Re: [Reduce-algebra-developers] Differentiation rule for new function

[abpetrov <abp...@uf...>]

I tried this rule with generalization
DerivNew := { df( asum( a(i), {{i, 1, 10}}), a(~i1)) => asum_trans(
asum( a(i), {{i, 1, 10}}, df, a(i1))) }$
let DerivNew$
df( asum( a(i), {{i, 1, 10}}), a(i1));

the result is 0 too.
Also I tried more general rule
DerivNew := { df (asum(~~f(~~y)), ~~x) => asum_trans( asum(f(y)), df, x) }$

with the same result.

I am not sure that operator df applied before that rule, in this case I
can not
extend differentiation table with new functions. Of course, it is
necessary to check this in sources.

About lower. I agree with you about the incompatibility, but I don't
like when variables can be
written without good style with lower- and uppercase letters. It is bad
to read that program in my opinion.
I think the difference in one operator it is not so bad.


26.08.2014 16:44, Rainer Schöpf пишет:
> On Mon, 25 Aug 2014 at 00:19 -0000, abpetrov wrote:
>
>  > You are right, If I will differentiate function. But I did some
>  > substitution with the help of the rule.
>  > I did not any real differentiation:
>  > 
>  > DerivNew := { df( asum( a(i), {{i, 1, 10}}), a(i1)) => asum_trans( asum( a(i), {{i, 1, 10}}), df, a(i1)) }$
>
> But you used the df operator. A substitution rule like the above is tried 
> _after_ the standard differentiation. Since the latter returns 0, the rule 
> doesn't apply.
>
> You could use your own operator in place of df, but then you need to define 
> all properties like linearity or the product rule.
>
> It's much simpler to modify your rule, as I suggested in my last mail message.
>
>  > About switch "lower". It is works with csl-version of Reduce, it is the
>  > same as input_case for psl-Reduce,
>
> If you are aware of the incompatibility, then everything is fine.
>
>   Regards,
>    Rainer
>