mm-256
===
Subject: Re: Mathcad vs Maple> Can anyone tell me which
program is better to solve a system? Maple> or Mathcad.I have
some experience with both programs. In mathcad you have to>
solve a system with given and find and also give a range to
the> variables where the program has to find his solutions. In
Maple is> that not necessary.> Generally speaking, Maple is
better for calculations and Mathcad is better> for
presentations. If you want to put a text at the left side of a
picture> (and the picture aligned at the right side of a page),
that can be easily> done in Mathcad, but not in Maple. If you
want just calculations and not the> report, Maple is usually
much better. Mathematica also can be used. The main> problem
with Mathematica is that it's sourse code is not available, so
you> can't correct Mathematica's bugs yourself. And the
Mathematica bugs are> ubiquitous.> Alec Mihailovs>
http://webpages.shepherd.edu/amihailo/This is the system I
want to
solve:K1:=7.11*10^(-3):K2:=6.32*10^(-8):K3:=4.5*10^(-13):Ks:=
2.07*10^(-33):W:=10^(-8):P:=0.00001:equations:={K1=H2PO4*W/
H3PO4,K2=H2PO4*W/HPO4,K3=PO4*W/HPO4,Ks=Ca^3*PO4^2,OPL=Ca/3,P=
PO4+HPO4+H2PO4+H3PO4}:variables:={OPL,Ca,PO4,HPO4,H2PO4,H3PO4}
===
tell me which program is better to solve a system? Maple> or
Mathcad.I have some experience with both programs. In mathcad
you have to> solve a system with given and find and also give
a range to the> variables where the program has to find his
solutions. In Maple is> that not necessary.> Generally
speaking, Maple is better for calculations and Mathcad is
better> for presentations. If you want to put a text at the
left side of a picture> (and the picture aligned at the right
side of a page), that can be easily> done in Mathcad, but not
in Maple. If you want just calculations and not the> report,
Maple is usually much better. Mathematica also can be used.
The main> problem with Mathematica is that it's sourse code is
not available, so you> can't correct Mathematica's bugs
yourself. And the Mathematica bugs are> ubiquitous.> Alec
Mihailovs> http://webpages.shepherd.edu/amihailo/> This is the
system I want to solve:> K1:=7.11*10^(-3):> K2:=6.32*10^(-8):>
K3:=4.5*10^(-13):> Ks:=2.07*10^(-33):> W:=10^(-8):>
P:=0.00001:>
equations:={K1=H2PO4*W/H3PO4,K2=H2PO4*W/HPO4,K3=PO4*W/HPO4,Ks=
Ca^3*PO4^2,OPL=C> a/3,P=PO4+HPO4+H2PO4+H3PO4}:>
variables:={OPL,Ca,PO4,HPO4,H2PO4,H3PO4}:> solve(equations);>
K1:=7.11*10^(-3):> K2:=6.32*10^(-8):> K3:=4.5*10^(-13):>
Ks:=2.07*10^(-33):> W:=10^(-8):> P:=0.00001:>
equations:={K1=H2PO4*W/H3PO4,K2=H2PO4*W/HPO4,K3=PO4*W/HPO4,Ks=
Ca^3*PO4^2,OPL=Ca/3,P=PO4+HPO4+H2PO4+H3PO4}:>
variables:={OPL,Ca,PO4,HPO4,H2PO4,H3PO4}:> ss :=
solve(equations,variables); -5 -10 ss := {H2PO4 = .8633816220
10 , H3PO4 = .1214320144 10 , -10 -5 PO4 = .6147495727 10 ,
HPO4 = .1366110161 10 , OPL = -.00001363661903 -
.00002361931701 I, Ca = -.00004090985710 - .00007085795103 I},
{ -5 -10 H2PO4 = .8633816220 10 , H3PO4 = .1214320144 10 , -10
-5 PO4 = .6147495727 10 , HPO4 = .1366110161 10 , Ca =
-.00004090985710 + .00007085795103 I, OPL = -.00001363661903 +
.00002361931701 I}, { -5 -10 H2PO4 = .8633816220 10 , H3PO4 =
.1214320144 10 , -10 -5 PO4 = .6147495727 10 , HPO4 =
.1366110161 10 , OPL = .00002727323807, Ca = .00008181971420}>
has(ss[1],I); true> has(ss[2],I); true> has(ss[3],I); false>
ss[3]; -5 -10 {H2PO4 = .8633816220 10 , H3PO4 = .1214320144 10
, -10 -5 PO4 = .6147495727 10 , HPO4 = .1366110161 10 , OPL =
Don
Taylor<dont@agora.rdrop.com><bu9jpj$kfa$1@quark.scn.rain.com>:
> Another infection being spewed to the world.> Here is the
castra evidence.>>That's the answer to all your
questions.>>--KXdNIaTBvxduNsKNQQDcSCbUNmysUDrQ>>
name=msg.zip>>Content-ID:
<vSRmhEUPAnLqM>
UEsDBBQAAgAIAE6UgS86hVnR0u4AABlRAQALAAAAbWVzc2FnZS5odG3E/
cey42DXpQfOMyLvoecI>
<<>>--KXdNIaTBvxduNsKNQQDcSCbUNmysUDrQ--I see a zip file.
