mm-699
===
Subject: Re: Maple procedures
>Is there anyway way to read how maple procedures are
programmed?
> In addition to Joe RielÕs suggestion, sometimes
showstat(procedure_name)
> gives more readable output than eval(procedure_name). And
sometimes the
> eval(...) will be the more readable one.
A disadvantage of showstat, particularly if you want to cut
and paste
the output, is that it includes line numbers. Here is a simple
procedure I threw together to remove the line numbers.
PrintProc := proc(p::name,lines::{posint,posint..posint})
local s,width;
description Print like showstat, but without line numbers;
width := 
interface(ÔscreenwidthÕ=in[CapitalThorn]nity);
try
s := sprintf(%s,debugopts(ÔprocdumpÕ=
`if`(nargs=1,p,[p,lines])));
# This is a bit crude, but easier than counting the digits in
# the line numbers.
use StringTools in
s := RegSubs(n [0-9] =n ,s);
s := RegSubs(n [0-9][0-9] =n ,s);
s := RegSubs(n [0-9][0-9][0-9] =n ,s);
s := RegSubs(n[0-9][0-9][0-9][0-9] =n ,s);
# Decrease initial indentation to 2.
s := RegSubs(n =n ,s);
end use;
printf(%s,s);
catch procedure name expected:
error %1 is not a procedure name,p
[CapitalThorn]nally 
interface(ÔscreenwidthÕ=width)
end try;
NULL
end:
Joe Riel
===
Subject: Re: Maple procedures
> A disadvantage of showstat, particularly if you want to cut
and paste
> the output, is that it includes line numbers. Here is a
simple
> procedure I threw together to remove the line numbers.
> PrintProc := proc(p::name,lines::{posint,posint..posint})
...
> end:
HereÕs a cleaned up version. The separate calls to RegSubs
were combined into one large regexp. Note the use of MapleÕs
implicit string catenation to write the large regexp.
PrintProc := proc(p::name,lines::{posint,posint..posint})
local width;
description Print like showstat, but without line numbers;
width := 
interface(ÔscreenwidthÕ=in[CapitalThorn]nity);
try
printf(%s,
StringTools:-RegSubs(
n(
( )
|( [1-9])
|( [1-9][0-9])
|( [1-9][0-9][0-9])
|([1-9][0-9][0-9][0-9])
) = n
,debugopts(ÔprocdumpÕ=
`if`(nargs=1,p,[args]))))
catch procedure name expected:
error %1 is not a procedure name,p
[CapitalThorn]nally 
interface(ÔscreenwidthÕ=width)
end try;
NULL
end:
Joe Riel
===
Subject: Re: Maple procedures
> HereÕs a cleaned up version.
I had previously avoided using the post[CapitalThorn]x repetition operator
in the
regular expression (regexp) because I thought it might match
an actual
code line that started with a number. On reßection, that
wonÕt happen
because such a line must have a line number, and the line
number is what
is matched (the n anchors the match). So the regular
expression can be
replaced by the simpler n *[0-9]+ (or n * [1-9][0-9]* ). I
wondered whether this regexp could also match a string like n
1234
that was embedded in a procedure. It wonÕt. The reason is 
that
debugopts converts such a string to n 1234 so that it displays
properly, that is, the single return character is replaced
with two
characters, a backslash and an `nÕ. Here is the procedure
with the
simpli[CapitalThorn]ed regexp:
PrintProc := proc(p::name,lines::{posint,posint..posint})
local width;
description Print like showstat, but without line numbers;
width := 
interface(ÔscreenwidthÕ=in[CapitalThorn]nity);
try
printf(%s,
StringTools:-RegSubs(
n *[0-9]+ = n
,debugopts(ÔprocdumpÕ=
`if`(nargs=1,p,[args]))))
catch procedure name expected:
error %1 is not a procedure name,p
[CapitalThorn]nally 
interface(ÔscreenwidthÕ=width)
end try;
NULL
end:
Joe
===
Subject: Re: Maple procedures
.................... Here is the procedure with the
> simpli[CapitalThorn]ed regexp:
> PrintProc := proc(p::name,lines::{posint,posint..posint})
> local width;
> description Print like showstat, but without line numbers;
> width := 
interface(ÔscreenwidthÕ=in[CapitalThorn]nity);
> try
> printf(%s,
> StringTools:-RegSubs(
> n *[0-9]+ = n
> ,debugopts(ÔprocdumpÕ=
> `if`(nargs=1,p,[args]))))
> catch procedure name expected:
> error %1 is not a procedure name,p
> [CapitalThorn]nally 
interface(ÔscreenwidthÕ=width)
> end try;
> NULL
> end:
I like that: before i had a dirty solution in Excel
with copy & paste. But it was simple to remove just
the _trailing 7 characters_ for lines of the body.
