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Topic: Delta functions.
Replies: 14   Last Post: Apr 22, 2013 8:58 AM

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Waldek Hebisch

Posts: 263
Registered: 12/8/04
Re: Delta functions.
Posted: Apr 20, 2013 7:14 PM
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clicliclic@freenet.de wrote:
> clicliclic@freenet.de schrieb:

> >
> > As I usually succeed in consistently computing with Dirac delta's, I've
> > felt no need to look into research on this. And while I don't know if
> > such research exists, my gut feeling is that the delta's cannot be
> > tweaked to qualify as members of your "field". By the way, since FriCAS
> > is a strongly typed system, what type does it assign to delta(x) where x
> > is a (say) complex irrational number?
> >

> Oops, this was nonsense: for 'complex' read 'real'. The Dirac delta
> makes sense for real arguments only, albeit in as many dimensions as one
> likes: it lives in R^n only: The flexibility required of the test
> functions cannot be achieved on C.
> Martin.

ATM there is no delta finction in FriCAS. The place to add it
is 'Expression' domain. More precisly (since 'Expression'
need a parameter) domains like 'Expression(Integer)',
'Expression(Fraction(Integer))', 'Expression(AlgebraicNumber)'.

Note that analytically, delta at a complex number makes perfect
sense if you chose apropriate theory of distributions.
Similarly, in some theories of distributions you can
freely multiply them. This is one of the reasons I want
algebraic theory: such theory can be much more flexible
than usual analytic approach.

Also, in Maple 'Dirac(x)' does not mean delta at point 'x',
but inverse image of delat at 0 via 'x'. If 'x' is a one
variable in multivariate context you get Lebesqu'e measure
at appropriate hyperplane. Using this convention 'Dirac(3)'
is just 0.

Waldek Hebisch

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