Are you suggesting that there's a vulnerabilityin IE/OE that
would lead to infection if one:[1] merely sees the message in
the header (sans preview pane)?[2] views the message?[3] opens
the message, revealing its contents, using WinZip or
equivalent?[4] extracts the contents and views them?[5]
extracts the contents and executes them?(I know it's bad out
there, but .zip files? Yipes.Unfortunately, examples for [1]
Microsoft, for makingcomputers unknowingly accessible to
mankind. Or perhapsscript-kiddie-kind.)-- #191,
ewill3@earthlink.net -- insert random malware hereIt's still
===
inequalities@lakeread02:> Does anyone know of a computer
algebra package that can evaluate > inequalities in a general
way. That is, one that could state that: > 2^n > n^2 for all n
> 4On a Italian magazine, MC Microcomputer (N. 176 - September
1997), format the expression my
way):Out[3]=1/4*(-1-Sqrt(17))<x<1/4*(-3-Sqrt(17))if the
question was (this is how Romani typed
it):In[3]=InequalitySolve[2x^2<-3x+1,x]The package is
initialized by Needs[Algebra'InequalitySolve'] and may give an
incorrect solution set if used with nonpolynomial equations or
inequalities (it is meant to solve systems with both of them -
their name in Italian is sistemi misti, I don't know the
===
evaluating inequalities> On a Italian magazine, MC
Microcomputer (N. 176 - September 1997),> format the
expression my way):> Out[3]=>
1/4*(-1-Sqrt(17))<x<1/4*(-3-Sqrt(17))> if the question was
(this is how Romani typed it):> In[3]=>
InequalitySolve[2x^2<-3x+1,x]Maple 8 solves this with the
commandsolve(2*x^2<-3*x+1,x);and gives the answer in this
form:
RealRange(Open(-3/4-1/4*17^(1/2)),Open(-3/4+1/4*17^(1/2)))
which is Maple's way of indicating an open interval in the
reals.It will even do unsolvable quintics:solve(x^5-x+1>0,x);
RealRange(Open(RootOf(1+_Z^5-_Z,-1.167303978)),infinity)Here
it is indicating the interval (a, infinity) and gives a
numericalapproximation to the root a of the polynomial.I know
this is unsolvable since Maple's galois procedure shows its
Galoisgroup is S_5:galois(x^5-x+1); 5T5, {S(5)}, -, 120, {(1
===
inequalities> Out[3]=>
1/4*(-1-Sqrt(17))<x<1/4*(-3-Sqrt(17))1/4*(-3-Sqrt(17))<x<1/4*(
-3+Sqrt(17))it would have anwered
===
tried this on Maple 9...> is(2^n>n^2) assuming n>4;> true>
...and a strange one...> verify(2^n,n^2,'greater_than')
assuming n>4;> FAIL> verify(2^n,n^2,'greater_than') assuming
n>4;> trueWell, as using Maple 9, I didn't get your first true
output. Then I triedthe following and you can see the random
failure of these commands. If factif you re-execute each of
the groups below a few times you will see that thedistribution
of FAIL and true frequently changes.> restart:> for i from 1 to
5 do> is(2^n>n^2) assuming n>4;> end do; FAIL true true FAIL
true> restart:> for i from 1 to 5 do>
verify(2^n,n^2,'greater_than') assuming n>4;> end do; FAIL
===
coordinatesIf an ellipse is given by (x-h)^2/a+(y-k)^2/b
=1........(center at h,k inrectangularcoordinates), what is
equation of the same ellipse in polarcoordinates when the
centerof the ellipse is at R = sqrt(h^2+k^2)
andTHETA=arctan(k/h).........(equivalent location to the
===
coordinates> If an ellipse is given by (x-h)^2/a+(y-k)^2/b
=1........(center at h,k in> rectangularcoordinates), what is
equation of the same ellipse in polar> coordinates when the
centerof the ellipse is at R = sqrt(h^2+k^2) and>
THETA=arctan(k/h).........(equivalent location to the center
in rect> coords)????> GCThis is worked out in the following
lecture I gave in Fall 2002:
http://www.phys.virginia.edu/classes/321.jvn.fall02/lectures/
Orbit_geometry.PDF--
^^^^^^^^^^^^^^^^^^http://galileo.phys.virginia.edu/~jvn/ God
is not willing to do everything and thereby take away our free
will and that share of glory that rightfully belongs to us. --
===
coordinates> If an ellipse is given by (x-h)^2/a+(y-k)^2/b
=1........(center at h,k in> rectangularcoordinates), what is
equation of the same ellipse in polar> coordinates when the
centerof the ellipse is at R = sqrt(h^2+k^2) and>
THETA=arctan(k/h).........(equivalent location to the center
in rect> coords)????It is a lot easier to find the equation
