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D.4.7.6 gwalk
Procedure from library grwalk.lib (see grwalk_lib).
- Syntax:
- gwalk(ideal i);
gwalk(ideal i, intvec v, intvec w);
- Type:
- ideal
- Purpose:
- compute the standard basis of the ideal, calculated via
the improved Groebner walk algorithm from the ordering
"(a(v),lp)", "dp" or "Dp"
to the ordering "(a(w),lp)" or "(a(1,0,...,0),lp)".
Example:
| | LIB "grwalk.lib";
//** compute a Groebner basis of I w.r.t. lp.
ring r = 32003,(z,y,x), lp;
ideal I = zy2+yx2+yx+3,
z3x+y3+zyx-yx2-yx-3,
z2yx3-y5+z2yx2+y3x2+y2x3+y3x+y2x2+3z2x+3y2+3yx,
zyx5+y6-y4x2-y3x3+2zyx4-y4x-y3x2+zyx3-3z2yx+3zx3-3y3-3y2x+3zx2,
yx7-y7+y5x2+y4x3+3yx6+y5x+y4x2+3yx5-6zyx3+yx4+3x5+3y4+3y3x-6zyx2+6x4+3x3-9zx;
gwalk(I);
==> _[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;
pwalk;
std;
stdfglm;
twalk.
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