dilog(x)

[Grégory Vanuxem]

Hello,

First there is a small typo in FSFUN:

dilog: dilog(z) is the dilogaritm;
A missing 'h'.

But I do not understand what this function computes in FriCAS, usually
it is a special case of polylogarithm of order 2.

In SAGE via https://sagecell.sagemath.org/
dilog(0.7) => 0.889377624286039

WolframAlpha also (https://www.wolframalpha.com/input?i=dilog%5B0.7%5D)

From https://en.wikipedia.org/wiki/Polylogarithm, there is a
disambiguation note with lix) (logarithmic integral) and it seems the
code use it, but I still don't understand this result in FriCAS:

(3) -> dilog(0.7)

(3) 0.3261295100_7547606953_084133
Type: Complex(Float)

- Greg

[Waldek Hebisch]

On Fri, May 31, 2024 at 06:52:11PM +0200, Grégory Vanuxem wrote:
> Hello,
>
> First there is a small typo in FSFUN:
>
> dilog: dilog(z) is the dilogaritm;
> A missing 'h'.
>
> But I do not understand what this function computes in FriCAS, usually
> it is a special case of polylogarithm of order 2.

We have definition in LiouvillianFunctionCategory:

dilog : % -> %
++ dilog(x) returns the dilogarithm of x, i.e.
++ the integral of \spad{log(x) / (1 - x) dx}.

It is releated to 'polylog(2, x)':

(13) -> polylog(2, x)

(13) dilog(- x + 1)
Type: Expression(Integer)

>
> In SAGE via https://sagecell.sagemath.org/
> dilog(0.7) => 0.889377624286039

(14) -> dilog(0.3)

(14) 0.8893776242_8603873859_98408
Type: Complex(Float)

> WolframAlpha also (https://www.wolframalpha.com/input?i=dilog%5B0.7%5D)

OK. We inherited this definition from original Axiom sources.
And I did literature research and our definition agrees with
what I found in research papers about dilogarithm and
polylogaritms.

It is tempting to change definition, but given usage in math
litarature and our previous use I kept what we had.

> >From https://en.wikipedia.org/wiki/Polylogarithm, there is a
> disambiguation note with lix) (logarithmic integral)

'li(x)' is logarithmic integral, quite a different thing than
dilogarithm. Some folks use 'Li' as name of polylogarthim,
that could be confusing.

> and it seems the
> code use it, but I still don't understand this result in FriCAS:
>
> (3) -> dilog(0.7)
>
> (3) 0.3261295100_7547606953_084133
> Type: Complex(Float)
>
> - Greg
>

> --
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--
Waldek Hebisch

[Grégory Vanuxem]

Le ven. 31 mai 2024 à 20:25, Waldek Hebisch <de...@fricas.org> a écrit :
>
> On Fri, May 31, 2024 at 06:52:11PM +0200, Grégory Vanuxem wrote:
> > Hello,
> >
> > First there is a small typo in FSFUN:
> >
> > dilog: dilog(z) is the dilogaritm;
> > A missing 'h'.
> >
> > But I do not understand what this function computes in FriCAS, usually
> > it is a special case of polylogarithm of order 2.
>
> We have definition in LiouvillianFunctionCategory:
>
> dilog : % -> %
> ++ dilog(x) returns the dilogarithm of x, i.e.
> ++ the integral of \spad{log(x) / (1 - x) dx}.
>
> It is releated to 'polylog(2, x)':
>
> (13) -> polylog(2, x)
>
> (13) dilog(- x + 1)
> Type: Expression(Integer)
>
> >
> > In SAGE via https://sagecell.sagemath.org/
> > dilog(0.7) => 0.889377624286039
>
> (14) -> dilog(0.3)
>
> (14) 0.8893776242_8603873859_98408
> Type: Complex(Float)

Exactly what I found too after, trying to reproduce an issue with the
triple patch from Qian with official FriCAS.

> > WolframAlpha also (https://www.wolframalpha.com/input?i=dilog%5B0.7%5D)
>
> OK. We inherited this definition from original Axiom sources.
> And I did literature research and our definition agrees with
> what I found in research papers about dilogarithm and
> polylogaritms.
>
> It is tempting to change definition, but given usage in math
> litarature and our previous use I kept what we had.

My source was Internet here, I can understand your point of view.
I will look at the Expressin domain to khow it is handled so.

> > >From https://en.wikipedia.org/wiki/Polylogarithm, there is a
> > disambiguation note with lix) (logarithmic integral)
>
> 'li(x)' is logarithmic integral, quite a different thing than
> dilogarithm. Some folks use 'Li' as name of polylogarthim,
> that could be confusing.
>
> > and it seems the
> > code use it, but I still don't understand this result in FriCAS:
> >
> > (3) -> dilog(0.7)
> >
> > (3) 0.3261295100_7547606953_084133
> > Type: Complex(Float)
> >
> > - Greg
> >
> > --
> > You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group.
> > To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel...@googlegroups.com.
> > To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/CAHnU2dYjsQt6%3DEq4Gva7FkfS6Y1e8-VDSV7YEqymeONB8zPqOQ%40mail.gmail.com.
>
> --
> Waldek Hebisch
>
> --
> You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group.
> To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel...@googlegroups.com.

> To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/ZloWMwzCmoPxItaT%40fricas.org.