>
> Maybe the following session might help you. Maybe it's still not what
> you want, since you are left with mysum expressions that you have to
> interpret yourself (by adding even more rules to the system).
>
Ok, thanks. That solves the problem.
One more question.
How do I change GENSYM-generated variable name to something human-readable?
Eval doesn't work:
(1) -> test_eqn := exp( symbol( GENSYM()$Lisp ) * x )
G59678 x
(1) %e
Type: Expression(Integer)
(2) -> test_eqn
G59678 x
(2) %e
Type: Expression(Integer)
(3) -> eval( test_eqn, [ G59678 = N ] )
G59678 x
(3) %e
Type: Expression(Integer)
(4) -> eval( test_eqn, [ x = N ] )
G59678 N
(4) %e
Type: Expression(Integer)
среда, 23 апреля 2014 г., 19:37:03 UTC+4 пользователь Ralf Hemmecke написал:
>
> > If I simply define and use a rule
> >
> > exp_to_bessel_rule := rule exp( sqrt(-1) * z * sin(t) ) == besselJ( N,
> z
> > ) * exp( sqrt( -1 ) * N * t )
> > exp_to_bessel_rule( test_eqn )
> >
> > then I'll get expression with 2 identical summation indices ( 'N' in
> this
> > case ), which is clearly not something I want.
>
> Right. That's clear. The problem is that your besselJ(N, ...) is only a
> workaround to some other problem.
>
> You want sum_{N=-\infty}^\infty foo(N) as a result. N is bound.
>
> As Waldek said, you have to invent your own operator for the infinite sum.
>
> I experimented with
>
> mysum := operator 'mysum
> mysum(minusInf, plusInf, N +-> besselJ(N, a) * exp( %i * N * t ))
>
> to represent your sum. Unfortunately +-> cannot be used in that place.
>
> Maybe the following session might help you. Maybe it's still not what
> you want, since you are left with mysum expressions that you have to
> interpret yourself (by adding even more rules to the system).
>
> Anyway, I think what is below is in the spirit of what Waldek suggested.
>
> Ralf
>
>
> (1) -> )clear completely
> All user variables and function definitions have been cleared.
> All )browse facility databases have been cleared.
> Internally cached functions and constructors have been cleared.
> )clear completely is finished.
> (1) -> mysum := operator 'mysum
>
> (1) mysum
> Type:
> BasicOperator
> (2) -> mi -- represents minusInfinity
>
> (2) mi
> Type:
> Variable(mi)
> (3) -> pi -- represents plusInfinity
>
> (3) pi
> Type:
> Variable(pi)
> (5) -> B(N, l, h, a, t) == mysum(l, h, N, besselJ(N, a) * exp(sqrt(-1) *
> N * t ))
> Compiled code for bess has been cleared.
> Type:
> Void
> (6) -> bess(a,t) == (N:Symbol:=symbol GENSYM()$Lisp;B(N,mi,pi,a,t))
> 1 old definition(s) deleted for function or rule bess
> Type:
> Void
> (7) -> bess(a,t)
> Compiling function B with type (Symbol,Variable(mi),Variable(pi),
> Variable(a),Variable(t)) -> Expression(Integer)
> Compiling function bess with type (Variable(a),Variable(t)) ->
> Expression(Integer)
>
> +---+
> G658 t\|- 1
> (7) mysum(mi,pi,G658,%e besselJ(G658,a))
> Type:
> Expression(Integer)
> (8) -> bess(a,t)
>
> +---+
> G659 t\|- 1
> (8) mysum(mi,pi,G659,%e besselJ(G659,a))
> Type:
> Expression(Integer)
> (9) -> test_eqn := exp(sqrt(-1)*a*sin(omg*t))*exp(sqrt(-1)*b*sin(2*omg*t))
>
> +---+ +---+
> a\|- 1 sin(omg t) b\|- 1 sin(2omg t)
> (9) %e %e
> Type:
> Expression(Integer)
> (10) -> exp_to_bessel_rule := rule exp(sqrt(-1)*z*sin(t)) == bess(z,t)
>
> +---+
> z\|- 1 sin(t)
> (10) %e == 'bess(z,t)
> Type:
> RewriteRule(Integer,Integer,Expression(Integer))
> (11) -> exp_to_bessel_rule( test_eqn )
> Compiling function B with type (Symbol,Variable(mi),Variable(pi),
> Variable(b),Polynomial(Integer)) -> Expression(Integer)
> Compiling function bess with type (Variable(b),Polynomial(Integer))
> -> Expression(Integer)
> Compiling function B with type (Symbol,Variable(mi),Variable(pi),
> Variable(a),Polynomial(Integer)) -> Expression(Integer)
> Compiling function bess with type (Variable(a),Polynomial(Integer))
> -> Expression(Integer)
>
> (11)
> +---+
> 2G688 omg t\|- 1
> mysum(mi,pi,G688,%e besselJ(G688,b))
> *
> +---+
> G691 omg t\|- 1
> mysum(mi,pi,G691,%e besselJ(G691,a))
> Type:
> Expression(Integer)
>
>
>
--
You received this message because you are subscribed to the Google Groups
"FriCAS - computer algebra system" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/fricas-devel.
For more options, visit https://groups.google.com/d/optout.
