is handling of Inf/Infinity/infinity affected by the 1st call to symbolics?

[Dima Pasechnik]

Here is an ugly bug I just ran in at https://trac.sagemath.org/ticket/18920#comment:98

it looks as if setting a symbolic taylor expansion like

sage: g(x)=taylor(log(x),x,1,6); g # log can be replaced by sin with the same end result

---a call that takes a lot of time, probably because some big stuff is initialised behind the scenes---

breaks handling of infinities (by updated Maxima, I guess): namely, I get a SIGFPE on

sage: plot(log(x),(x,0,2))

Does this look possible, and where would one look for the cause of this?

 

[Ralf Stephan]

As you already noticed that the bug depends on the ECL/Maxima

version, let me just add that there is no need for taylor() (Maxima)

if you use series() (Pynac) which is way faster. Also there is

https://trac.sagemath.org/ticket/6119

Regards,

[Dima Pasechnik]

well, taylor() was there as it came from the doctest showing the problem with ECL 16.1.3.

Anything that triggers loading ECL/Maxima library interface readies  the bug to go off, anyway.

Then something like 

     plot(log(x),(x,0.0,2.0))

does trigger the crash itself. And it appears that the latter does not use ECL/Maxima, right?

(invoking this plot() before calling taylor() does not lead to a problem).

[Dima Pasechnik]

It was triggered by old non-conforming feature of ECL 16.1.2; ECL 16.1.3 is more standard-conforming,

and so for our purposes we need to explicitly disable SIGFPE traps. Took a while to understand, sorry for noise.

[Peter Luschny]

Hi Ralf!

R> there is no need for taylor() (Maxima)

R> if you use series() (Pynac) which is way faster.

I cannot reproduce your claim, in the contrary.

Please consider this simple example:

def num(m, n, ser):

    z = var('z')

    w = exp(2 * pi * I / m)

    o = sum(exp(z * w^k) for k in range(m)) / m

    f = 1 / o

    if ser:

        t = f.series(z, n + 1)

    else:

        t = taylor(f, z, 0, n + 1)

    return factorial(n) * t.coefficient(z, n) 

ser = lambda m,n: sum(binomial(m*n,m*k)*num(m,m*k,true )*k/n for k in (1..n))

tay = lambda m,n: sum(binomial(m*n,m*k)*num(m,m*k,false)*k/n for k in (1..n))

---

import time

print time.clock()

print [[tay(m,n) for n in (1..6)] for m in (1..5)]

print time.clock()

print [[ser(m,n) for n in (1..6)] for m in (1..5)]

print time.clock()

In fact if I would not have killed the program I think 

the series version would still run. 

If I have misunderstood, please do enlighten me. 

Peter

[Ralf Stephan]

On Wednesday, January 18, 2017 at 3:22:20 PM UTC+1, Peter Luschny wrote:

I cannot reproduce your claim, in the contrary.

You are quite right. Your example is not accelerated by the recent

improvements. So I should have said way faster in many cases.

Regards,

[Ralf Stephan]

Actually the example makes it necessary to completely abandon

the original GiNaC series code and use Maxima as fallback in the

cases that cannot be handled by the fast rational Pynac series code.

Thanks!

[Ralf Stephan]

This is now

https://trac.sagemath.org/ticket/22201 

[Peter Luschny]

R> Actually the example makes it necessary to completely abandon

R> the original GiNaC series code and use Maxima as fallback in the

R> cases that cannot be handled by the fast rational Pynac series code.

Unfortunately this will not help much. Maxima/taylor is also

unable to compute these functions even for modest values of m

efficiently as you can see from the next example:

def P(m, n):

    x, z = var('x, z')

    if m == 1: return Integer(1) 

    w = exp(2 * pi * I / m)

    o = sum(exp(z * w^k) for k in range(m)) / m

    f = exp(z*x) * (exp(z) / o - 1)

    t = f.taylor(z, 0, n+1)

    return factorial(n) * t.coefficient(z, n) 

for m in [1,2,3,4,5,6,7,11,13]:

    print [m], [P(m, n).subs(x=0) for n in (0..10)]

AFAIK there is only one CAS which can handle these things 

(which are basic!) efficiently: Mathematica. So if I would

put something on trac it would be an enhancement request:

"Implement the Mittag-Leffler function!".

Peter

[Peter Luschny]

This is now

https://trac.sagemath.org/ticket/22201 

Thanks!

P.S. Do you know that there are functions which work correctly

but advertise to use instead functions which are buggy?

Hint: 22069