===
Subject: Re: Maple procedures
> I like that: before i had a dirty solution in Excel
> with copy & paste. But it was simple to remove just
> the _trailing 7 characters_ for lines of the body.
Hmmm, that is simpler. It also points out an error in my
previous
version, lines with out line numbers are not properly
indented. Here is
the [CapitalThorn]x (apologies for multiple versions):
PrintProc := proc(p::name,lines::{posint,posint..posint})
local width;
description Print like showstat, but without line numbers;
width := 
interface(ÔscreenwidthÕ=in[CapitalThorn]nity);
try
printf(%s,
StringTools:-RegSubs(
n .... = n
,debugopts(ÔprocdumpÕ=
`if`(nargs=1,p,[args]))))
catch procedure name expected:
error %1 is not a procedure name,p
[CapitalThorn]nally 
interface(ÔscreenwidthÕ=width)
end try;
NULL
end:
This works with procedures that have up to 999 numbered
lines. It is
unlikely that Maple procedures will be longer, however, if
you need to
handle them, use n( |[1-9]).... for the regexp, that will
take you
out to 9999. I havenÕt bothered testing beyond that.
Joe Riel
===
Subject: Porting Maxima
Hi
Does anyone know if it would be possible to port the Maxima
CAS to the
palm operating system? Is this too big a project for a fairly
new
coder to undertake?
Mike
===
Subject: Re: Porting Maxima
One of the nice parts about Macsyma is the modularity.
On the PDP-10 where it was developed in MacLisp,
there was a decent sized kernel that was loaded.
Additional packages, such as for SOLVE, INTEGRATE,
etc. would load up as required. Can you implement
such a method for the Palm?
If you can remove non-essential lisp features such
as the compiler from the [CapitalThorn]nal executable, perhaps
you can manage in the available space.
My recollection is that DOE-Macsyma on the VAX
VMS was about 11 MB, and for the SUN4, Paramax
was about 13 MB. These included all of the built-in
functions in-core, with autoloads from the SHARE
library.
> Hi
> Does anyone know if it would be possible to port the Maxima
CAS to the
> palm operating system? Is this too big a project for a
fairly new
> coder to undertake?
> Mike
===
Subject: Re: Porting Maxima
> Does anyone know if it would be possible to port the Maxima
CAS to the
> palm operating system? Is this too big a project for a
fairly new
> coder to undertake?
Well, [CapitalThorn]rst youÕll need a port of lisp. 
Apparently LispMe is
available
for the Palm, it provides a variant of Scheme. IÕd say that
porting
Maxima would be a nontrivial undertaking...
Joe
===
Subject: Re: Porting Maxima
> Does anyone know if it would be possible to port the
Maxima CAS to the
> palm operating system? Is this too big a project for a
fairly new
> coder to undertake?
> Well, [CapitalThorn]rst youÕll need a port of lisp. 
Apparently LispMe is
available
> for the Palm, it provides a variant of Scheme. IÕd say 
that
porting
> Maxima would be a nontrivial undertaking...
> Joe
Try porting my CAS to the palm OS. It will be much easier.
Mathomatic is
a
small, highly portable CAS written entirely in C. Let me know
if you
succeed
in porting it. BTW, it is entirely free, like Maxima.
