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From: JBGM on 11 Feb 2007 15:33
Hello everyone. I have a very simple problem in which the HP 50g fails
miserably, and the TI-89 solves only by half. I cannot get the
solution to a simple equation in the HP50g:
SOLVE('LN(X)+SIN(X)+X^2=0', 'X') I receive the error: "SOLVE Error:
Not reducible to a rational expression" I have changed the
configuration parameters in MODE > CAS without success.

Is there any configuration setting or parameter I am missing? Should I
use another function? SOLVE works fine with a trivial equation; when I
enter SOLVE(' X^2-4*X+8=0', 'X'), it returns {X=2-2*I, X=2+2*i}, which
is correct.

The TI-89 finds half the answer to the initial problem using the
complex solver command "cSolve(LN(X)+SIN(X)-X^2=0, X)" The TI-89
returns 0.490672, which is the real root. TI's real solver "solve"
finds the real root too. But the TI-89 fails to return the complex
root 0.8775 + 0.2558i

The tests were done with PC emulators for HP 50g and TI-89. Could
someone help, please? I would expect the HP 50g to actually find the
complex root, or at the very least the real root, since there is
consensus in the scientific community that HP 50g is superior to the
TI-89 for advanced math. Or is the TI-89 superior? I am trying to
decide which one is better for advanced math in order to purchase it.

Before someone answers that I should use Maple or Mathematica (how do
you think I obtained the complex root?), here goes the explanation:
I'm a professional mathematician who wants to use a CAS in a handheld
device for a research project. I have to do massive symbolic
computations while I move across large library's shelves, so carrying
a laptop is simply annoying.

From: Steen Schmidt on 11 Feb 2007 16:45
JBGM wrote:

> Hello everyone. I have a very simple problem in which the HP 50g fails
> miserably, and the TI-89 solves only by half. I cannot get the
> solution to a simple equation in the HP50g:
> SOLVE('LN(X)+SIN(X)+X^2=0', 'X') I receive the error: "SOLVE Error:
> Not reducible to a rational expression" I have changed the
> configuration parameters in MODE > CAS without success.

The SOLVE command on the HP can really only find rational roots unless
the solution variable is easily isolated. The same is the case on the
TI if you want exact answers. When the TI fails to find an exact root,
it tries a numeric approach. On the HP you get an error box instead,
and you'll manually have to try the numeric approach (the ROOT command
on the HP).

Finding the real root 0.490672... takes 14.9 seconds on the TI, while
ROOT does it in 1.1 seconds on the HP. Both only return one root
without an estimate on how many other potential roots exist. I think
the HP is better in this case (same features but faster performance).

> The TI-89 finds half the answer to the initial problem using the
> complex solver command "cSolve(LN(X)+SIN(X)-X^2=0, X)" The TI-89
> returns 0.490672, which is the real root. TI's real solver "solve"
> finds the real root too. But the TI-89 fails to return the complex
> root 0.8775 + 0.2558i

Warning: you are operating with different signs on your 'X^2' term - I
assume you in the latter case mean negative 'X^2', or else your complex
root is wrong. What you need on the HP is the great program SolveSys -
you can find it on hpcalc.org.

Now do X=A+B*i SUBST, copy the expression and do RE on one copy and IM
on the other, plug the two expressions into SolveSys and solve. Presto,
it spits out A=0.877484... and B=0.255824...

It seems complicated but it took me less than 30 seconds. I do not know
how to accomplish the same on my TI89. As with all numerical root
finding the real challenge is to know when you have found all roots and
then finally remove any false roots (the latter is usually easily done
by trial insertion of course).

Cheers,
Steen
From: Virgil on 11 Feb 2007 16:47
In article <1171225989.989056.246130(a)l53g2000cwa.googlegroups.com>,
"JBGM" <Literatronica(a)gmail.com> wrote:

> Hello everyone. I have a very simple problem in which the HP 50g fails
> miserably, and the TI-89 solves only by half. I cannot get the
> solution to a simple equation in the HP50g:
> SOLVE('LN(X)+SIN(X)+X^2=0', 'X') I receive the error: "SOLVE Error:
> Not reducible to a rational expression" I have changed the
> configuration parameters in MODE > CAS without success.
>
> Is there any configuration setting or parameter I am missing? Should I
> use another function? SOLVE works fine with a trivial equation; when I
> enter SOLVE(' X^2-4*X+8=0', 'X'), it returns {X=2-2*I, X=2+2*i}, which
> is correct.
>
> The TI-89 finds half the answer to the initial problem using the
> complex solver command "cSolve(LN(X)+SIN(X)-X^2=0, X)" The TI-89
> returns 0.490672, which is the real root. TI's real solver "solve"
> finds the real root too. But the TI-89 fails to return the complex
> root 0.8775 + 0.2558i
>
> The tests were done with PC emulators for HP 50g and TI-89. Could
> someone help, please? I would expect the HP 50g to actually find the
> complex root, or at the very least the real root, since there is
> consensus in the scientific community that HP 50g is superior to the
> TI-89 for advanced math. Or is the TI-89 superior? I am trying to
> decide which one is better for advanced math in order to purchase it.
>
> Before someone answers that I should use Maple or Mathematica (how do
> you think I obtained the complex root?), here goes the explanation:
> I'm a professional mathematician who wants to use a CAS in a handheld
> device for a research project. I have to do massive symbolic
> computations while I move across large library's shelves, so carrying
> a laptop is simply annoying.

