solve group - Maple Help
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DEtools

  

solve_group

  

represent a Lie Algebra of symmetry generators in terms of derived algebras

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

solve_group(G, y(x))

Parameters

G

-

list of symmetry generators

y(x)

-

dependent and independent variables

Description

• 

solve_group receives a list G of infinitesimals corresponding to symmetry generators that generate a finite dimensional Lie Algebra G, and returns a representation of the derived algebras of G.

• 

Derived algebras  of G are defined recursively as follows:

  

 is G;

  

 is the Lie Algebra obtained by taking all possible commutators of ;

  

in general,  is the Lie Algebra obtained by taking all possible commutators of .

• 

Since G is assumed to be finite, there exists a positive integer  with the following properties:

  

(i)  =

  

(ii)  is the smallest integer possessing property (i).

• 

solve_group returns a list  of  lists of symmetries with the following properties:

  

The symmetries inside the list  form the basis for

  

The symmetries inside the lists  and  together form the basis for .

  

In general, the symmetries inside the first  lists of  together form the basis for .

  

In other words, map(op, L[1..n+1-i]) is a basis for .

  

The group G is solvable if  is the zero group. If G is solvable then the first element of the returned list  will be the empty list [].

• 

This function is part of the DEtools package, and so it can be used in the form solve_group(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[solve_group](..).

Examples

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See Also

canoni

DEtools

DEtools/reduce_order

dsolve,Lie

equinv

eta_k

PDEtools

symgen

Xcommutator

 


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