mm-431
===
Subject: Re: Nedd helpSummarized problem number of people in
party = 40 if x is number of mush room and y is number of
cheesesticks,x >= 40*2y >= 40*30.15*y + 0.25*x <= 45now, use
that to solve your homework problem.Ts is the problem:> You
are planning a party and want to have two types of snacks:>
Stuffed mushroom and cheese sticks. Each mushroom costs about
$0.25> and each cheese stick will cost about $0.15. You want
enough to make> so that each person> can have at least two
stuffed mushroom and three cheese sticks. There> are going to
be at most 40 people at the party and you don't want to> spend
more than $45.> Write a system of linear equations that sows
the various numbers of> stuffed mushrooms and cheese sticks
that you could make.I would really appreciate anybody who can
help and tell me what those> two equations are. I came up with
the first one> 2x(0.25)+ 3y(0.15) <= 45
===
Subject: Re: Maple
problem by support1.mathforum.org (8.11.6/8.11.6/The Math
Forum, $Revision: 1.9 primary) id i0RF7ZB26576;1. Currently,
the most active group for discussing any kinds of problem in
Maple. 2. Give and receive help for the mathematical software
Maple. Questions at all levels are welcome.
http://groups.yahoo.com/group/maple-assist/3. Discussing bugs
in Maple 9, suggestions for improvement, and differences with
earlier versions of Maple. Ts group is NOT for general
questions about Maple.
http://groups.yahoo.com/group/maple-new/4. Three servers fully
dedicated to description of Maple bugs and workarounds in all
versions, to be reinforced dramatically witn the span of the
several upcoming months http://www.cybertester.com/
http://maple.bug-list.org/ http://www.CAS-testing.org/ There
are also 2 inactive now groups where a lot of useful info
could be found.5. The Maple User Group (MUG) was an electronic
mailing list designed to give Maple users an opportunity to
discuss applications, problems and issues with other users.
are available as text files from
http://www.scg.uwaterloo.ca/~maple_gr/Digests/6. Discussing
bugs in Maple 8, suggestions for improvement, and differences
with earlier versions of Maple. Ts group is NOT for general
questions about Maple. http://groups.yahoo.com/group/maple8/
===
Subject: Re: Non-dard analysisOriginator:
bellenot@haar>Consider the collection of sets I1, I2, I3, ...
, In, ...>Where I1 = {1}, I2 = {1,2}, I3 = {1,2,3},...,In =
{1,2,3,...,n},...>for natural numbers n. That is, Ij is the
set of natural numbers less>than or equal to j.>Define a set S
to be finite if there is a 1-1 mapping of S onto In for>some
natural number n.>Define a finite set S to be larger than a
natural number n, if there>is a natural number m and a 1-1 map
of S onto Im with m > n.> >Consider further the following
countable collection of sentences:>1. There exists a finite
set S1 larger than 1.>2. There exists a finite set S2 larger
than 2.>...>n. There exists a finite set Sn larger than
n.>...>Clearly any finite subset of ts collection is
consistent. [let j be>the largest index of a sentence in the
finite subset, then, for>example, Ij+1 provides the model]By compactness, the whole collection is consistent and
therefore there>is a model with the property that there exists
a finite set S wch is>larger than n for any n. Ts is clearly a
contradiction.Your error is assuming that `finite in the new
model' means `finitein the usual sense'. People that do
non-dard stuff often call`model finite' sometng like *finite
or hyperfinite to make thedistinction clear.>[S finite implies
by definition that there exists some natural number>n, such
that S can be mapped 1-1 onto In. But S larger than n
implies,>again by definition, that S can be mapped 1-1 onto Im
for some natural>number m > n]In the new model ts is still
true, but there are more integers.--
http://www.math.fsu.edu/~bellenot
===
Subject: Re: Non-dard
analysis> Consider the collection of sets I1, I2, I3, ... ,
In, ...> Where I1 = {1}, I2 = {1,2}, I3 = {1,2,3},...,In =
{1,2,3,...,n},...> for natural numbers n. That is, Ij is the
set of natural numbers less> than or equal to j.> Define a set
S to be finite if there is a 1-1 mapping of S onto In for> some
natural number n.I once heard a joke based on the above
definitionQ: What is the difference between a theoretical
physicist and a mathematician?A: A theoretical physicist
defines a set S to be finite if there is a 1-1 mapping of S
onto In for some natural number n A mathematician defines a
set S to be finite if there is a 1-1 mapping of S onto In for
some natural number n OR the set is empty.-- Use of tools
distinguishes Man from Beast. And UNIX users from WINDOZE
lusers.
===
Subject: LISP routines to do symbolic
differentiation... I'm looking for a lisp routine that will do
symbolic differentiationof a function, given (obviously) an
expression in prefix notation and whatvariable it is being
differentiated against... Sometng like(differentiate '(* x x))
=> (* 2 x)Obviously that's a simple homework assignment... But,
what I need it foris to do these functions: power +,*,-,/ Exp
(Although, perhaps I don't need Exp, I can just use (pow E X)
Log... I dunno what I'm going to do about ts function tho...
Hmmm But, I need Erf (The error function) But, I suppose,
derivative of Erf is easy enough, to encode... Actually, I can
live with it, if it doesn't differentiate Erf out the
box...Here's what I want to do. I want to integrate a function
(Exp[((Log[X1/X0]-m)/sd)^2/2] Log[a X1 + b])/X1 (/ (* (exp (/
(pow (/ (- (log (/ X1 X0)) m) sd) 2) 2)) (log (+ (* a X1) b)))
X1) (It's the PDF of a lognormal distributed X1 from X0 * log
of a linear function of X1...) (The actual function is a
little more complicated, but, ts is the basic idea)I'm hoping
to try to use genetic programming to create a function
who'sderivative is the function above... Is ts feasible? Is ts
a good wayto approach ts problem of mine? So, the fitness
criteria would behow far off the generated function is from
the one I'm asking for...(But, first, I'd like some equivalent
of freshmeat for open sourced stuffor cpan for perl stuff for
lisp... Does such a beast exist?) Bannerjee-- The measure of
love is what one is willing to give up for it. -- Geoffrey
Fielding - Pandora and the Flying Dutchman PGP Key:
http://www.hex21.com/~/-public.asc Key fingerprint = 421D B4C2
2E96 B8EE 7190 A0CF B42F E71C 7FC3 AD96 SSH2 Key:
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http://www.hex21.com/~/-ssh1.pubOpenSSH Key:
http://www.hex21.com/~/-openssh.pubCipherKnight Seals:
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http://www.hex21.com/~/-certificate.gif.cs256 Decrypt with
CipherSaber2 N=256, Password=WelcomeJedi! (No
quotes)
===
Subject: Re: LISP routines to do symbolic
differentiation> ...> I'm looking for a lisp routine that will
do symbolic differentiation> of a function ...Have you checked
http://sourceforge.net/projects/maxima/ ?
===
Subject: Re: LISP
routines to do symbolic differentiation> ...> I'm looking for
a lisp routine that will do symbolic differentiation> of a
function, given (obviously) an expression in prefix notation
and what> variable it is being differentiated against...
