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May 16, 2007, 5:25:20 AM5/16/07

to

"Another computer algebra system" has a function, identify(), which

attempts to guess the exact expression that evaluates to a particular

numerical value.

attempts to guess the exact expression that evaluates to a particular

numerical value.

Example:

In[1]:= N[3Pi+3/2,10]

Out[1]= 10.92477796

> identify(10.92477796);

3

- + 3 Pi

2

Is there a package with similar functionality for Mathematica?

Szabolcs

May 17, 2007, 5:57:55 AM5/17/07

to

I think there is a package of Ted Ersek but I am not sure!

Check www.wolfram.com and its archives.

Check www.wolfram.com and its archives.

Dimitris

=CF/=C7 Szabolcs =DD=E3=F1=E1=F8=E5:

May 17, 2007, 6:10:05 AM5/17/07

to

As I remember, at IMS'06 (Avignon) Stephen Wolfram (via remote link-up)

played with a function to do just that. Did I remember correctly?

played with a function to do just that. Did I remember correctly?

If so, I cannot recall the name of the function, so I don't know whether

the function made it into 6.0. The closest thing I can find is

RootApproximant, but that doesn't seem to "recognize" an expression

involving a transcendental number.

Szabolcs wrote:

> "Another computer algebra system" has a function, identify(), which

> attempts to guess the exact expression that evaluates to a particular

> numerical value.

>

> Example:

>

> In[1]:= N[3Pi+3/2,10]

>

> Out[1]= 10.92477796

>

> > identify(10.92477796);

> 3

> - + 3 Pi

> 2

>

> Is there a package with similar functionality for Mathematica?

>

> Szabolcs

>

--

Murray Eisenberg mur...@math.umass.edu

Mathematics & Statistics Dept.

Lederle Graduate Research Tower phone 413 549-1020 (H)

University of Massachusetts 413 545-2859 (W)

710 North Pleasant Street fax 413 545-1801

Amherst, MA 01003-9305

May 17, 2007, 6:35:37 AM5/17/07

to

Hi,

The built-in function *Rationalize* and the add-on package

NumberTheory`Rationalize` should be the closest equivalent to the

function identify().

In[1]:=

x = N[3*Pi + 3/2]

Out[1]=

10.92477796076938

In[2]:=

Rationalize[x, 0]

Out[2]=

569958623/52171186

In[3]:=

x - %

Out[3]=

0.

In[4]:=

$Version

Out[4]=

"5.2 for Microsoft Windows (June 20, 2005)"

HTH,

Jean-Marc

May 18, 2007, 6:17:39 AM5/18/07

to

Hi. This is not the best solution, but here's one idea I use.

It's not the best solution, because I can't find a way to make Mathematica's

Hyperlinks dynamic.

In other words, once a hyperlink is made (Entered), it appears the address

is locked in stone.

Maybe an expert can jump in and make this dynamic.

It's not the best solution, because I can't find a way to make Mathematica's

Hyperlinks dynamic.

In other words, once a hyperlink is made (Entered), it appears the address

is locked in stone.

Maybe an expert can jump in and make this dynamic.

A number we know nothing about...(??)

n = 6.283185307179586

Set the variable to something you would like to use. For me...

NumberToSearch = n;

Re-Enter this equation (Shift Enter), and then click the link.

Hyperlink["Click Here: Plouffe's Inverter",

StringReplace["http://bootes.math.uqam.ca/cgi-bin/ipcgi/lookup.\

pl?Submit=GO+&number=#&lookup_type=simple",

"#" :> ToString[Evaluate[NumberToSearch], InputForm,

NumberMarks -> False]]]

The above click shows it might be 2 Pi.

For your example, I took the full value:

n=10.92477796076938

This number didn't work. Sometimes it won't work if the number is large.

I don't know what "large" means, but the program really works with

fractions.

I decided to divided the number by 3.

NumberToSearch = 10.92477796076938/3

3.641592653589793

If I re-enter the Hyperlink, and click the link, the solution is Pi+1/2.

Multiply by 3 to get your equation.

Reference: http://pi.lacim.uqam.ca/eng/

--

HTH :>)

Dana DeLouis

Windows XP & Mathematica 6.0 & Help files 5.2 :>~

"Szabolcs" <szho...@gmail.com> wrote in message

news:f2eim0$t2f$1...@smc.vnet.net...

May 18, 2007, 6:30:09 AM5/18/07

to

As soon as I hit send, I thought of another way. Don't know why I didn't

think of this sooner. I just modified mine to the following...

think of this sooner. I just modified mine to the following...

RealLookup[NumberToSearch_Real] := Module[

{

s1 = "Click Here: Plouffe's Inverter on: ",

s2 = ToString[NumberToSearch, InputForm, NumberMarks -> False],

link = "http://bootes.math.uqam.ca/c\

gi-bin/ipcgi/lookup.pl?Submit=GO+&number=#&lookup_type=simple"

},

Hyperlink[StringJoin[s1, s2], StringReplace[link, "#" :> s2]]

]

RealLookup[NumberToSearch_] :=

StringJoin["Number must be Real, not: ",

ToString[NumberToSearch, InputForm]]

RealLookup[2.*Pi]

<...Link here...>

n = 3*Pi + 3/2;

RealLookup[n/3.]

<...Link here...>

RealLookup[n/3]

"Number must be Real, not: (3/2 + 3*Pi)/3"

RealLookup["Dog"]

"Number must be Real, not: Dog"

--

HTH :>)

Dana DeLouis

Windows XP & Mathematica 6, and 5.2 Help. :>~

"Szabolcs" <szho...@gmail.com> wrote in message

news:f2eim0$t2f$1...@smc.vnet.net...

