#### D.4.32.4 modJanet

Procedure from library `rstandard.lib` (see rstandard_lib).

Usage:
  modJanet(I,i); I is an ideal, i an integer (optional).

Return:
  ideal, a Janet basis for I using modular methods.

Purpose:
  Computes a Janet basis for the ideal given by the generators in I using modular techniques.
  If second argument is 0 then the result is not verified.

Example:

    LIB "rstandard.lib";
    ring R=0,(t,x,y,z),ds;
    ideal i=
    5t3x2z+2t2y3x5,
    7y+4x2y+y2x+2zt,
    3tz+3yz2+2yz4;
    ideal j=modJanet(i);  j;
    ==> Length of Janet basis: 3
    ==> Length of Janet basis: 3
    ==> Length of Janet basis: 3
    ==> Length of Janet basis: 3
    ==> Length of Janet basis: 3
    ==> Length of Janet basis: 3
    ==> Length of Janet basis: 3
    ==> Length of Janet basis: 3
    ==> Length of Janet basis: 3
    ==> Length of Janet basis: 3
    ==> Length of Janet basis: 3
    ==> Length of Janet basis: 3
    ==> Length of Janet basis: 3
    ==> j[1]=y
    ==> j[2]=tz
    ==> j[3]=ty
    ring S=0,(x,y,z),dp;
    poly p1 =x2y*(47x5y7z3+28xy5z8+63+91x5y3z7);
    poly p2 =xyz*(57y6+21x2yz9+51y2z2+15x2z4);
    poly p3 =xy4z*(74y+32x6z7+53x5y2z+17x2y3z);
    poly p4 =y3z*(21x2z6+32x10y6z5+23x5y5z7+27y2);
    poly p5 =xz*(36y2z2+81x9y10+19x2y5z4+79x4z6);
    ideal i =p1,p2,p3,p4,p5;
    ideal j=modJanet(i,0);  j;
    ==> Length of Janet basis: 9
    ==> Length of Janet basis: 9
    ==> Length of Janet basis: 9
    ==> Length of Janet basis: 9
    ==> Length of Janet basis: 9
    ==> Length of Janet basis: 9
    ==> Length of Janet basis: 9
    ==> Length of Janet basis: 9
    ==> Length of Janet basis: 9
    ==> Length of Janet basis: 9
    ==> Length of Janet basis: 9
    ==> Length of Janet basis: 9
    ==> Length of Janet basis: 9
    ==> j[1]=x2y
    ==> j[2]=x3y
    ==> j[3]=x4y
    ==> j[4]=y5z
    ==> j[5]=x5y
    ==> j[6]=xy3z3
    ==> j[7]=xy5z
    ==> j[8]=xy4z3
    ==> j[9]=x5z7+36/79xy2z3

See also: rJanet.

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