Sometng like> (differentiate '(* x x)) => (* 2 x)The routine
is d, in the code below.(defun d(e v)(if(atom e)(if(eq e v)1
0)(funcall(or(get(car e)'d)#'undef)e v)))(defun undef(e
v)`(d,e,v))(defun r(op s)(setf(get op'd)(compile()`(lambda(e
v)(let((x(cadr e)))(list'*(subst x'x',s)(d x v)))))))(r'cos'(*
-1(sin x)))(r'sin'(cos x))(r'exp'(exp x))(r'log'(expt x
-1))(setf(get'+'d)#'(lambda(e v)`(+,@(mapcar #'(lambda(r)(d r
v))(cdr e)))))(setf(get'*'d)#'(lambda(e v)`(*,e(+,@(mapcar
#'(lambda(r)`(*,(d r v)(expt,r -1)))(cdr
e))))))(setf(get'expt'd)#'(lambda(e v)`(*,e,(d`(*,(caddr
e)(log,(cadr e)))v))))For an explanation,
seehttp://www.cs.berkeley.edu/~fateman/papers/
deriv.pdfObviously that's a simple homework assignment... But,
what I need it for> is to do these functions: > power> +,*,-,/>
Exp (Although, perhaps I don't need Exp, I can just use (pow E
X)> Log... I dunno what I'm going to do about ts function
tho... Hmmm> But, I need Erf (The error function) But, I
suppose, derivative of> Erf is easy enough, to encode...
Actually, I can live with it,> if it doesn't differentiate Erf
out the box...You will have to add 1 line.Here's what I want to
do.> I want to integrate a function>
(Exp[((Log[X1/X0]-m)/sd)^2/2] Log[a X1 + b])/X1> (/ (* (exp (/
(pow (/ (- (log (/ X1 X0)) m) sd) 2) 2)) (log (+ (* a X1) b)))
X1) (It's the PDF of a lognormal distributed X1 from X0 * log
of a linear> function of X1...) (The actual function is a
little more complicated, but, ts is> the basic idea)I'm hoping
to try to use genetic programming to create a function who's>
derivative is the function above... Is ts feasible?Not really,
unless you like exponential, and possibly non-terminating
search. Is ts a good way> to approach ts problem of mine? So,
the fitness criteria would be> how far off the generated
function is from the one I'm asking for...And ts fitness
criterion is...?? How close is (x-1)*(x+1) to x^2-1?Ts problem
is known to be recursively undecidable. Look it up.(But, first,
I'd like some equivalent of freshmeat for open sourced stuff>
or cpan for perl stuff for lisp... Does such a beast
exist?)You mean a collection of programs written in lisp like
the CMU AI arcve? BannerjeeGood luck. Maybe you will come up
with some better ideas in the future.
===
Subject: Re: LISP
routines to do symbolic differentiation> You will have to add
1 line.Yep... (r 'erf '(/ (* 2 (exp (- (* x x))))
(sqrt(pi))))> And ts fitness criterion is...?? How close is
(x-1)*(x+1) to x^2-1?> Ts problem is known to be recursively
undecidable. Look it up.I underd... But, I've tried
Mathematica to integrate the function I have,and it doesn't
come back... I took that initially as meaning it was
effectivelyunsolvable... BUT, I came up with a set of
functions f(x)g'(x) such thatf(x)g'(x) + f'(x)g(x) wouldn't
symbolically integrate with Mathematica,if given in an
appropriate form, but, would symbolically integrate ifgiven in
another form. (at least it terminates quick... Ts onedidn't
even terminate in one form, but, in another form, solved
itpretty quickly...)Anyhow, the specifics of f(X) and g'(X)
that I mentioned above were f(X) = 4 3 X (3 (5 + ku) sd + 12
sd sk (m - Log[--]) - X0 2 X 2 6 (-3 + ku) sd (m - Log[--]) +
X0 X 4 X 3 (-3 + ku) (m - Log[--]) + 4 sd sk (-m + Log[--]) )
X0 X0 2 2 (m - Log[X/X0]) /(2 sd ) 5 / (24 E Sqrt[2 Pi] sd X)
(Basically that same tweak to the pdf that I mentioned
above)and g'(X) = Log[a X + b]Mathematica can't symbolically
integrate ts: ExpandAll(f(x)g'(x)+g(x)f'(x))(It can if, it's
not expanded... But, the fact that it can't do it, spellsto
me, that it's _possible_ for a function that Mathematica
claims to beunable to integrate, to in fact be integrable
analytically.)I underd that notng can absolutely guarantee an
answer... But,in the specific case you mention, I tnk I could
write sometng thatwould figure out that those two are the
same... (the heuristic I'm tnkingof would always _try_ to have
the lowest precedence operator at the outermostlisp expression.
So, always try to have sums of products...) In any case,whether
or not the heuristic works, all I'm hoping for from the GP
routine isa set of good _looking_ attempts... and, then I can
decide if that gives meany extra direction is all. Here's the
mathematica notebook at
http://www.hex21.com/~/mathematica_oddity/#relevantIf all ts
still isn't a good way of symbolically integrating F1[X]DG1[X]
(as defined in the link above), then I'dappreciate any pointers
to some good way of doing so... (I've alreadytried
Mathematica...)> You mean a collection of programs written in
lisp like the CMU AI arcve?> Good luck. Maybe you will come up
with some better ideas in the future.I hope so!--What do you
know about hell? Would you like me to show you? -- Lyta,
Babylon 5 PGP Key: http://www.hex21.com/~/-public.asc Key
fingerprint = 421D B4C2 2E96 B8EE 7190 A0CF B42F E71C 7FC3
AD96 SSH2 Key: http://www.hex21.com/~/-ssh2.pub SSH1 Key:
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http://www.hex21.com/~/-certificate.gif.cs256 Decrypt with
CipherSaber2 N=256, Password=WelcomeJedi! (No
quotes)
===
Subject: Re: LISP routines to do symbolic
differentiation> You will have to add 1 line.Yep...> (r 'erf
'(/ (* 2 (exp (- (* x x)))) (sqrt(pi))))And ts fitness
criterion is...?? How close is (x-1)*(x+1) to x^2-1?> Ts
problem is known to be recursively undecidable. Look it up.> I
underd... But, I've tried Mathematica to integrate the function
I have,> and it doesn't come back... I took that initially as
meaning it was effectively> unsolvable... BUT, I came up with
a set of functions f(x)g'(x) such that> f(x)g'(x) + f'(x)g(x)
wouldn't symbolically integrate with Mathematica,> if given in
an appropriate form, but, would symbolically integrate if>
given in another form. (at least it terminates quick... Ts
one> didn't even terminate in one form, but, in another form,
solved it> pretty quickly...> )Anyhow, the specifics of f(X)
and g'(X) that I mentioned above were f(X) = > 4 3 X> (3 (5 +
ku) sd + 12 sd sk (m - Log[--]) - > X0> > 2 X 2> 6 (-3 + ku)
sd (m - Log[--]) + > X0> > X 4 X 3> (-3 + ku) (m - Log[--]) +
4 sd sk (-m + Log[--]) )> X0 X0> > 2 2> (m - Log[X/X0]) /(2 sd
) 5> / (24 E Sqrt[2 Pi] sd X)> > (Basically that same tweak to
the pdf that I mentioned above)and g'(X) = Log[a X +
b]Mathematica can't symbolically integrate ts:>
ExpandAll(f(x)g'(x)+g(x)f'(x))(It can if, it's not expanded...
But, the fact that it can't do it, spells> to me, that it's
_possible_ for a function that Mathematica claims to be>
unable to integrate, to in fact be integrable analytically.)I
underd that notng can absolutely guarantee an answer... But,>
in the specific case you mention, I tnk I could write sometng
that> would figure out that those two are the same... (the
heuristic I'm tnking> of would always _try_ to have the lowest
precedence operator at the outermost> lisp expression. So,
always try to have sums of products...) In any case,> whether
or not the heuristic works, all I'm hoping for from the GP
routine is> a set of good _looking_ attempts... and, then I
can decide if that gives me> any extra direction is all.
