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.
    Author:
    Heinz Kredel

    • 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