In the HP48/48/50 series, the ROOT command finds the approximate real
root, as does the numerical solver (accessed by left shift 7 on the 49
and 50) and find the correct real root to 12 significant digits.

If you use the SOLVESYS library, available at http://www.hpcalc.org/,
different versions for the 48 versus the 49/50 series, you can
approximate several complex solutions as well as the real solution by
starting with complex guesses.

One such complex solution is about -1.39010-i*0.98289

Are you sure that X = 0.8775 + 0.2558i is a root?
On my HP49, 'LN(X)+SIN(X)+X^2' evaluates to 1.40912+0.89784*i for that
value of X.
From: Veli-Pekka Nousiainen on 11 Feb 2007 16:57
Have you tried the numerical solvers like ROOT ?
It returns the real root

"JBGM" <Literatronica(a)gmail.com> wrote in message
news:1171225989.989056.246130(a)l53g2000cwa.googlegroups.com...
> Hello everyone. I have a very simple problem in which the HP 50g fails
> miserably, and the TI-89 solves only by half. I cannot get the
> solution to a simple equation in the HP50g:
> SOLVE('LN(X)+SIN(X)+X^2=0', 'X') I receive the error: "SOLVE Error:
> Not reducible to a rational expression" I have changed the
> configuration parameters in MODE > CAS without success.
>
> Is there any configuration setting or parameter I am missing? Should I
> use another function? SOLVE works fine with a trivial equation; when I
> enter SOLVE(' X^2-4*X+8=0', 'X'), it returns {X=2-2*I, X=2+2*i}, which
> is correct.
>
> The TI-89 finds half the answer to the initial problem using the
> complex solver command "cSolve(LN(X)+SIN(X)-X^2=0, X)" The TI-89
> returns 0.490672, which is the real root. TI's real solver "solve"
> finds the real root too. But the TI-89 fails to return the complex
> root 0.8775 + 0.2558i
>
> The tests were done with PC emulators for HP 50g and TI-89. Could
> someone help, please? I would expect the HP 50g to actually find the
> complex root, or at the very least the real root, since there is
> consensus in the scientific community that HP 50g is superior to the
> TI-89 for advanced math. Or is the TI-89 superior? I am trying to
> decide which one is better for advanced math in order to purchase it.
>
> Before someone answers that I should use Maple or Mathematica (how do
> you think I obtained the complex root?), here goes the explanation:
> I'm a professional mathematician who wants to use a CAS in a handheld
> device for a research project. I have to do massive symbolic
> computations while I move across large library's shelves, so carrying
> a laptop is simply annoying.
>


From: Matteo on 11 Feb 2007 17:03

JBGM ha scritto:

> Hello everyone. I have a very simple problem in which the HP 50g fails
> miserably, and the TI-89 solves only by half. I cannot get the
> solution to a simple equation in the HP50g:
> SOLVE('LN(X)+SIN(X)+X^2=0', 'X') I receive the error: "SOLVE Error:
> Not reducible to a rational expression" I have changed the
> configuration parameters in MODE > CAS without success.
>
> Is there any configuration setting or parameter I am missing? Should I
> use another function? SOLVE works fine with a trivial equation; when I
> enter SOLVE(' X^2-4*X+8=0', 'X'), it returns {X=2-2*I, X=2+2*i}, which
> is correct.
>
> The TI-89 finds half the answer to the initial problem using the
> complex solver command "cSolve(LN(X)+SIN(X)-X^2=0, X)" The TI-89
> returns 0.490672, which is the real root. TI's real solver "solve"
> finds the real root too. But the TI-89 fails to return the complex
> root 0.8775 + 0.2558i
>
> The tests were done with PC emulators for HP 50g and TI-89. Could
> someone help, please? I would expect the HP 50g to actually find the
> complex root, or at the very least the real root, since there is
> consensus in the scientific community that HP 50g is superior to the
> TI-89 for advanced math. Or is the TI-89 superior? I am trying to
> decide which one is better for advanced math in order to purchase it.
>
> Before someone answers that I should use Maple or Mathematica (how do
> you think I obtained the complex root?), here goes the explanation:
> I'm a professional mathematician who wants to use a CAS in a handheld
> device for a research project. I have to do massive symbolic
> computations while I move across large library's shelves, so carrying
> a laptop is simply annoying.


Hp49g+ (50G) can solve this equation numerically. it is obviusly that
it can. :-)
you must use the command 'root' in this way:
in user rpl mode

3: 'ln(x)+sin(x)+x^2=0' the equation
2: 'x' the indipendent variable
1: 2. the initial value of the
variable
---> root

and you have the solution.
if you want complex solutions you must put a complex initial value for
x. With this command (root) you find only one solution....

About calculator cas : I haven't a TI89, but I think that both ti89
and hp49(50) are the most powerful calc with cas in the world. I like
a lot the hp cas because every day I discover new features like
particular systems flags for solve exact and simbolic big linear
sistems 70*70 :) :) :), ecc....and hp has a so powerful programming
language that the only thing that you can do i to have dreams...

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