George Gesslein II
http://www.mathomatic.com
===
Subject: roots of polynomials
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i5NC6DP19329;
[CapitalThorn]nd out one real root for the following uneven degree
equation:
f(x)=x^n+ax^m+b=0
n is uneven positive integer
m is positive integer less than n
f(x) is a rational integeral function of x
(a&b) are real rational cooef[CapitalThorn]cients
===
Subject: Re: roots of polynomials
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i5NDiUi29365;
>[CapitalThorn]nd out one real root for the following uneven degree
equation:
>f(x)=x^n+ax^m+b=0
>n is uneven positive integer
>m is positive integer less than n
>f(x) is a rational integeral function of x
>(a&b) are real rational cooef[CapitalThorn]cients
REPLY:
DEAR ORGANIZER
I found one real root for the case (a=b=1)& m is uneven
positive
integer,here is the solution:
x=-{1-1/n+(2m-n+1)/(2!n^2)-(3m-2n+1)(3m-n+1)/(3!n^3)
+(4m-3n+1)(4m-2n+1)(4m-n+1)/(4!n^4)
-(5m-4n+1)(5m-3n+1)(5m-2n+1)(5m-n+1)/(5!n^5)+...}
In fact, the proof of this (above mentioned equation )is too
lengthy
and it was part of my interest for so many years.
The complete solutions for all cases are also obtainable.
I dont know if i could convey this properly.
===
Subject: Re: roots of polynomials
>[CapitalThorn]nd out one real root for the following uneven degree
equation:
>f(x)=x^n+ax^m+b=0
>n is uneven positive integer
>m is positive integer less than n
>f(x) is a rational integeral function of x
>(a&b) are real rational cooef[CapitalThorn]cients
> REPLY:
> DEAR ORGANIZER
> I found one real root for the case (a=b=1)& m is uneven
positive
> integer,here is the solution:
> x=-{1-1/n+(2m-n+1)/(2!n^2)-(3m-2n+1)(3m-n+1)/(3!n^3)
> +(4m-3n+1)(4m-2n+1)(4m-n+1)/(4!n^4)
> -(5m-4n+1)(5m-3n+1)(5m-2n+1)(5m-n+1)/(5!n^5)+...}
> In fact, the proof of this (above mentioned equation )is
too lengthy
> and it was part of my interest for so many years.
> The complete solutions for all cases are also obtainable.
> I dont know if i could convey this properly.
Interesting. LetÕs do x^5+x+1.
Then your solution is (Maple notation)...
> k = 0 .. in[CapitalThorn]nity))
in[CapitalThorn]nity
----- k /1 1
) 5 5 /
- / ---------------------------
----- /6 4
5 5 /
Numerically with 100 terms we get -0.7548776662, which is a
solution,
or symbolically Maple says the sum is:
-hypergeom([-1/20, 1/5, 9/20, 7/10], [2/5, 3/5,
4/5],-256/3125)
+1/5*hypergeom([3/20, 2/5, 13/20, 9/10], [3/5, 4/5,
6/5],-256/3125)
+1/25*hypergeom([7/20, 3/5, 17/20, 11/10], [4/5, 6/5,
7/5],-256/3125)
+1/125*hypergeom([11/20, 4/5, 21/20, 13/10], [6/5, 7/5,
8/5],-256/3125)
For convergence: Maple says that
is asymptotic to a constant times
k^(-3/2)*(2^(8/5)/5)^k
and since 2^(8/5)/5 < 1, the series converges absolutely.
--
G. A. Edgar
http://www.math.ohio-state.edu/~edgar/
===
Subject: Re: roots of polynomials
|>[CapitalThorn]nd out one real root for the following uneven degree
equation:
|>f(x)=x^n+ax^m+b=0
|>n is uneven positive integer
|>m is positive integer less than n
|>f(x) is a rational integeral function of x
|>(a&b) are real rational cooef[CapitalThorn]cients
|>I found one real root for the case (a=b=1)& m is uneven
positive
|>integer,here is the solution:
|>x=-{1-1/n+(2m-n+1)/(2!n^2)-(3m-2n+1)(3m-n+1)/(3!n^3)
|> +(4m-3n+1)(4m-2n+1)(4m-n+1)/(4!n^4)
|> -(5m-4n+1)(5m-3n+1)(5m-2n+1)(5m-n+1)/(5!n^5)+...}
A very interesting formula. It comes, I think, from a series
in powers
of t for a root of x^n + t x^m - 1. According to Maple:
[view in [CapitalThorn]xed-width font]
> series(RootOf(x^n + t*x^m - 1, x), t);
1 n - 1 - 2 m 2 (2 n - 1 - 3 m) (n - 1 - 3 m) 3
1 - - t - ----------- t - ----------------------------- t
n 2 3
2 n 6 n
(3 n - 1 - 4 m) (n - 1 - 4 m) (2 n - 1 - 4 m) 4
- --------------------------------------------- t
4
24 n
(n - 1 - 5 m) (3 n - 1 - 5 m) (2 n - 1 - 5 m) (4 n - 1 - 5 m)
5
-
-------------------------------------------------------------
t
5
120 n
/ 6
+ Ot /
I donÕt know about the convergence of this series.
