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Re: Delta functions.
Posted:
Apr 20, 2013 7:14 PM


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 hebisch@math.uni.wroc.pl