Here's the mathematica notebook at>
http://www.hex21.com/~/mathematica_oddity/#relevantIf all ts
still isn't a good way of symbolically integrating>
F1[X]DG1[X] (as defined in the link above), then I'd>
appreciate any pointers to some good way of doing so... (I've
already> tried Mathematica...)You mean a collection of
programs written in lisp like the CMU AI arcve?> Good luck.
Maybe you will come up with some better ideas in the future.I
hope so!-- > What do you know about hell? Would you like me to
show you?> -- Lyta, Babylon 5 PGP Key:
http://www.hex21.com/~/-public.asc> Key fingerprint = 421D
B4C2 2E96 B8EE 7190 A0CF B42F E71C 7FC3 AD96> SSH2 Key:
http://www.hex21.com/~/-ssh2.pub> SSH1 Key:
http://www.hex21.com/~/-ssh1.pub> OpenSSH Key:
http://www.hex21.com/~/-openssh.pub> CipherKnight Seals:>
http://www.hex21.com/~/-seal.tar.bz2.cs256>
http://www.hex21.com/~/-seal.zip.cs256>
http://www.hex21.com/~/-certificate.gif.cs256> Decrypt with
CipherSaber2 N=256, Password=WelcomeJedi! (No quotes)I confess
I am a bit confused as to what exactly you did
usingMathematica. I'll make a few comments based on what I
have seen ints thread and the one at the URL given
above.First, at the URL you posted some definite integrals.
These may usemethods other than indefinite integration, and
moreover can spend timeattempting to assess conditions for
convergence. Hence the timings mayhave little to do with those
of the corresponding indefiniteintegrals. For example, you
have:ff[a_, b_, c_, d_, e_, f_, X_] := (a + b*X + c*X^2 +
d*X^3 + e*X^4 +f*X^5)* Exp[-(((X -
m)/sd)^2)/2]/(Sqrt[2*Pi]*sd)In the version I have (wch I tnk
behaves similarly to the currentstreet version), we get for
the indefinite integral:In[5]:=
InputForm[Timing[Integrate[ff[a, b, c, d, e, f, X]*((X
-m)/sd)^5, x]]]Out[5]//InputForm= {0.4200000000000014*Second,
-((x*(m - X)^5*(a + X*(b + X*(c + X*(d + X*(e + f*X))))))/
(E^((m - X)^2/(2*sd^2))*Sqrt[2*Pi]*sd^6))}For the definite
integral:In[6]:= InputForm[Timing[Integrate[ff[a, b, c, d, e,
f, X]*((X -m)/sd)^5, {X,-Infinity,Infinity},
Assumptions->sd>0]]]Out[6]//InputForm= {7.67*Second, 15*sd*(b
+ 2*c*m + m^2*(3*d + m*(4*e + 5*f*m)) + 7*(d + 2*m*(2*e +
5*f*m))*sd^2 + 63*f*sd^4)}Version 4.2 of Mathematica did
indeed hang on ts. But, as I noted,ts is unrelated to the
behavior for the indefinite integral (wchworks fine in that
version).For the integration in the present thread, I'm
guessing you want to dosometng
like:InputForm[Timing[Integrate[(Exp[((Log[X1/X0]-m)/sd)^2/2]*
Log[a*X1 + b])/X1, {X1,1,X0},
Assumptions->{sd>0,X0>1,Im[m]==0,a>0,b>0}]]]First, I'll note
that Mathematica does not do ts particularindefinite
integration. As you and Richard Fateman both note, it maywell
be the case that it can be done if the integrand given in
somedifferent mathematically equivalent form. Moreover, as
Richard Fatemansurmised, Mathematica does not have a full
implementation of the Rischmethod, hence one can indeed pose
problems for wch an elementaryantiderivative exists, but is
not found by Mathematica (though oftenthe special function
methods will find a non-elementary representationin such
cases).For the definite integral posed above, Mathematica also
does notnguseful. Offhand I do not know if ts indicates a bug
or if theintegration is simply beyond the technology we have
available. I planto look into it.I'm not sure what exactly you
have in mind to do from here. If it isto find antiderivatives
using genetic programming, it ain't gonna work(but no need to
take my word for that if you have available time andwant to
try it out).
===
Subject: Re: LISP routines to do symbolic
differentiation[deleted]> Version 4.2 of Mathematica did
indeed hang on ts. But, as I noted,> ts is unrelated to the
behavior for the indefinite integral (wch> works fine in that
version).Right... (I have 4.2, unfortunately can't quite
afford the upgrade justyet, but, your telling me that it can
solve certain tngs that 4.2 can'tBut, the reason why I needed
to have it integrate from -Infinity to Infinity,is because,
(in that ince) I have to compute the 5th moment of the
functionoverall, so I need it from -Infinity to Infinity...
Basically, if youlook at
http://www.hex21.com/~/mathematica_oddity/index.htmlat the
top, you'll see what I did... I made a polynomial adjustmentto
Exp[-z^2/2]/Sqrt[2Pi] * polynomial(z) such that
Integrate[f(z),{z,-Infinity,Infinity} == 1
Integrate[f(z)*z,{z,-Infinity,Infinity} == 0
Integrate[f(z)*z^2,{z,-Infinity,Infinity} == 1
Integrate[f(z)*z^3,{z,-Infinity,Infinity} == skewness
Integrate[f(z)*z^4,{z,-Infinity,Infinity} == kurtosisand ask
mathematica to solve for the coefficients of the
polynomial...Mathematica does that as you can see from that
url...> For the integration in the present thread, I'm
guessing you want to do> sometng like:>
InputForm[Timing[Integrate[(Exp[((Log[X1/X0]-m)/sd)^2/2]*>
Log[a*X1 + b])/X1, {X1,1,X0},>
Assumptions->{sd>0,X0>1,Im[m]==0,a>0,b>0}]]]It's _slightly_
off.. X1 should go from {X1,lo,} and the Assumptions would
be{X0>0,X1>0,(a*lo+b)>0,(a*+b)>0,sd>0,Im[m]==0}> First, I'll
note that Mathematica does not do ts particular> indefinite
integration. As you and Richard Fateman both note, it may>
well be the case that it can be done if the integrand given in
some> different mathematically equivalent form. Moreover, as
Richard Fateman> surmised, Mathematica does not have a full
implementation of the Risch> method, hence one can indeed pose
problems for wch an elementary> antiderivative exists, but is
not found by Mathematica (though often> the special function
methods will find a non-elementary representation> in such
cases).> For the definite integral posed above, Mathematica
also does notng> useful. Offhand I do not know if ts indicates
a bug or if the> integration is simply beyond the technology we
have available. I plan> to look into it.> I'm not sure what
exactly you have in mind to do from here. If it is> to find
antiderivatives using genetic programming, it ain't gonna
work> (but no need to take my word for that if you have
available time and> want to try it out).Well, no, the genetic
programming, is just a means to an end... What Ineed is to
integrate that function... Actually tho, the functionwith the
polynomial correction for skewness and kurtosis... How
it'ssolved... I don't really care that much... The trouble is
that numericalintegration of that integral is taking way too
long for me... That's whyI'm looking to symbolically integrate
it... (It takes too long, because,ts is actually a simpler
version, the real problem involves multipleX's, so it looks
like F[n_,regions_] := Sum[Integrate @@ Join[{Product[PDF[0,
1, sk, ku, (Log[Subscript[X, i]/Subscript[X, i - 1]] -
Subscript[m, i])/Subscript[sd, i]]/ (Subscript[X,
i]*Subscript[sd, i]), {i, 1, n}]* Log[1 + Sum[Subscript[a,
i]*Subscript[X, j, i] + Subscript[b, i], {i, 1, n}]]},
Table[{Subscript[X, i], Subscript[lo, j, i], Subscript[, j,
i]}, {i, 1, n}]], {j, 1, regions}] for different n's, and j's,
with n ranging fairly small (1-7) but j rangingfrom (2-10000 or
more) (I guess j has no upper limit really)I was hoping to
symbolically integrate it to speed up the calculationis all...
