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D.15.18.3 frandwalk
Procedure from library rwalk.lib (see rwalk_lib).
- Syntax:
- frwalk(ideal i, int radius);
frwalk(ideal i, int radius, intvec v, intvec w);
- Type:
- ideal
- Purpose:
- compute the standard basis of the ideal w.r.t. the
lexicographical ordering or a weighted-lex ordering,
calculated via the Random Fractal walk algorithm.
Example:
| | LIB "rwalk.lib";
ring r = 0,(z,y,x), lp;
ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
int reduction = 0;
frandwalk(I,2);
==> _[1]=y9-y7x2-y7x-y6x3-y6x2-3y6-3y5x-y3x7-3y3x6-3y3x5-y3x4-9y2x5-18y2x4-9y\
2x3-27yx3-27yx2-27x
==> _[2]=zx-2/27y8x2-2/27y8x+1/9y7+2/27y6x4+4/27y6x3+2/27y6x2+2/27y5x5+4/27y5\
x4+2/27y5x3+1/9y5x2+1/9y5x+1/9y4x3+1/9y4x2-1/3y4-1/3y3x+2/27y2x9+8/27y2x8\
+4/9y2x7+8/27y2x6+2/27y2x5+5/9yx7+5/3yx6+5/3yx5+5/9yx4+x5+2x4+x3
==> _[3]=zy2+yx2+yx+3
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See also:
awalk1;
awalk2;
groebner;
gwalk;
pwalk;
std;
stdfglm;
twalk.
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