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D.12.4.14 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
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