(PDF[0,1,sk,ku,Z] is the normal pdf times a polynomial chosen
such that
Integrate[PDF[0,1,sk,ku,Z]*Z^2,{Z,-Infinity,Infinity}]==sk and
Integrate[PDF[0,1,sk,ku,Z]*Z^3,{Z,-Infinity,Infinity}]==ku --
PGP Key: http://www.hex21.com/~/-public.asc Key fingerprint =
421D B4C2 2E96 B8EE 7190 A0CF B42F E71C 7FC3 AD96 SSH2 Key:
http://www.hex21.com/~/-ssh2.pub SSH1 Key:
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http://www.hex21.com/~/-openssh.pubCipherKnight Seals:
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CipherSaber2 N=256, Password=WelcomeJedi! (No
quotes)
===
Subject: Re: LISP routines to do symbolic
differentiation > BUT, I came up with a set of functions
f(x)g'(x) such that> f(x)g'(x) + f'(x)g(x) wouldn't
symbolically integrate with Mathematica,> if given in an
appropriate form, but would symbolically integrate if> given
in another form.For the sake of curiosity, how does
Mathematica compare to Macsyma init's ability to integrate ts
sort of tng?
===
Subject: Re: LISP routines to do symbolic
differentiation Mathematica's inability tofind a closed form
for an integral does not mean that the integralcannot be
expressed in closed form. You can study the variouscomponents
of the Risch integration procedure wch in someways provides a
decision for integrability, but that is subjectto the ability
to simplify expressions. Ts latter taskturns out to be
undecidable for even a modestly complicated domain(Daniel
Richardson, 1968), so even if Mathematica implementedthe Risch
'algorithm' it might not solve a problem posed in
anunanticipated form.It would probably also be a mistake to
believe that the Rischmethods are fully implemented in
Mathematica, though tsmight change from time to time.
Integration of special functions(like erf) might not use these
methods anyway.so: if Mathematica can't do an integral in
closed form, all youcan conclude is that it can't do that
integral in closed form.And if you simplified it differently,
perhaps it could do theintegral then. Or not.Same for Macsyma
and Maple and Axiom and Reduce and Mupad and...RJF>BUT, I
came up with a set of functions f(x)g'(x) such that>f(x)g'(x)
+ f'(x)g(x) wouldn't symbolically integrate with
Mathematica,>if given in an appropriate form, but would
symbolically integrate if>given in another form.> For the
sake of curiosity, how does Mathematica compare to Macsyma in>
it's ability to integrate ts sort of tng?
===
Subject: Re: LISP
routines to do symbolic differentiation: Mathematica's
inability to: find a closed form for an integral does not mean
that the integral: cannot be expressed in closed form.: You can
study the various: components of the Risch integration
procedure wch in some: ways provides a decision for
integrability, but that is subject: to the ability to simplify
expressions. Ts latter task: turns out to be undecidable for
even a modestly complicated domain: (Daniel Richardson, 1968),
so even if Mathematica implemented: the Risch 'algorithm' it
might not solve a problem posed in an: unanticipated
form.Daniel Richardson result is an artifact of s definition
of equalty ofexpressions. If you take different definition of
equality (used by Risch)and add an assumption about numbers
(no unexpected equalities between transcendental numbers) then
equality of elementary functions is decidable.The needed
assumption is a long ding open problem. : It would probably
also be a mistake to believe that the Risch: methods are fully
implemented in Mathematica, though ts: might change from time
to time. Integration of special functions: (like erf) might
not use these methods anyway.: so: if Mathematica can't do an
integral in closed form, all you: can conclude is that it
can't do that integral in closed form.: And if you simplified
it differently, perhaps it could do the: integral then. Or
not.The main point is that Risch methods have very gh
complexity, so even full implementation is expected to run out
of resources. On the other hand one can have four results:i)
integral doneii) out of resourcesiii) proven lack of
elementary antideriveiv) lack of elementary antiderive if the
number theoretic assumption is trueUnfortunatly, Mathematica
(and other programs) does not tell wch of ii), iii) or iv)
holds.Of course non-elementary functions like erf make tngs
more complicated,but if lump lack of apropriate algorithm with
lack of resources then stillyou have four outcames.-- ,
===
Subject: Re: LISP routines to do symbolic differentiation> :
Mathematica's inability to> : find a closed form for an
integral does not mean that the integral> : cannot be
expressed in closed form.: You can study the various> :
components of the Risch integration procedure wch in some> :
ways provides a decision for integrability, but that is
subject> : to the ability to simplify expressions. Ts latter
task> : turns out to be undecidable for even a modestly
complicated domain> : (Daniel Richardson, 1968), so even if
Mathematica implemented> : the Risch 'algorithm' it might not
solve a problem posed in an> : unanticipated form.Daniel
Richardson result is an artifact of s definition of equalty
of> expressions. If you take different definition of equality
(used by Risch)> and add an assumption about numbers (no
unexpected equalities between > transcendental numbers) then
equality of elementary functions is decidable.1. Assuming
sometng that you do not know is true is not the way to resolve
questions about decidability.> The needed assumption is a long
ding open problem. 2. I believe you are referring to
Schanuel's conjecture, but there is no expectation that ts
resolution will be easy.3. I do not know what you mean about
different definitions of equality, but it would be appropriate
for one newsgroup, sci.math.symbolic, to elaborate. There are
certainly issues like is (x-1)/(x^2-1) = 1/(x+1) considering
what happens at x=-1 or x=1. There are also functions that are
cont, but not necessarily the same cont, like
atan(x)+atan(1/x). Its derivative is zero, so it must be a
cont. Wch cont depends on whether x>0 or x<0.There are
functions that are zero except at an infinite number of
points.4. Integration in terms of elementary functions, or
elementary functions extended by some set of additional
functions defined by integrals, is essentially a parlor trick.