> "Another computer algebra system" has a function, identify(), which

> attempts to guess the exact expression that evaluates to a particular

> numerical value.

>

> Example:

>

> In[1]:= N[3Pi+3/2,10]

>

> Out[1]= 10.92477796

>

> > identify(10.92477796);

>

May 18, 2007, 6:42:57 AM5/18/07

to

May 18, 2007, 6:47:30 AM5/18/07

to

Mathematica can "recognize" algebraic numbers, by using the function

RootApproximant (or the function Recognize in the Legacy

NumberTherory package):

RootApproximant (or the function Recognize in the Legacy

NumberTherory package):

ToRadicals[RootApproximant[N[Sqrt[2] + Sqrt[3], 30]]]

Sqrt[5 + 2*Sqrt[6]]

This may not look so impressive until you check:

FullSimplify[Sqrt[2] + Sqrt[3] - Sqrt[5 + 2*Sqrt[6]]]

0

Anyway, doing this for algebraic numbers has a solid mathematical

basis: the so called LLL Lattice Reduction) algorithm. I don=92t know, =

however, of any mathematical basis for "recognizing" transcendentals, =

except by means of stored values or some other "ad hoc" approach

(essentially "sophisticated guessing")

Andrzej Kozlowski

On 17 May 2007, at 18:59, Murray Eisenberg wrote:

> As I remember, at IMS'06 (Avignon) Stephen Wolfram (via remote link-=

> up)

> played with a function to do just that. Did I remember correctly?

>

> If so, I cannot recall the name of the function, so I don't know

> whether

> the function made it into 6.0. The closest thing I can find is

> RootApproximant, but that doesn't seem to "recognize" an expression

> involving a transcendental number.

>

> Szabolcs wrote:

>> "Another computer algebra system" has a function, identify(), which

>> attempts to guess the exact expression that evaluates to a particular

>> numerical value.

>>

>> Example:

>>

>> In[1]:= N[3Pi+3/2,10]

>>

>> Out[1]= 10.92477796

>>

>>> identify(10.92477796);

>> 3

>> - + 3 Pi

>> 2

>>

>> Is there a package with similar functionality for Mathematica?

>>

>> Szabolcs

>>

>

May 19, 2007, 4:35:20 AM5/19/07

to

dimitris wrote:

> I think there is a package of Ted Ersek but I am not sure!

> Check www.wolfram.com and its archives.

> I think there is a package of Ted Ersek but I am not sure!

> Check www.wolfram.com and its archives.

Thanks for everyone who replied! I learned a lot today.

I did not find the package by Ted Ersek, but I found another one by Eric

Weisstein:

http://library.wolfram.com/infocenter/MathSource/5087/

The relevant file is Simplify.m

Interesting functions are ToExact and TranscendentalRecognize.

In another thread someone mentioned a website which can be used for

similar purposes:

http://pi.lacim.uqam.ca/eng/

May 19, 2007, 4:51:36 AM5/19/07

to

When I run that code and click the link, my browser shows a "File not

found!" error page.

found!" error page.

--

May 19, 2007, 5:10:15 AM5/19/07

to

>>--

>>Murray Eisenberg mur...@math.umass.edu

>>Mathematics & Statistics Dept.

>>Lederle Graduate Research Tower phone 413 549-1020 (H)

>>University of Massachusetts 413 545-2859 (W)

>>710 North Pleasant Street fax 413 545-1801

>>Amherst, MA 01003-9305

>>

>>Murray Eisenberg mur...@math.umass.edu

>>Mathematics & Statistics Dept.

>>Lederle Graduate Research Tower phone 413 549-1020 (H)

>>University of Massachusetts 413 545-2859 (W)

>>710 North Pleasant Street fax 413 545-1801

>>Amherst, MA 01003-9305

>>

A common approach is to use a predefined basis of transcendentals, e.g

certain powers of e, pi, gamma, and maybe some set of radicals of

"small" integers. One then seeks rational combinations of these that

give the input value to close approximation. This step typically uses

LLL or PSLQ.

Simple code to demonstrate the concept was presented in TMJ back in 1996

(and based on some email and maybe news group correspondence from late

1995). The reference is below.

Transcendental Recognition. In: Tricks of the Trade, Paul Abbott editor.

The Mathematica Journal 6(2):29-30 (1996).

To obtain electronically go to:

http://www.mathematica-journal.com/issue/v6i2/

Scroll to Tricks of the Trade (under Tutorials), click to download the

notebook, go to "Trancendental Recognition" section.

I'll mention that a perusal of documentation suggests the identify()

function for the most part uses this approach.

Daniel Lichtblau

Wolfram Research

May 20, 2007, 2:51:39 AM5/20/07

to

Thanks again for all the replies!

I think that I need to explain that I sent this message before I

received the replies from Dana DeLouis and Roman, but for some reason it

arrived with a delay of 2 days.

May 21, 2007, 6:09:46 AM5/21/07

to

Murray Eisenberg wrote:

> When I run that code and click the link, my browser shows a "File not

> found!" error page.

>

> When I run that code and click the link, my browser shows a "File not

> found!" error page.

>

It is because of the line break in the URL. Make sure that after you

paste it, you remove the spaces which got inserted between ...

"ipcgi/lookup." and "pl?Submit" ...

Szabolcs

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