There certainly has been tension, over the years, between

using a small set of functions in results

with possibly complicated arguments

versus a larger set of functions with simpler arguments.

Maxima doesn't use division (too complicated?) for a/b

but uses a * (b^(-1)).

Incomplete Gamma Functions versus erf() is another example.

A more extreme example, the 1F1 Confluent Hypergeometric Functions

can be used instead of the exponential, since

Maxima knows this. Type hypergeometric([a],[a],z);

http://dlmf.nist.gov/13.1

I have no idea if using the hypergeometric() notation has advantages in, say

doing integrals. But it might.

Assuming (or hoping) the internal programs will attempt transformations

to make

the algorithms work better, we are left with considering transformations

to make the results easier for human to comprehend. Perhaps extending

the features already available via demovre and exponentialize, we could

have a general simplify(expression, favorites=[sin,cos]) versus

simplify(expression,favorites=[exp,log])

where the "favorites" list could include bessel_j, hypergeometric, ...

This kind of transformation recipe is provided in some of the competing

CAS. I don't know how effective they really are.

RJF

On 7/18/2017 11:00 PM, Robert Dodier wrote:

> On 2017-07-18, Raymond Toy <***@gmail.com> wrote:

>

>> Yeah, if we can fix deficiencies, we should. But Richard is also

>> right. One persons idiosyncracy is another's feature. And it's hard

>> to tell which is which.

> It was probably a mistake for me to use the word "idiosyncrasy." Recall

> that the point of departure was that Maxima simplifies (-a)^x to

> a^x*(-1)^x in the presence of assume(a > 0). It seems unlikely that

> anyone actually considers that desirable, and even if they did, it's

> still inconsistent with (-2)^x --> (-2)^x.

>

> Mostly what I want to promote is the idea that we can and should fix

> stuff, and we need not fear the weight of the past as we do so.

>

> Robert Dodier

>

>

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