Inverse of an action
In this section, we illustrate the functionality of the kernel functions on the Lie Group R. We quote from S. Lie 1930:
"Eine bekannte Gruppe dieser Art ist die folgende:
welche drei Parameter ,
,
enthält. Führt man die beiden Transformationen
nacheinander aus, so erhält man:
wo ,
,
als Functionen von den a und b durch die Relationen..."
So far from S. Lie. We tranform the above expression to match for proper coefficients
.
The coefficients are easily read of the last fraction. However, the command GInv solves these kind of inverse problems. However, the coordinates have to be named {
,...,
} and {
,...,
} and input to GInv is the expression for {
,...,
}◦{
,...,
}.
The output of GInv is a function, which maps {,...,
} to the inverse element
coordinates. If debug mode is on, GInv also states the necessary conditions, on which subset the formula is valid.
Created by Mathematica (September 30, 2006) | ![]() |