The real question of interest to people using or building
computer algebra systems is generally (a) definite
integration, perhaps symbolic in parameters, or (b) can you
find a form for the integral in terms of ANY expression, not
just elementary.I've written (actually, to sci.math.symbolic)
on why Risch integrationis not 'the solution' to ts,
interesting as it may seem to theoreticians.> >.. snip...The
main point is that Risch methods have very gh complexity, so >
even full implementation is expected to run out of
resources.Why do you say ts? Do you have any evidence from
some benchsfrom some computer algebra systems that suggest
they bog down becausethey are doing some integration using the
Risch algorithm? I havenever heard of any. People do not tend
to integrate arbitrarily large integrands, and so asymptotic
analysis is not particularly important. Even if it were, I see
no reason to tnk that the load onresources should be especially
worse than many other computations thatare routinely performed
on small to moderate expressions.Ts is not to say it easy. For
example, sparse polynomial division worst case takes
exponential time. Divide (x^(1000)-1) by (x+1). You get 1000
terms.In general, a division with input of size O(n) can
produce O(10^n) terms.So what? We don't say, Don't do
division, it can run out of resources> the other hand one can
have four results:i) integral done> ii) out of resources> iii)
proven lack of elementary antiderive> iv) lack of elementary
antiderive if the number theoretic assumption is
trueUnfortunatly, Mathematica (and other programs) does not
tell wch of > ii), iii) or iv) holds.(v) Error in
implementation resulting in an incorrect integral.(vi) Error
in implementation resulting in failure to integrate.(vii)
Incomplete implementation of Risch algorithm so integral not
found (ts is likely to be sometng the program can
report!)(viii) {QUITE LIKELY, I TNK} Failure of the related
simplification routines to find appropriate differential field
extensions in wch to express the integrand thereby displaying
the appropriate algebraic independence, and hence failing,
even though an answer might exist.(ix) integral done, but in a
form so peculiar as to be useless for any further work, using
(say) complex exponentials and algebraics when elementary
functions like cos and tan would do.Of course non-elementary
functions like erf make tngs more complicated,> but if lump
lack of apropriate algorithm with lack of resources then
still> you have four outcames.Most programmers would not lump
stack overflow with I forgot to write the programIf there are
further responses I suggest they go to sci.math.symbol
only.--> >
===
Subject: Re: LISP routines to do symbolic
differentiation: 1. Assuming sometng that you do not know is
true is not the way to : resolve questions about
decidability.You reduce problem that looks harder to a problem
that looks simpler. It is accepted way -- you do not solve the
whole problem, but it isstill definite progress.: > The needed
assumption is a long ding open problem. : 2. I believe you are
referring to Schanuel's conjecture, but there is no :
expectation that ts resolution will be easy.Yes.: 3. I do not
know what you mean about different definitions of equality, :
but it would be appropriate for one newsgroup,
sci.math.symbolic, to : elaborate. There are certainly issues
like is (x-1)/(x^2-1) = 1/(x+1) : considering what happens at
x=-1 or x=1. There are also functions that : are cont, but not
necessarily the same cont, like : atan(x)+atan(1/x). Its
derivative is zero, so it must be a cont. : Wch cont depends
on whether x>0 or x<0.: There are functions that are zero
except at an infinite number of points.Risch considers
differential fields composed of functions. It is
essentialytreating functions as formulas modulo simplification
laws. So (x-1)/(x^2-1)is equal to 1/(x+1). On the other hand
you can not tell what is the value of (x)^{1/2} (that is of
squre root) at x=1 -- squre root of x is treated as whole.
That approach is well suited to symbolic calculations,since it
sidesteps analytical difficulties due to brancng. Thereis a
theorem that you can map finitely generated differential field
intomeromorpc functions (even analytic, if you restict domain).
Howeversuch mapping is non-unique. I only skimmed Richardson
result, but AFAIR important part is thatyou can encode
diofantine equation into brancng behaviour of yourfunctions. :
4. Integration in terms of elementary functions, or elementary
functions : extended by some set of additional functions
defined by integrals, is : essentially a parlor trick. The
real question of interest to people : using or building
computer algebra systems is generally (a) definite :
integration, perhaps symbolic in parameters, or (b) can you
find a form : for the integral in terms of ANY expression, not
just elementary.: I've written (actually, to sci.math.symbolic)
on why Risch integration: is not 'the solution' to ts,
interesting as it may seem to theoreticians.Mathematica
_always_ give you a formula, it may be just a useless one. If
you want precise answer you must limit what expression you
acceptas an answer. One can invent a new usefull class of
expressions, butI do not expect current computer algebra
systems to do so. On the other hand knowing that integral is
non-elementary can help findinga usefull answer.: > The main
point is that Risch methods have very gh complexity, so : >
even full implementation is expected to run out of resources.:
Why do you say ts? Do you have any evidence from some benchs:
from some computer algebra systems that suggest they bog down
because: they are doing some integration using the Risch
algorithm? I have: never heard of any. People do not tend to
integrate arbitrarily large : integrands, and so asymptotic
analysis is not particularly important. : Even if it were, I
see no reason to tnk that the load on: resources should be
especially worse than many other computations that: are
routinely performed on small to moderate expressions.: Ts is
not to say it easy. For example, sparse polynomial division :
worst case takes exponential time. Divide (x^(1000)-1) by
(x+1). You : get 1000 terms.: In general, a division with
input of size O(n) can produce O(10^n) terms.: So what? We
don't say, Don't do division, it can run out of resourcesThe
point is that when you run program on a computer it does not
matterif problem is decidable or not. What matters is if the
program can handleyour question. If problem is decidable you
may still run out of resources(or the program may give you an
answer even for undecidable problem). In the other words:
there is no warranty. You may hope for the best (and you
frequently get it), but no warranty. Coming back to
integration, I do not have an example at hand. But the
integration algoritm in some cases have to handle
polynomialsof degree proportional to absolute values of
coefficients of your function.For transcendental functions
(logarithm included) those polynomials dependon multiple
variables. So, the algorithm is at least doubly exponential.If
your function contains irrational algbraic expressions then
reallyheavy macnery kicks in. Practically, if complexity is
exponential or bigger then pretty small inputs can be too
big.By the way, I was tnking of doing a simple implementation
of Rischalgorithm. However, I quickly realized that I will run
of memory on quite simple examples unless I implement a lot of
tricks to make intermediateexpressions smaller. : > the other
hand one can have four results:: > : > i) integral done: > ii)
out of resources: > iii) proven lack of elementary antiderive:
> iv) lack of elementary antiderive if the number theoretic
assumption is true: > : > Unfortunatly, Mathematica (and other
programs) does not tell wch of : > ii), iii) or iv) holds.: (v)
Error in implementation resulting in an incorrect integral.:
(vi) Error in implementation resulting in failure to
integrate.That is self-evident. When you write a textbook you
do not write Ts theorem is true unless I made a mistake. My
point was thattypical computer algebra system does not show
important information,even though the program have it. Claim
that there are no elementaryintegral gives some usefull info.:
(vii) Incomplete implementation of Risch algorithm so integral
not found : (ts is likely to be sometng the program can
report!): (viii) {QUITE LIKELY, I TNK} Failure of the related
simplification : routines to find appropriate differential
field extensions in wch to : express the integrand thereby
displaying the appropriate algebraic : independence, and hence
failing, even though an answer might exist.If you stay witn
elementary functions then there are only twopossibilites (for
full Risch):i) Schaunel conjecture is falseii) intermediate
expressions are too big : (ix) integral done, but in a form so
peculiar as to be useless for any : further work, using (say)
complex exponentials and algebraics when : elementary
functions like cos and tan would do.Risch algorithm gives
minimal differential field. AFAIK it is possible to modify
algorithm to give real answer if it exists. However, in
general the user have to transform the answer to a usefull
form --I tnk that the main problem is that algorithm gives
expanded formwch may be just too big.: > : > Of course
non-elementary functions like erf make tngs more complicated,:
> but if lump lack of apropriate algorithm with lack of
resources then still: > you have four outcames.: Most
programmers would not lump stack overflow with I forgot to
write : the programFor the user point of view it is the same:
the program can not do it,and quite different from: there are
no solutions.--
===
Subject: Re: LISP routines to do symbolic
differentiation<snip to the ability to simplify expressions.
Ts latter task> turns out to be undecidable for even a
modestly complicated domain<snip Same for Macsyma and Maple
and Axiom and Reduce and Mupad and...RJFI take it that the
and... followed by RJF means that you disagreewith Penrose on
humans not being bound by Godel's theorems? :-)-- Use of tools
distinguishes Man from Beast. And UNIX users from WINDOZE
lusers.
