| #### D.7.2.2 derivate Procedure from library `ainvar.lib` (see ainvar_lib). Usage: derivate(m,id); m matrix, id poly/vector/ideal Assume: m is an nx1 matrix, where n = number of variables of the basering Return: poly/vector/ideal (same type as input), result of applying the vector field by the matrix m componentwise to id; Note: the vector field is m[1,1]*d/dx(1) +...+ m[1,n]*d/dx(n) Example:
    LIB "ainvar.lib";
    ring q=0,(x,y,z,u,v,w),dp;
    poly f=2xz-y2;
    matrix m[6][1] =x,y,0,u,v;
    derivate(m,f);
    ==> -2y2+2xz
    vector v = [2xz-y2,u6-3];
    derivate(m,v);
    ==> 6u6*gen(2)-2y2*gen(1)+2xz*gen(1)
    derivate(m,ideal(2xz-y2,u6-3));
    ==> _[1]=-2y2+2xz
    ==> _[2]=6u6

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