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D.7.2.7 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 often 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
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