NZMATH  1.2.0
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nzmath.poly.termorder Namespace Reference


class  MultivarTermOrder
class  TermOrderInterface
class  UnivarTermOrder


def weight_order (weight, tie_breaker=None)
def _total_degree_lexicographic (left, right)
def _total_degree_reverse_lexicographic (left, right)
def _sort_with_cmp (seq, mycmp)
 for compatibility function More...


string _INTERFACE_MSG = "%s is interface"
 ascending_order = UnivarTermOrder(cmp)
 lexicographic_order = MultivarTermOrder(cmp)
 total_degree_lexicographic_order = MultivarTermOrder(_total_degree_lexicographic)
 total_degree_reverse_lexicographic_order = MultivarTermOrder(_total_degree_reverse_lexicographic)

Detailed Description

Term Order for polynomials.

Function Documentation

◆ _sort_with_cmp()

def nzmath.poly.termorder._sort_with_cmp (   seq,

for compatibility function

Return the sorted seq by using the comparator function mycmp.

Definition at line 389 of file

Referenced by nzmath.poly.termorder.UnivarTermOrder.format(), and nzmath.poly.termorder.MultivarTermOrder.format().

◆ _total_degree_lexicographic()

def nzmath.poly.termorder._total_degree_lexicographic (   left,
Total degree lexicographic (or graded lexicographic) term order :
  L < R iff
  (1) sum(li) < sum(ri) or
  (2) sum(li) = sum(ri) and
      there exists i s.t. l0 == r0, ..., l(i-1) == r(i-1), li < ri.

Definition at line 355 of file

References nzmath.compatibility.cmp.

◆ _total_degree_reverse_lexicographic()

def nzmath.poly.termorder._total_degree_reverse_lexicographic (   left,
Total degree reverse lexicographic (or graded reverse
lexicographic) term order :
  L < R iff
  (1) sum(li) < sum(ri) or
  (2) sum(li) = sum(ri) and
      there exists i s.t. ln == rn, ..., l(i+1) == r(i+1), li > ri.

Definition at line 368 of file

References nzmath.compatibility.cmp.

◆ weight_order()

def nzmath.poly.termorder.weight_order (   weight,
  tie_breaker = None 
Return a comparator of weight ordering.

The weight ordering is defined for arguments x and y that x < y
if w.x < w.y (dot products) or w.x == w.y and tie breaker tells
x < y.

The option 'tie_breaker' is another comparator that will be used
if dot products with the weight vector leaves arguments tie.  If
the option is None (default) and a tie breaker is indeed necessary
to order given arguments, a TypeError is raised.

Definition at line 331 of file

References nzmath.compatibility.cmp.

Variable Documentation


string nzmath.poly.termorder._INTERFACE_MSG = "%s is interface"

Definition at line 10 of file

◆ ascending_order

nzmath.poly.termorder.ascending_order = UnivarTermOrder(cmp)

Definition at line 231 of file

◆ lexicographic_order

nzmath.poly.termorder.lexicographic_order = MultivarTermOrder(cmp)

Definition at line 383 of file

◆ obj


Definition at line 399 of file

◆ total_degree_lexicographic_order

nzmath.poly.termorder.total_degree_lexicographic_order = MultivarTermOrder(_total_degree_lexicographic)

Definition at line 384 of file

◆ total_degree_reverse_lexicographic_order

nzmath.poly.termorder.total_degree_reverse_lexicographic_order = MultivarTermOrder(_total_degree_reverse_lexicographic)

Definition at line 385 of file