D.6.2.3 actionIsProper

Procedure from library ainvar.lib (see ainvar_lib).

Usage:

actionIsProper(m); m matrix

Assume:

m is a nx1 matrix, where n = number of variables of the basering

Return:

int = 1, if the action defined by m is proper, 0 if not

Note:

m defines a group action which is the exponential of the vector field m[1,1]*d/dx(1) +...+ m[1,n]*d/dx(n)

Example:

LIB "ainvar.lib";
ring rf=0,x(1..7),dp;
matrix m[7][1];
m[4,1]=x(1)^3;
m[5,1]=x(2)^3;
m[6,1]=x(3)^3;
m[7,1]=(x(1)*x(2)*x(3))^2;
actionIsProper(m);
→ 0
ring rd=0,x(1..5),dp;
matrix m[5][1];
m[3,1]=x(1);
m[4,1]=x(2);
m[5,1]=1+x(1)*x(4)^2;
actionIsProper(m);
→ 1