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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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