D.6.2.2 derivate

Procedure from library ainvar.lib (see ainvar_lib).

Usage:

derivate(m,id); m matrix, id poly/vector/ideal

Assume:

m is a 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