D.6.2.7 furtherInvar

Procedure from library ainvar.lib (see ainvar_lib).

Usage:

furtherInvar(m,id,karl,q); m matrix, id,karl ideals, q poly, n int

Assume:

karl,id,q are invariant under the vector field m,
moreover, q must be a variable

Return:

list of two ideals, the first ideal contains further invariants of the vector field

m = sum m[i,1]*d/dx(i) with respect to id,p,q,

i.e. we compute elements in the (invariant) subring generated by id which are divisible by q and divide them by q as much as possible the second ideal contains all invariants given before if n=1, a different algorithm is chosen which is sometimes faster (default: n=0)

Example:

LIB "ainvar.lib";
ring r=0,(x,y,z,u),dp;
matrix m[4][1];
m[2,1]=x;
m[3,1]=y;
m[4,1]=z;
ideal id=localInvar(m,z,y,x),localInvar(m,u,y,x);
ideal karl=id,x;
list in=furtherInvar(m,id,karl,x);
in;
→ [1]:
→    _[1]=y2z2-8/3xz3-2y3u+6xyzu-3x2u2
→ [2]:
→    _[1]=-1/2y2+xz
→    _[2]=1/3y3-xyz+x2u
→    _[3]=x