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D.15.15.2 rwalk
Procedure from library rwalk.lib (see rwalk_lib).
- Syntax:
- rwalk(ideal i, int radius);
if size(#)>0 then rwalk(ideal i, int radius, intvec v, intvec w);
intermediate Groebner bases are not reduced if reduction = 0
- Type:
- ideal
- Purpose:
- compute the standard basis of the ideal, calculated via
the Random walk algorithm from the ordering
"(a(v),lp)", "dp", "Dp" or "M"
to the ordering "(a(w),lp)", "(a(1,0,...,0),lp)" or "M".
Example:
| | LIB "rwalk.lib";
// compute a Groebner basis of I w.r.t. lp.
ring r = 32003,(z,y,x), lp;
ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z;
int radius = 1;
int perturb_deg = 2;
rwalk(I,radius,perturb_deg);
==> _[1]=y9-y7x2-y7x-y6x3-y6x2-3y6-3y5x-y3x7-3y3x6-3y3x5-y3x4-9y2x5-18y2x4-9y\
2x3-27yx3-27yx2-27x
==> _[2]=zx+8297y8x2+8297y8x+3556y7-8297y6x4+15409y6x3-8297y6x2-8297y5x5+1540\
9y5x4-8297y5x3+3556y5x2+3556y5x+3556y4x3+3556y4x2-10668y4-10668y3x-8297y2\
x9-1185y2x8+14224y2x7-1185y2x6-8297y2x5-14223yx7-10666yx6-10666yx5-14223y\
x4+x5+2x4+x3
==> _[3]=zy2+yx2+yx+3
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See also:
awalk1;
awalk2;
fwalk;
groebner;
gwalk;
pwalk;
std;
stdfglm;
twalk.
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