===
Subject: Re: LISP routines to do symbolic
differentiation> I'm hoping to try to use genetic programming
to create a function who's> derivative is the function
above... Is ts feasible? Is ts a good way> to approach ts
problem of mine? So, the fitness criteria would be> how far
off the generated function is from the one I'm asking for...>
(But, first, I'd like some equivalent of freshmeat for open
sourced stuff> or cpan for perl stuff for lisp... Does such a
beast exist?)Perl stuff for LISP?For Scheme code, wch may or
may not be easily translated to LISP, there's JACAL. Then
there's also a LISP mockup of Mathematica (cf.
http://http.cs.berkeley.edu/~fateman/mma.mailer -- the
download url is in the message).The genetic programming idea
sounds weird (searcng an infinite dimensional space with a
finite number of genes), but I suppose it's feasible provided
you don't expect an exact symbolic antiderivative, and you
have the right functions in your genetic space. But then, I
don't know much about genetic programming, so my opinion is
moot. In any case, I'd be interested to know how you set that
up.--
===
Subject: Re: LISP routines to do symbolic
differentiationmaxima.sourceforge.net> ...> I'm looking for a
lisp routine that will do symbolic differentiation> of a
function, given (obviously) an expression in prefix notation
and what> variable it is being differentiated against...
Sometng like> (differentiate '(* x x)) => (* 2 x)> Obviously
that's a simple homework assignment... But, what I need it
for> is to do these functions:> power> +,*,-,/> Exp (Although,
perhaps I don't need Exp, I can just use (pow E X)> Log... I
dunno what I'm going to do about ts function tho... Hmmm> But,
I need Erf (The error function) But, I suppose, derivative of>
Erf is easy enough, to encode... Actually, I can live with
it,> if it doesn't differentiate Erf out the box...> Here's
what I want to do.> I want to integrate a function>
(Exp[((Log[X1/X0]-m)/sd)^2/2] Log[a X1 + b])/X1> (/ (* (exp (/
(pow (/ (- (log (/ X1 X0)) m) sd) 2) 2)) (log (+ (* a X1) b)))
X1)> (It's the PDF of a lognormal distributed X1 from X0 * log
of a linear> function of X1...)> (The actual function is a
little more complicated, but, ts is> the basic idea)> I'm
hoping to try to use genetic programming to create a function
who's> derivative is the function above... Is ts feasible? Is
ts a good way> to approach ts problem of mine? So, the fitness
criteria would be> how far off the generated function is from
the one I'm asking for...> (But, first, I'd like some
equivalent of freshmeat for open sourced stuff> or cpan for
perl stuff for lisp... Does such a beast exist?)> Bannerjee>
--> The measure of love is what one is willing to give up for
it. --> Geoffrey Fielding - Pandora and the Flying Dutchman>
PGP Key: http://www.hex21.com/~/-public.asc> Key fingerprint =
421D B4C2 2E96 B8EE 7190 A0CF B42F E71C 7FC3 AD96> SSH2 Key:
http://www.hex21.com/~/-ssh2.pub> SSH1 Key:
http://www.hex21.com/~/-ssh1.pub> OpenSSH Key:
http://www.hex21.com/~/-openssh.pub> CipherKnight Seals:>
http://www.hex21.com/~/-seal.tar.bz2.cs256>
http://www.hex21.com/~/-seal.zip.cs256>
http://www.hex21.com/~/-certificate.gif.cs256> Decrypt with
CipherSaber2 N=256, Password=WelcomeJedi! (No
quotes)
===
Subject: About my research by support1.mathforum.org
(8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id
i0UE5Qa08714;not send the paper to referees for
considerations.Generally it was not suitable for their
Journal.Particularly the Applied Mathematics Journal insisted
that they areparticularly looking for the applications of
Mathematics.Initially I felt since the Bessel differential
equations are usedeverywhere, their Journal is the one.Well, a
lot of computations involved and I have combined my
newScientific computations (as two separate papers). Possibly
ts was the main reason for suitability. They just have togo
through the actual computations with possible programming.
These are concrete papers on new trigonometric Bessel
functions and wedo not have gamma and p functions as they
appear in Yn(t).We have new Bessel functions Mn(t) and Bn(t)
(named after myinitials).There is a beautiful application
relative to zeroes of Besselfunctions.All computations
justified with respect to old Bessel functions Jn(t)and Yn(t)
and all expansions of infinite series are matcng.We are
entering a new world of Mathematics and fundamental
decisionsare needed to be taken by editors.Eventually the new
science is here and I will write my lecture noteswhether a
paper is published or not.The paper for A class polynomial III
was sent to the Journal ofAlgebra.Ts is algebra of the 21st
century, full of solving quintic equationswith integrals and
differential equations and no group theory andGalois theory is
present.I hope the Journal of Algebra find it suitable for
their journal.
===
Subject: Re: About my researchThe following
is a second order differential equation resulted fromn=5 i.e.
a quintic solved in the class polynomial II .You can see Maple
cannot evaluate the solution for alpha (t)=t andbeta(t)=exp
(t)and many many more.I have all solutions as polynomial
solutions for all alpha(t) andbeta(t) independent of
integrals.Also I have solved the polynomial in the class for
all n, ts meansthat all differential equations associated (wch
all are second orderlinear differential equations for all n)
are solvable with nointegration, for all alpha(t) and beta(t).
Also the irreduciblepolynomials.Polynomials in the new science
are corner stone of solvingdifferential equations.Second order
linear differential equations are fundamental to studiesof
classical equations. Ts coupled with my Riccati
differentialequations creates significant advancements in
solving equations.How they can predict that future research
will not have significantuse of these equations?, when
computers cannot solve with theircurrent
algorithms.Dr.M.BastiThe Maple code, I hope you can read
it.DE5 :=
diff(diff(y(t),t),t)-(-6250*alpha(t)*beta(t)^2*diff(diff(beta(
t),t),t)+20*alpha(t)^5*beta(t)*diff(diff(alpha(t),t),t)-8*
alpha(t)^6*diff(diff(beta(t),t),t)-6250*beta(t)^2*diff(alpha(t
),t)*diff(beta(t),t)+6250*alpha(t)*beta(t)*diff(beta(t),t)^2-
50*alpha(t)^4*beta(t)*diff(alpha(t),t)^2+32*alpha(t)^5*diff(
alpha(t),t)*diff(beta(t),t)+15625*beta(t)^3*diff(diff(alpha(t)
,t),t))/(-6250*alpha(t)*beta(t)^2*diff(beta(t),t)+20*alpha(t)^
5*beta(t)*diff(alpha(t),t)-8*alpha(t)^6*diff(beta(t),t)+15625*
beta(t)^3*diff(alpha(t),t))*diff(y(t),t)+(-3125*diff(alpha(t),
t)*beta(t)^2*diff(diff(beta(t),t),t)-4*diff(alpha(t),t)*alpha(
t)^5*diff(diff(beta(t),t),t)+1250*diff(alpha(t),t)*beta(t)*
diff(beta(t),t)^2+14*diff(alpha(t),t)^2*alpha(t)^4*diff(beta(t
),t)+4*diff(beta(t),t)*alpha(t)^5*diff(diff(alpha(t),t),t)+
3125*diff(beta(t),t)*beta(t)^2*diff(diff(alpha(t),t),t)-20*
diff(alpha(t),t)^3*beta(t)*alpha(t)^3+250*diff(beta(t),t)^3*
alpha(t))/(-6250*alpha(t)*beta(t)^2*diff(beta(t),t)+20*alpha(t
)^5*beta(t)*diff(alpha(t),t)-8*alpha(t)^6*diff(beta(t),t)+
15625*beta(t)^3*diff(alpha(t),t))*y(t);
===
Subject: Re: About
my researchHere we go again... Basti trumpets about all these
solutions, butforgets that nickpicking little detail: showing
just one! No wonderthe editors of these journals are probably
using s submissions towrap fish in.Basti, you need to get
together with . If you twopartnered up you could really churn
out some work!Caesar Garcia< UNSUBTIATED CLAIMS >
===
Subject:
Re: About my researchThe solutions and purposes are all
explained in the paper and thesequence of papers.comes into
existence,Ask the question from the mediocre editors and
referees.
