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D.7.2.3 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
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