Top
Back: standard
Forward: weierstr_lib
FastBack:
FastForward:
Up: teachstd_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.12.5.14 localstd

Procedure from library teachstd.lib (see teachstd_lib).

Usage:
localstd(id); id = ideal

Return:
A standard basis for a local degree ordering, using Lazard's method.

Note:
The procedure homogenizes id w.r.t. a new 1st variable local@t, computes a SB w.r.t. (dp(1),dp) and substitutes local@t by 1. Hence the result is a SB with respect to an ordering which sorts first w.r.t. the subdegree of the original variables and then refines it with dp. This is the local degree ordering ds.
localstd may be used in order to avoid cancellation of units and thus to be able to use option(contentSB) also for local orderings.

Example:
 
LIB "teachstd.lib";
ring R = 0,(x,y,z),ds;
ideal i  = xyz+z5,2x2+y3+z7,3z5+y5;
localstd(i);
==> _[1]=y5+3z5
==> _[2]=3x4y3z8-4x3y3z9+6x2y4z9+3y5z10
==> _[3]=3x4z13-4x3z14+6x2yz14+3y2z15
==> _[4]=3x4yz12-4x3yz13+6x2y2z13+3y3z14
==> _[5]=2x2z9+x2y2z8+y3z9
==> _[6]=2x2y4z5+y7z5-3x2yz9
==> _[7]=6y2z10-3x2y3z8+4xy3z9-3y4z9
==> _[8]=3x2y2z8+3y3z9+2xy4z8
==> _[9]=18z14-4xy6z8+3y7z8-9x2yz12
==> _[10]=xyz+z5
==> _[11]=3xz6-y4z5
==> _[12]=3y3z6+2xy4z5-3xyz9
==> _[13]=y4z5-2xz9-xy2z8
==> _[14]=3z10+2xyz9+xy3z8
==> _[15]=2x2z5+y3z5-xyz8
==> _[16]=y4z-2xz5+yz8
==> _[17]=3z6+2xyz5-y2z8
==> _[18]=2x2+y3+z7


Top Back: standard Forward: weierstr_lib FastBack: FastForward: Up: teachstd_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4-0-3, 2016, generated by texi2html.