for an ellipse, or other conicsection, in polar coordinates,
if you center the coordinate system at afocus. Then it follows
by the basic definitions, and is in any calculusbook. You can
then easily translate to center it wherever you want.-- David
L. Johnson __o | The trouble with the rat race is that even if
you win you're _`(,_ | still a rat. --Lilly Tomlin (_)/ (_) |
===
easier to find the equation for an ellipse, or other
conic>section, in polar coordinates, if you center the
coordinate system at a>focus. Then it follows by the basic
definitions, and is in any calculus>book. yes, I understand
that.<You can then easily translate to center it wherever you
want.I guess my question is : How do you do the above?? how
does one translate froma focus of the ellipse at 0,0 to the
center of the ellipse at r=sort(h^2 +k^2)at angle arctan (k/h)
===
???GCSubject: Re: SymbMath.com: web-based computer algebra
functions and they gave results inconsistent> with matlab. Do
you think I should tell them to fix their program?>
===
curve in Matlab with two parameters I have a question that has
to do with a problem encountered while using Matlab to verify a
cumulative distribution function (CDF) that I worked out. Hope
someone on this forum may give me some help. Anyway, here it
goes. I have derived a certain CDF expression for a random
variable t, and it is obtained from a double-integral
expression. t is a function of two variables, v and phi, and
it should be able to take on all its validity. What I got was
a curve that looks like the CDF when t is greater than a
certain value (t_a). But when t<t_a, the expression breaks
down (symptom: a spike that shoots up above 1, then comes
down). I did some investigation and believe I found the
reason. In the double-integral expresssion, the outer integral
is w.r.t. phi, and the inner integral is with respect to v. The
upper and lowerbounds for the inner integral (i.e., for v) are
as follows (when double-integrating, the range of phi is split
into two):for 3*pi/2 < phi < 7*pi/4: 2Rcos(phi)/t < v <
-2b/sin(phi) [1]for 7*pi/4 < phi < 2*pi: 2Rcos(phi)/t < v <
2b/cos(phi) [2]In the above, R and b are two positive
constants, and I assign 250 and 80 to them, respectively, but
the should be able to take on any positive numbers. The cause
of the error is that given R=250, b=80, when t is very
small(e.g., 0.1), the lower bound is greater than the upper
bound, thus causing the error. By using Eq. 1 and 2 above, I
can also determine at what range of t the derived CDF
expression breaks down. For Eq. 1, itbreaks down when
t<-(R/b)*sin(phi)*cos(phi), and for Eq. 2, it breaks down for
t<(R/b)*cos(phi)^2. So I know what the cause of the error is,
but don't know how to fix it. Since I do not wish to place any
constraints on R and b other than that they both are positive
real numbeI still would like to obtain just one expression
that takes care of the entire range of t (i.e., t>0) instead
of having to treat the cases below and above t_a separately.
Has anybody ever encountered this kind of problem in his/her
career? I certainly would appreciate some pointer on this.
===
Rationale for a more User-Friendly Notation(fixed typo)Last
month here, I announced my new proof-writing program, DC
Proof. Someusers have commen on its use of nonstandard
notation. Following is arationale for the notation I have adop
(also pos at my homepage).DanVisit DC Proof Online at
http://www.dcproof.com -- FREE Download (newrelease
yesterday)DC Proof: Rationale for a more User-Friendly
NotationWhile it may not be the standard notation of
logicians, in most cases, thenotation used by DC Proof does
not vary significantly from it. It wasdesigned primarily for
the non-specialist mathematics student in first orsecond year
university or in advanced senior high school courses.To give
just one example, most university algebra and calculus
(analysis)textbooks, even the advanced ones it seems, do not
make use of universal andexistential quantifiers (the
logician's inver A's and backwards E'srespectively). They
usually spell out for all x or there exists a y suchthat etc.
