lang.Object
edu.jas.poly.TermOrderByName

public class TermOrderByName extends 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 Details

    • 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 Details

    • TermOrderByName

      public TermOrderByName()
  • Method Details

    • 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(List<List<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