===
Subject: Re: About my research>The solutions and
purposes are all explained in the paper and the>sequence of
papers.>comes into existence,>Ask the question from the
mediocre editors and referees.> If you believe you are not
being heard properly by editors and referees,completely
unmathematical, you will be seen. Perhaps ask the audience wch
journal would be best for a write-up(and have a draft write-up
ready for those who are interested).Listen carefully to their
comments.-- Adams served two terms as Vice President and one
as President, but lostreelection. Later s son became President
despite losing the popular vote.That son lost s reelection
attempt badly. Now story is repeating itself.
===
Subject: Re:
About my researchI had previously asked for a copy of the
papers, butgot no response.If the referees read any of the
other postings I maderegarding your previous claims, perhaps
they recognizedthat the same refutations I supplied then,
apply now as well.You will recall, for example, the claim that
a tn tubeof functions existed outside the general solution
ofthe ODE. In fact, upon competent examination, thealleged tn
tube disappeared, because of your failureto properly simplify
2 distinct forms of an expression.Not being able to directly
transform one to the other,you claimed that they were
different. I took the derivativeof the difference, simplified
that derivative to 0, andthus the difference is cont. For one
value of theindependent variable, the difference is 0, and
hence isalways 0, so the 2 forms are the same expression.In
other cases, you supplied answers wch failed toverify.If you
can't supply a sample result now for testing,why should anyone
believe your claims, wch in thepast have been found to be the
results of incorrectreasoning (and/or wishful tnking)? Why
would youassume that the editors are mediocre? Therefutation I
have provided to your ownreasoning doesn't make me mediocre,
does it?Claiming that phenomena are described by Riccati
equations is the same asclaiming that they are describedby 2nd
order differential equations, as one form canbe turned into the
other by a change of variables. It istrue that some features
become more prominent in oneform or the other, and that
numerical solutions can benefitfrom certain of the forms. But
you are still looking at thesame results.> The solutions and
purposes are all explained in the paper and the> sequence of
papers.> comes into existence,> Ask the question from the
mediocre editors and referees.> >
===
hjSubject: Re: About my
researchWhat is the solution for y(t) expressed as?What is the
purpose of having such convolutedcoefficients?> The following
is a second order differential equation resulted from> n=5
i.e. a quintic solved in the class polynomial II .> You can
see Maple cannot evaluate the solution for alpha (t)=t and>
beta(t)=exp (t)and many many more.> I have all solutions as
polynomial solutions for all alpha(t) and> beta(t) independent
of integrals.> Also I have solved the polynomial in the class
for all n, ts means> that all differential equations
associated (wch all are second order> linear differential
equations for all n) are solvable with no> integration, for
all alpha(t) and beta(t). Also the irreducible> polynomials.>
Polynomials in the new science are corner stone of solving>
differential equations.> Second order linear differential
equations are fundamental to studies> of classical equations.
Ts coupled with my Riccati differential> equations creates
significant advancements in solving equations.> How they can
predict that future research will not have significant> use of
these equations?, when computers cannot solve with their>
current algorithms.> > Dr.M.Basti> The Maple code, I hope you
can read it.> DE5
:=diff(diff(y(t),t),t)-(-6250*alpha(t)*beta(t)^2*diff(diff(
beta(t),t),t)+20*alpha(t)^5*beta(t)*diff(diff(alpha(t),t),t)-8
*alpha(t)^6*diff(diff(beta(t),t),t)-6250*beta(t)^2*diff(alpha(
t),t)*diff(beta(t),t)+6250*alpha(t)*beta(t)*diff(beta(t),t)^2-
50*alpha(t)^4*beta(t)*diff(alpha(t),t)^2+32*alpha(t)^5*diff(
alpha(t),t)*diff(beta(t),t)+15625*beta(t)^3*diff(diff(alpha(t)
,t),t))/(-6250*alpha(t)*beta(t)^2*diff(beta(t),t)+20*alpha(t)^
5*beta(t)*diff(alpha(t),t)-8*alpha(t)^6*diff(beta(t),t)+15625*
beta(t)^3*diff(alpha(t),t))*diff(y(t),t)+(-3125*diff(alpha(t),
t)*beta(t)^2*diff(diff(beta(t),t),t)-4*diff(alpha(t),t)*alpha(
t)^5*diff(diff(beta(t),t),t)+1250*diff(alpha(t),t)*beta(t)*
diff(beta(t),t)^2+14*diff(alpha(t),t)^2*alpha(t)^4*diff(beta(t
),t)+4*diff(beta(t),t)*alpha(t)^5*diff(diff(alpha(t),t),t)+
3125*diff(beta(t),t)*beta(t)^2*diff(diff(alpha(t>
),t),t)-20*diff(alpha(t),t)^3*beta(t)*alpha(t)^3+250*diff(beta
(t),t)^3*alpha(t>
))/(-6250*alpha(t)*beta(t)^2*diff(beta(t),t)+20*alpha(t)^5*
beta(t)*diff(alpha(>
t),t)-8*alpha(t)^6*diff(beta(t),t)+15625*beta(t)^3*diff(alpha(
t),t))*y(t);> >
===
Subject: Re: About my researchLeo your
statements are only good for layman. I have been working
onthese topics for over 20 years, I consider you a kid in
mathematicsand you do not know what you are talking about.No
scientific work will be presented here, I have done a lot.
===
Subject: Re: About my researchRead very carefully what I
had said in my postings.An example of one or two, wch I am not
even sure had beenaccomplished well, will not substitute for
the phenomena, wch I haddescribed.Once ts research is
developed you have ample times to expressyourself in the
seminars and publish what you have been saying.Please relax
and I just wanted to say that here is another Universe
inmathematics and until you are in it you cannot see the
galaxies.
===
Subject: Re: About my research / suggestion for
refereeingThere are many many journals in mathematics. Dr.
Bastihas chosen some of the most prestigious ones in wchto try
publish s results.I suggest that he find some other journals,
typicallypublished for profit by various companies, or
innon-Western countries, who may havedifferent operating
rules. Some encourage a writerto suggest referees. Thus if Dr.
Basti can forward (say)three academic mathematicians' names to
the editor,(or to one of the associate editors)the paper will
probably be sent to one or more ofthose suggested referees.It
may be sent to other reviewers chosen bythe editor, or not.
And the editor will presumablyread it as well.Since these
papers are published --for a profit-- thetendency of the
publishers is to accept papers witha lower threshold. There
is, at least in my mind,a erarchy of such journals. Some are
pretty good.Some are mixed. Some are worse. (Committees
evaluatingcandidates for tenure sometimes don't underd ts,to
the benefit of poorly-qualified candidates..)Anyway, for these
journals it then becomes important for Dr. Bastito identify
some experts -- in the area of differentialequations,
presumably-- who he tnks will be willing toserve as a referee
for s papers and who might sayts should be published.Good
luck.
===
Subject: Re: About my researchRead very carefully what
I had said in my postings.An example of one or two, wch I am
not even sure had beenaccomplished well, will not substitute
for the phenomena, wch I haddescribed.Once ts research is
developed you have ample times to expressyourself in the
seminars and publish what you have been saying.Please relax
and I just wanted to say that here is another Universe
inmathematics and until you are in it you cannot see the
galaxies.By the way mediocrity will not be measured by
publications.Prof.Shu is a Prof. At Brown University and
editor of severalJournals, with 250 or more publications.You
can see that how profound plosopcal differences we have.He
believes that mainly most of the differential equations
inapplications do not have polynomial solutions and I believe
the naturehas first structured differential equations based on
polynomials.Note: sometimes Google will confirm posting but
apparently the issuewill not be recorded properly (ts is the
second time I am posting).Normally the postings will be seen
almost immediately on my AOLNewsgroup.
