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D.2.3.14 sort
Procedure from library general.lib (see general_lib).
- Usage:
- sort(id[,v,o,n]); id = ideal/module/intvec/list
sort may be called with 1, 2 or 3 arguments in the following way:
sort(id[,v,n]); v=intvec of positive integers, n=integer,
sort(id[,o,n]); o=string (any allowed ordstr of a ring), n=integer
- Return:
- a list l of two elements:
| l[1]: object of same type as input but sorted in the following way:
- if id=ideal/module: generators of id are sorted w.r.t. intvec v
(id[v[1]] becomes 1-st, id[v[2]] 2-nd element, etc.). If no v is
present, id is sorted w.r.t. ordering o (if o is given) or w.r.t.
actual monomial ordering (if no o is given):
NOTE: generators with SMALLER(!) leading term come FIRST
(e.g. sort(id); sorts backwards to actual monomial ordering)
- if id=list or intvec: sorted w.r.t. < (indep. of other arguments)
- if n!=0 the ordering is inverse, i.e. w.r.t. v(size(v)..1)
default: n=0
l[2]: intvec, describing the permutation of the input (hence l[2]=v
if v is given (with positive integers))
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- Note:
- If v is given id may be any simply indexed object (e.g. any list or
string); if v[i]<0 and i<=size(id) v[i] is set internally to i;
entries of v must be pairwise distinct to get a permutation id.
Zero generators of ideal/module are deleted
If 'o' is given, the input is sorted by considering leading terms
w.r.t. the new ring ordering given by 'o'
Example:
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