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- #Copyright (c) 2008, Riccardo De Maria
- #All rights reserved.
- from .polmap import *
- from .pol import *
- def Jmat(vars):
- """ Simplectic matrix or order 2 n
- >>> from lie import *
- >>> print Jmat('x px y py z pz'.split())
- pz=- 1.0*z
- px=- 1.0*x
- py=- 1.0*y
- y=py
- x=px
- z=pz
- """
- d=polmap()
- vars=list(vars)
- while vars:
- q,p=vars.pop(0),vars.pop(0)
- d[q]=pol(p)
- d[p]=-pol(q)
- return d
- def parder(p,vars):
- """ Return derivative of the pol p given a vector of var
- >>> from lie import *
- >>> f=pol('l*(p**2+q**2)/2.')
- >>> print parder(f,'qp')
- q=q*l
- p=p*l
- """
- d=polmap()
- for i in vars:
- d[i]=p.der(i)
- return d
- def lieop(f,vars):
- """ Return the lie operator for f
- >>> from lie import *
- >>> f=pol('l*(p**2+q**2)/2.')
- >>> Lf=lieop(f,'qp')
- >>> print Lf
- q=p*l
- p=- 1.0*q*l
- >>> print Jmat('qp')*parder(f,'qp')
- q=p*l
- p=- 1.0*q*l
- >>> print Lf*polmap(q='q',p=0)
- q=0
- p=- 1.0*q*l
- >>> print Lf*polmap(p='p',q=0)
- q=p*l
- p=0
- """
- d=polmap()
- vars=list(vars)
- while vars:
- q,p=vars.pop(0),vars.pop(0)
- d[q]=f.der(p)
- d[p]=-f.der(q)
- return d
- def pbracket(f,g,vars):
- out=0
- vars=list(vars)
- while vars:
- q,p=vars.pop(0),vars.pop(0)
- out+=f.der(q)*g.der(p) - f.der(p)*g.der(q)
- return out
- def pmbracket(f,g,vars):
- out=polmap()
- for i in g:
- out[i]=pbracket(f,g[i],vars)
- return out
- def idmap(vars):
- vars=list(vars)
- g=polmap()
- for i in vars:
- g[i]=pol(i)
- return g
- def liexp(f,vars):
- vars=list(vars)
- g=idmap(vars)
- out=polmap(g)
- out+=pmbracket(f,g,vars)
- out+=pmbracket(f,pmbracket(f,g,vars),vars)
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