===
Subject: Re: About my
researchIf my competent refutation of your incompetent efforts
and misstatementsin numerous prior postings qualify me as a
layman, then what appellationwould you apply to yourself?If
you tnk my efforts are of so little value, then refute them
with theevidence I have requested, namely, your claimed
solution. We will thenbe able to test it and see if there is
some merit to it.Refusing to supply a copy of the paper for me
to review and refusing topost your answer for the problem you
posted does not give me confidence.You may be able to fool a
busy referee, but I have dissected yourmis-reasoningbefore.It
does not matter if you toiled for 10,000 years on a mistake.
Correct it.As a kid in mathematics you should be aware that I
edited the DOE-Macsymaversion for many years, correcting many
kinds of errors in the derivationsof specialfunction work, for
example, and rewriting the ode solvers.> Leo your statements
are only good for layman. I have been working on> these topics
for over 20 years, I consider you a kid in mathematics> and you
do not know what you are talking about.> No scientific work
will be presented here, I have done a lot.> >
===
Subject:
About my research by support1.mathforum.org (8.11.6/8.11.6/The
Math Forum, $Revision: 1.9 primary) id i0UF7sm14068;newsgroup
(Math.Froum),(I believe I have twice attempted).also to
Google.
===
Subject: About my researchnot send the paper to
referees for considerations.Generally it was not suitable for
their Journal.Particularly the Applied Mathematics Journal
insisted that they areparticularly looking for the
applications of Mathematics.Initially I felt since the Bessel
differential equations are usedeverywhere, their Journal is
the one.Well, a lot of computations involved and I have
combined my newScientific computations (as two separate
papers).Possibly ts was the main reason for suitability. They
just have togo through the actual computations with possible
programming.These are concrete papers on new trigonometric
Bessel functions and wedo not have gamma and p functions as
they appear in Yn(t).We have new Bessel functions Mn(t) and
Bn(t) (named after myinitials).There is a beautiful
application relative to zeroes of Besselfunctions.All
computations justified with respect to old Bessel functions
Jn(t)and Yn(t) and all expansions of infinite series are
matcng.We are entering a new world of Mathematics and
fundamental decisionsare needed to be taken by
editors.Eventually the new science is here and I will write my
lecture noteswhether a paper is published or not.The paper for
A class polynomial III was sent to the Journal ofAlgebra.Ts is
algebra of the 21st century, full of solving quintic
equationswith integrals and differential equations and no
group theory andGalois theory is present.I hope the Journal of
Algebra find it suitable for their journal.
===
Subject: Re:
About my researchI would like to thank Mr. Montgomery's
comments.The nature of research is so addressing some very
classical issuessuch as new methods of solutions of Bessel and
new methods ofsolutions of polynomials and Riccati.As you know
I have posted enough materials for a few years here andnow I
have reached into presenting the issues in publications.I have
my own options to write my lecture notes and dessiminate
itsomehow; I hope that ts is not the only avenue for me.I have
new mathematical sciences in hand, and I underd all theproblems
of new science in process.considerations.Journal of Algebra.I
have a lot more papers if I can publish some.
===
Subject: Re:
About my researchPossibly you are wondering why suddenly I
have been talking about newmethods of solving polynomials,
differential equations, integrals andBessel functions, etc.The
answer is that about 23 years ago I had decided to devote
mylifetime research on exact solutions of Riccati
differentialequations.It turns out that the nature has
structured its most fundamentalphenomena witn the Riccati
differential equations.The reason that others in the past did
not obtain these results wasbecause their research originated
from other sources particularly withrespect to
polynomials.Plosopcally I believe that the nature structured
differentialequations based on polynomials (in its fundamental
characteristic).I have the acces to the main source now and you
can too if youconsider ts reseach.
===
Subject: Re: About my
researchRead very carefully what I had said in my postings.An
example of one or two, wch I am not even sure had
beenaccomplished well, will not substitute for the phenomena,
wch I haddescribed.Once ts research is developed you have
ample times to expressyourself in the seminars and publish
what you have been saying.Please relax and I just wanted to
say that here is another Universe inmathematics and until you
are in it you cannot see the galaxies.By the way mediocrity
will not be measured by publications.Prof.Shu is a Prof. At
Brown University and editor of severalJournals, with 250 or
more publications.You can see that how profound plosopcal
differences we have.He believes that mainly most of the
differential equations inapplications do not have polynomial
solutions and I believe the naturehas first structured
differential equations based on polynomials.
===
Subject: Re:
About my researchI would like to add to my previous memo
regarding the selection ofreferees.Certainly the Journals can
have their own editors and referees, butexternal referees can
be appointed.The Journals can have their criteria of selection
process for theexternal examiners.papers.A powerful new science
is here and I hope we finally settle the minordifferences and
let the new science to flourish.
===
Subject: Re: About my
researchYou all know the journals for wch I have submitted my
papers.The associated editors are listed on the journals and
you may suggestany comments you may have to me, in the
newsgroup or directly to theeditors in cef or to the
colleagues of them.The new science is growing since the last
20 years and the public andmathematicians must have access to
ts dynamic science.I hope that the editors realize their
responsibilities to themathematicians, scientists and the
public at large.As usual I am continuing my research in ts
universe of mathematics.
===
Subject: Re: About my research for
the note by R.Fateman. It is certainly a good suggestionto
have selection of referees by myself or others.submissions. As
I see ts is day 23 such that still they are lookingfor
appointment of associate editors to one of my papers. Looks
likethe issue of referees is possibly of some concern.or any
other Journals for wch I have submitted papers can accept
anoutside list of referees, then I will notify the readers of
tsnewsgroup for an appropriate input.I hope that they can
underd that ts is a very unconventionalscientific paper and
thus an unusual solution is needed.If I hear any more
suggestions from the corresponding Journals, I willlet you
know.
===
Subject: Maple & Mathematica packages, Math ArtsNew
Maple and Mathematica packages on Graph Tree
sitehttp://www.graphtree.com/1. differential geometry
calculations2. polynomial approximations for LDE's and
functionsMath Arts:1. Screensavers2.
Wallpapers--Norb
===
Subject: What is the difference between
Derive, Maple, Mathematica, MathCad, and other mathematical
software?What is the difference between Derive, Maple,
Mathematica, MathCad,and other mathematical
software?
===
Subject: found a program for Mathcad to Latex
conversion by support1.mathforum.org (8.11.6/8.11.6/The Math
Forum, $Revision: 1.9 primary) id i0VI8Yj14975;I somebody
(apart from me) is still interested in converting Mathcadto
Latex: You can do it with MathParser
(http://www.tilman.de/mathparser/ ) if you export your Mathcad
documentto MathML first.Greets Emil
===
Subject: Re: hmmDavid
Wilkinson pravi:> >so where does x^y = y^x when x > 0 and y >
0?>joex = y = 1 ?x = y = whatever?--
===
Subject: Re: Maple
libraries by support1.mathforum.org (8.11.6/8.11.6/The Math
Forum, $Revision: 1.9 primary) id i11IpVL04175;document as our
we began to figure ts out. It is at:You may find the following
helpful.http://www.upscale.utoronto.ca/GeneralInterest/
Harrison/Maple/MapleLibs.html
===
Subject: Wch is better at
plotting 3D vector fields? Derive, Maple, Mathematica,
MathCad, other mathematical software?Wch is better at plotting
3D vector fields? Derive, Maple,Mathematica, MathCad, other
mathematical software?