Singular

D.4.7.3 awalk1

Procedure from library `grwalk.lib` (see grwalk_lib).

Syntax:
awalk1(ideal i);
awalk1(ideal i, int n);
awalk1(ideal i, int n, intvec v, intvec w);
awalk1(ideal i, intvec v, intvec w);

Type:
ideal

Purpose:
compute the standard basis of the ideal, calculated via the first alternative algorithm from an ordering
"(a(v),lp)", "dp" or "Dp" to the ordering
"(a(w),lp)" or "(a(1,0,...,0),lp)"
with a perturbation degree n for the weight vector w.

Example:
 ```LIB "grwalk.lib"; ring r = 32003,(z,y,x), lp; ideal I = y3+xyz+y2z+xz3, 3+xy+x2y+y2z; awalk1(I,3); ==> _[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 ```
See also: awalk2; fwalk; groebner; gwalk; pwalk; std; stdfglm; twalk.