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# Edit detail for #6 integration result Gamma not TeXed correctly revision 6 of 7

 1 2 3 4 5 6 7 Editor: kratt6 Time: 2007/12/24 02:42:36 GMT-8 Note:

added:

From kratt6 Mon Dec 24 02:42:36 -0800 2007
From: kratt6
Date: Mon, 24 Dec 2007 02:42:36 -0800
Subject:
Message-ID: <20071224024236-0800@axiom-wiki.newsynthesis.org>

fixed in FriCAS


 Submitted by : (unknown) at: 2007-11-17T23:01:10-08:00 (15 years ago) Name : Axiom Version : default friCAS-20090114 Axiom-20050901 OpenAxiom-20091012 OpenAxiom-20110220 OpenAxiom-Release-141 Category : general Severity : critical serious normal minor wishlist Status : open pending closed Optional subject :   Optional comment :

integrate((x^2)*(%e^(-x^2)),x=0..%plusInfinity) does not give
sqrt(%pi)/4.

(new) --Bob McElrath,  Wed, 22 Dec 2004 21:57:46 -0600 replyanonymous [mathaction@axiom-developer.org] wrote:
integrate((x^2)*(%e^(-x^2)),x=0..%plusInfinity) does not give
sqrt(%pi)/4.
The answer it gives is correct (unless there is a new bug introduced
that is not on my axiom 0.20040831-1).  The gamma function has sqrt(pi)
for half-integer values.
fricasintegrate(x^2*(exp(-x^2)), x=0..%plusInfinity)
\begin{equation}
\label{eq1}{\sqrt{\pi}}\over 4\end{equation}
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)
fricasGamma(3/2)/2::Float
\begin{equation}
\label{eq2}{0.5}\ {\Gamma \left({1.5}\right)}\end{equation}
Type: Expression(Float)
fricassqrt(%pi)/4::Float
\begin{equation}
\label{eq3}0.4431134627_2637900682\end{equation}
Type: Expression(Float)
What I don't understand is why the integration result is so hard to
convert to a Float.  Appending ::Float to the integrate() command
fails.  Why?  If I type Gamma(3/2)/2 by hand it has no problem.
(new) --Bob McElrath?,  Wed, 22 Dec 2004 22:13:50 -0600 replyActually the text output is:
_ 3
| (-)
2
(28)  -----
2
Type: Union(f1: OrderedCompletion Expression Integer,...)

which I assume is the Gamma function, but the tex is converted improperly:
{{|{\overline {\ }}}
\left(
{{3 \over 2}}
\right)}
\over 2
\leqno(29)

i.e. clearly does not contain \Gamma.
{|{\overline {\ } == Gamma? --Bill Page,  Thu, 23 Dec 2004 01:32:23 -0600 replyIt is possible to convert this peculiar monogram to \Gamma for
display but I think the problem is more fundamental. Clearly AXIOM
does not have a consistent and complete representation of the Gamma
function. I think integrate should at least return a Gamma that can
be converted to Float or something of type Expression Integer like
sqrt(%pi)/4. But it seems that the current Gamma function always
agressively returns a DoubleFloat? value. This doesn't seem very
useful to me for symbolic computations.
{|{\overline {\ } == Gamma? --Bob McElrath?,  Thu, 23 Dec 2004 01:42:39 -0600 replyBill, What is the type that is returned there?  How can I get axiom to
print the entire type rather than ...?
I think therein lies the problem.  Note that
fricasintegrate(x^2*(exp(-x^2)), x=0..%plusInfinity)::InputForm
\begin{equation}
\label{eq4}\left(/ \ {\left(^\ {\left(pi \right)}\ {\left(/ \  1 \  2 \right)}\right)}\  4 \right)\end{equation}
Type: InputForm?
seems correct.
P.S. IssueTracker? + axiom rules.  Having axiom right here is so
powerful...  I will have to pay more attention to IssueTracker?.  I was
half thinking to strip it when (if) I fork zwiki.  Right now
IssueTracker? is a big hack that can't be uninstalled...
this is not a math bug, only the output is not as nice as it could be --kratt6,  Wed, 19 Jan 2005 08:34:21 -0600 replyCategory: Axiom Mathematics => Axiom User Interface
Severity: normal => minor
I think this is a math bug! --Bill Page,  Wed, 19 Jan 2005 08:54:51 -0600 replyI disagree. There is something fundamentally wrong here. The result of
fricasintegrate(x^2*(exp(-x^2)), x=0..%plusInfinity)
\begin{equation}
\label{eq5}{\sqrt{\pi}}\over 4\end{equation}
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)
Not only prints oddly without conversion to proper LaTeX? but also it
is not actually recognized "mathematically" as Gamma().
Further, there is something wrong with the implementation of Gamma()
itself because it only works numerically and is of no use symbolically.
It seems like there are two separate Gamma functions. The one produced
by the integration is "symbolic" but does not seem to be connected to
any appropriate logic.
this is not a mathbug, only the output is not as nice as it could be --Bill Page,  Wed, 19 Jan 2005 09:20:12 -0600 reply
Category: Axiom Mathematics => Axiom User Interface
Severity: normal => minor
:)

This shows where your priorities are Martin! But, thanks.
Some User Interface issue is involved here, but I don't
think that it is quite correct to classify it this way.
The issue is really what symbollic computations are
possible in Axiom involving Gamma? I would say that this
is more of a deficiency in the mathmatics.
... --kratt6,  Thu, 20 Dec 2007 11:33:13 -0800 replyName: #6 wrong integration result => #6 integration result Gamma not TeXed correctly
... --kratt6,  Sun, 23 Dec 2007 10:32:06 -0800 replyHere is a simple patch:
***************
*** 443,449 ****
dpi l    == "%pi"::Symbol::O
dfact x  == postfix("!"::Symbol::O, (ATOM(x)$Lisp => x; paren x)) dquote l == prefix(quote(first(l)::O), rest l) ! dgamma l == prefix(hconcat(super("|"::Symbol::O, "-"::Symbol::O)), l) setDummyVar(op, n) == setProperty(op, DUMMYVAR, n pretend None) dexp x == --- 443,468 ---- dpi l == "%pi"::Symbol::O dfact x == postfix("!"::Symbol::O, (ATOM(x)$Lisp => x; paren x))
dquote l == prefix(quote(first(l)::O), rest l)
!     dgamma l == prefix(super("|"::Symbol::O, "-"::Symbol::O), l)
! @
!
! It is certainly an abuse of [[OutputForm]] to produce a Gamma as done above.
! Originally, it was even worse:
! \begin{verbatim}
!     dgamma l == prefix(hconcat("|"::Symbol::O, overbar(" "::Symbol::O)), l)
! \end{verbatim}
! which was TeXed to
! $$! {|{\overline {\ }}} ! \left( ! {x} ! \right). !$$
!
! The right thing would be to introduce Greek letters in [[OutputForm]], but that
! should be coordinated with the new mathml package.
!
! <<package COMMONOP CommonOperators>>=
setDummyVar(op, n) == setProperty(op, DUMMYVAR, n pretend None)

dexp x ==

Warning: Gamma looks slightly different in ASCII then.  A better patch is discussed on the FriCAS? list, 23.12.2007
Martin
... --kratt6,  Sun, 23 Dec 2007 10:47:37 -0800 replyStatus: open => fix proposed
patch attached.  Observation by Bill Page transferred to new report #408
... --kratt6,  Mon, 24 Dec 2007 02:42:36 -0800 replyfixed in FriCAS?

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}
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