| #### D.4.10.3 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.

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