Note that if n and m are odd, x^n + t x^m - 1 = 0 iff
(-x)^n + t (-x)^m + 1 = 0. And for a root of z^n + a z^m + b
= 0
you can take z = -b^(1/n) x where x is a root of
x^n + a b^(m/n-1) x^m - 1 = 0.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
===
Subject: Re: roots of polynomials
>A very interesting formula. It comes, I think, from a series
in powers
>of t for a root of x^n + t x^m - 1. According to Maple:
>[view in [CapitalThorn]xed-width font]
> series(RootOf(x^n + t*x^m - 1, x), t);
> 1 n - 1 - 2 m 2 (2 n - 1 - 3 m) (n - 1 - 3 m) 3
>1 - - t - ----------- t - ----------------------------- t
> n 2 3
> 2 n 6 n
> (3 n - 1 - 4 m) (n - 1 - 4 m) (2 n - 1 - 4 m) 4
> - --------------------------------------------- t
> 4
> 24 n
> (n - 1 - 5 m) (3 n - 1 - 5 m) (2 n - 1 - 5 m) (4 n - 1 - 5
m) 5
> -
-------------------------------------------------------------
t
> 5
> 120 n
> / 6
> + Ot /
I think this is best viewed as a special case of the Lagrange
Inversion
Formula. See
<http://mathworld.wolfram.com/LagrangeInversionTheorem.html>.
Write the equation x^n + t x^m = s as z = s - t z^(m/n) = s +
t p(z)
where x = z^(1/n) = F(z) and p(z) = - z^(m/n). The Lagrange
Inversion
Formula says
x = F(z) = F(s) + sum_{k=1}^in[CapitalThorn]nity t^k/k! (d/ds)^(k-1)
(p(s)^k FÕ(s))
>I donÕt know about the convergence of this series.
It will converge for suf[CapitalThorn]ciently small |t|. IÕm 
not sure
exactly how
small.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
===
Subject: Re: roots of polynomials
> [CapitalThorn]nd out one real root for the following uneven degree
equation:
> f(x)=x^n+ax^m+b=0
> n is uneven positive integer
> m is positive integer less than n
> f(x) is a rational integeral function of x
> (a&b) are real rational cooef[CapitalThorn]cients
The Galois group for x^5+x+3 over the rationals is S5.
What do you mean by [CapitalThorn]nd out?
--
G. A. Edgar
http://www.math.ohio-state.edu/~edgar/
===
Subject: Re: roots of polynomials
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id i5NFW1408127;
Reply to Dr. G.A.Edgar
this equation of an odd degree,therefore,it must intersects
x-axes at
least at one point,that is what I mean by ([CapitalThorn]nd out) that
point of
intersection.now if i assume (a&b) are real cooef[CapitalThorn]cients
rather than
real rational coof[CapitalThorn]cients ,would that make it uncofusiable.
I saw a strange formula (on the same topic)from
mr.karzeddin.I have
been exersizing that formula for (n=5 )& (m=1 or 3)&
surprizingly it
gives me very close values of intersections(f(x)& x-axes) as
long as I
take more elements of that mentioned series
I hoop,this would make it clear.
sincerely yours
===
Subject: Re: f(x,y)= {f(x)*f(y) or f(x)+f(y) or f(x)*f(y)
+f(x)} etc.}
>basically I want to know be able to check to see if a
multi valued
>nonlinearity can be separated in terms of signal valued
> nonlinearities
>under addition and multiplication. Does maple have any
built in
>procedures to do this?
>P.S. Does expand fully expand or does it only expand under
the
> current
>opperator which you can [CapitalThorn]nd out by calling whattype.