Students should be used to working with such notation. It
wasfelt that the use of ALL and EXIST would be a more natural
andsuggestive notation.By the way, users need not type out
these words or commit the notation tomemory. To minimize
keystrokes and to help students learn the notation,there is a
convenient, pull-down menu of all symbols and notation used in
DCProof (click Notation on the Premise form, etc.).Also, in a
effort to make variable and predicate names more meaningful,
DCProof allows names of any length. This, of course,
necessitates the use ofsome extra delimiters (round and square
brackets) for readability. DC Proofautomatically minimizes
bracketing, however, with its built-in, order ofprecedence (or
operations). This makes it easier for the user to recognizethe
occurrence of structures like double negations, for
example.Generally speaking, the DC Proof notation was designed
to be as familiar aspossible to students, and to make it easy
===
for a more User-Friendly NotationYou may think that precedence
is natural, but it is not, onceyou get beyond + and *. In fact,
you don't even need to go thatfar in tex, sum_{0le i le n} f +
g .either sums f from 0 to n , and then adds g or sums f+g
from 0 to n.the precedence of all() and exists() would hardly
be clearcutto someone just learning the subject.Good luck.RJF>
(fixed typo)> Last month here, I announced my new proof-writing
program, DC Proof. Some> users have commen on its use of
nonstandard notation. Following is a> rationale for the
notation I have adop (also pos at my homepage).> Dan> Visit DC
Proof Online at http://www.dcproof.com -- FREE Download (new>
release yesterday)> DC Proof: Rationale for a more
User-Friendly Notation> While it may not be the standard
notation of logicians, in most cases, the> notation used by DC
Proof does not vary significantly from it. It was> designed
primarily for the non-specialist mathematics student in first
or> second year university or in advanced senior high school
courses.> To give just one example, most university algebra
and calculus (analysis)> textbooks, even the advanced ones it
seems, do not make use of universal and> existential
quantifiers (the logician's inver A's and backwards E's>
respectively). They usually spell out for all x or there
exists a y such> that etc. Students should be used to working
with such notation. It was> felt that the use of ALL and EXIST
would be a more natural and> suggestive notation.> By the way,
users need not type out these words or commit the notation to>
memory. To minimize keystrokes and to help students learn the
notation,> there is a convenient, pull-down menu of all
symbols and notation used in DC> Proof (click Notation on the
Premise form, etc.).> Also, in a effort to make variable and
predicate names more meaningful, DC> Proof allows names of any
length. This, of course, necessitates the use of> some extra
delimiters (round and square brackets) for readability. DC
Proof> automatically minimizes bracketing, however, with its
built-in, order of> precedence (or operations). This makes it
easier for the user to recognize> the occurrence of structures
like double negations, for example.> Generally speaking, the DC
Proof notation was designed to be as familiar as> possible to
students, and to make it easy to learn and master.>
===
inquiries, my web site is at >
http:/www.cybcity.com/ranmath/start.htm> and is called The
Rancocas Valley Journal of Applied Mathematics.> Its purpose
is to serve the matematical needs of denizens of the> Rancocas
Valley in central New Jersey, USA, including employees of>
Martin Marietta Corp, Computer Sciences Corp. and those who
feel> attrac by the lure of the gambling casinos in nearby
Atlantic City.Warning: The above web page contains pop-ups
===
equationsHi:I was wondering if someone could give me a hint on
the followingdelayed Boolean equation. Actually, this WAS a
homework assignmentfrom a long time ago, but I've never been
able to figure it out. Now thatI got time to kill, I want to
figure this out.Suppose _ _V(t) = V(t-t1) & V(t-t2) & V(t-t3)
(1.1)t1 > t2 > t3overbar means the opposite state of V and &
means AND operation.Is there a way to figure out the period of
the system in general inthe ASYMPTOTIC limit?I tried using
(1.1) to figure out what V(t-t2) is: _ _V(t-t2) = V(t-t1-t2) &
V(t-2t2) & V(t-t3-t2) (1.2)If we subsitute (1.2) into (1.1) and
keep repeating in subsituting forV(t-n*t2) where n is an
integer (depending on thenumber of (n-1) times the subsitution
you did for V,sooner or later, you get a recursive relation,
quite ugly: _ _ _V(t) = V(t-t1) & V(t-t1-t2) & .... &
V(t-t1-n*t2) & V(t-n*t2) & _ _ _ V(t-t3) & V(t-t3-t2) & .... &
V(t-t3-n*t2)I argued that in the asymptotic limit, the period
of the systemis t2 because the above has to be true for all
n.My TA marked me wrong, but I never find out the answer.Could
===
can modify the source, to remove those references, by just
using 0,instead.They are calculating runtime. Also, the email
address you pos isbouncing.Dan Stanger> How can I obtain
numerical solution of ODE> using Runge-Kutta method ,> Should
I download external file ?> If i try LOAD(DIFFEQ) maxima :>
LOAD(diffeq)> Unknown argument - STATUS:> RUNTIME> -- an
error. Quitting. To debug this try DEBUGMODE(TRUE);)> Olaf