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D.6.15.9 locstd
Procedure from library sing.lib (see sing_lib).
- Usage:
- locstd (id); id = ideal
- Return:
- a standard basis for a local degree ordering
- Note:
- the procedure homogenizes id w.r.t. a new 1st variable @t@, computes
a SB w.r.t. (dp(1),dp) and substitutes @t@ by 1.
Hence the result is a SB with respect to an ordering which sorts
first w.r.t. the order and then refines it with dp. This is a
local degree ordering.
This is done in order to avoid cancellation of units and thus
be able to use option(contentSB);
Example:
| | LIB "sing.lib";
ring R = 0,(x,y,z),ds;
ideal i = xyz+z5,2x2+y3+z7,3z5+y5;
locstd(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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