Home Online Manual
Top
Back: localInvar
Forward: sortier
FastBack: finvar_lib
FastForward: rinvar_lib
Up: ainvar_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

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