It is difficult to know before the fact which library will returnthe
expected result. Consider :
```
sage: var("x, a, b")
(x, a,
b)
sage: dgamma(x, a, b)=x^(a-1)*(1-x)^(b-1)/beta(a, b)
sage: with assuming(a>0, b>0): dgamma(x, a, b).integrate(x,0,1)
1
This is quasi-immediate. And of course so is :
sage: with assuming(a>0, b>0): dgamma(x, a+1, b+1).integrate(x,0,1)
1
But
sage: with assuming(a>0, b>0): dgamma(x, a+1, b+1).integrate(x,0,1,
algorithm=”sympy”)
gamma(a + 1)*hypergeometric((-b, a + 1), (a + 2,), 1)/(beta(a + 1, b +
1)*gamma(a
+ 2))
This is slow ; furthermore, simplifying this expression to 1 isn't trivialin
`sage`, the best way being `sympy.simplify`... Worse :
sage: with assuming(a>0, b>0): dgamma(x, a, b).integrate(x,0,1,
algorithm=”sympy”)
```
*never* returns…
I wouldn’t (currently) switch *default-to-maxima* for *default-to-sympy*…
HTH,
Le vendredi 18 décembre 2020 à 08:55:52 UTC+1, Sébastien Labbé a écrit :
> There is still a lot of room for improvement. SymPy could be tried first
>> when integrating expressions containing an absolute value, for one. We
>> already _fall back_ to giac/sympy if maxima throws an error; but when it
>> simply returns garbage, the problem goes unnoticed.
>>
>
> Why do we use maxima first as opposed to giac/sympy? Is it because it is
> faster than giac/sympy? Is it because it returns answers that are correct
> but for which giac/sympy returns incorrect results?
>
> It seems to me that a library returning wrong answer as opposed to no
> answer should not be the default.
>
> Sébastien
>
>
>
>
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