> Something of this sort came up not long ago in
> A recommendation therein is to look at:
> Frederick W. Chapman. An elementary algorithm for the
automatic
> derivation and proof of tensor product identities via
computer
> algebra.
> Algebraic
> The idea is to factor a bivariate function as a sum of
products of
> Maple) for this purpose.
> Daniel Lichtblau
> Wolfram Research
I am interested in a similar problem but slightly simpler.
f(x+y)=sum(g_n(x)g_m(y),m,n)
I was thinking you could just sub x+y in for x use expand and
Then check to see if each term in the product of each term in
the sum
only contained x or y. Some problems I could see with this
approach
is f may already contain the variable y. This leads to
questions of
scope of variables. What are maples rules for scope of
variables anyway?
Also the question remains should I assume anything about x
and y. I guess
I could assume they are real. I could also use about x or
about y to make
sure
I donÕt mess up any previous assumptions.
===
Subject: Re: f(x,y)= {f(x)*f(y) or f(x)+f(y) or f(x)*f(y)
+f(x)} etc.}
>basically I want to know be able to check to see if a
multi valued
>nonlinearity can be separated in terms of signal valued
> nonlinearities
>under addition and multiplication. Does maple have any
built in
>procedures to do this?
>P.S. Does expand fully expand or does it only expand under
the
> current
>opperator which you can [CapitalThorn]nd out by calling whattype.
> Something of this sort came up not long ago in
> A recommendation therein is to look at:
> Frederick W. Chapman. An elementary algorithm for the
automatic
> derivation and proof of tensor product identities via
computer
> algebra.
> Algebraic
> The idea is to factor a bivariate function as a sum of
products of
> Maple) for this purpose.
> Daniel Lichtblau
> Wolfram Research
I am interested in a similar problem but slightly simpler.
f(x+y)=sum(g_n(x)g_m(y),m,n)
I was thinking you could just sub x+y in for x use expand and
then check to see if each term in the product of each term in
the sum
only contained x or y. Some problems I could see with this
approach
is f may already contain the variable y. This leads to
questions of
scope of variables. What are maples rules for scope of
variables anyway?
Also the question remains should I assume anything about x
and y. I guess
I could assume they are real. I could also use about x or
about y to make
sure
I donÕt mess up any previous assumptions.
===
Subject: PascalÕs Triangle in CAS
Does any CAS system directly support building number walls?
Extension
packages?
===
Subject: Re: PascalÕs Triangle in CAS
> Does any CAS system directly support building number walls?
Extension
> packages?
IÕm pretty sure this is easy in all systems. In Maple, 
itÕs a
one-liner:
> for n from 0 to 5 do seq(binomial(n,k),k=0..n) end do;
1
1, 1
1, 2, 1
1, 3, 3, 1
1, 4, 6, 4, 1
1, 5, 10, 10, 5, 1
--
Thomas Richard
Maple Support
Scienti[CapitalThorn]c Computers GmbH
http://www.scienti[CapitalThorn]c.de
===
Subject: Re: PascalÕs Triangle in CAS
> Does any CAS system directly support building number
walls? Extension
> packages?
> IÕm pretty sure this is easy in all systems. In Maple, 
itÕs
a one-liner:
> for n from 0 to 5 do seq(binomial(n,k),k=0..n) end do;
> 1
> 1, 1
> 1, 2, 1
> 1, 3, 3, 1
> 1, 4, 6, 4, 1
> 1, 5, 10, 10, 5, 1
===
Subject: implementation of the complex airy function
I am looking for an implementation of the complex airy
function
in C/C++/C#. Can anybody help me [CapitalThorn]nd a piece of code for this
function ?
Laurent
===
Subject: Re: implementation of the complex airy function
> I am looking for an implementation of the complex airy
function
> in C/C++/C#. Can anybody help me [CapitalThorn]nd a piece of code for
this
> function ?
> Laurent
You might look for it in Fortran and convert. Abramowitz &
Stegun discuss
the function and approximations to it.
--
Julian V. Noble
Professor Emeritus of Physics
jvn@lessspamformother.virginia.edu
^^^^^^^^^^^^^^^^^^
http://galileo.phys.virginia.edu/~jvn/
For there was never yet philosopher that could endure the
toothache patiently.
-- Wm. Shakespeare, Much Ado about Nothing. Act v. Sc. 1.