Re: Ti92 solver [Haste makes waste]


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Re: Ti92 solver [Haste makes waste]



At 06:38 PM 11/04/98 -0500, RWW Taylor wrote:
>Haste makes waste, as they say...
>Certainly the use of the solver with "and", as suggested by Bill Risher,
would
>give you a quicker solution to this system of simultaneous equations. But of
>course this particular set of equations is a "toy" set, created really to
>foster some algebraic insight, and not needing a calculator to tackle.  Hope
>this isn't sounding like "sour grapes".  :-)}
I love exploring math, but when it comes down to just getting answers I can
usually find the fastest way.

>When you move up to more mysterious systems, you may well want to try to get
>some insight into the nature and number of solutions for your system before
>simple-mindedly grinding out an answer of some kind. Just because the
>calculator tells you "false" you cannot conclude that there is no
solution! In
>fact that little system of three simultaneous equations I posted this AM
can be
>represented as the three roots of a certain cubic polynomial, and a solution
>_does_ exist.
I apologize.  I spoke hastily.  According to my further studies, comprised
of this command (note the C, for complex):

CSolve(x+y+z=1 and x^2+y^2+z^2=2 and x^3+y^3+z^3=3,{x,y,z})

there ARE complex solutions, according to these results (i have no idea why
it approximated the coefficients, but since it did I have taken the liberty
to round them to small manageable values):

x=1.431+0i and y=-.215-.265i and z=-.215+.265i
OR
x=1.431-0i and y=-.215+.265i and z=-.215-.265i
OR
x=-.215+.265i and y=-.215-.265i and z=1.431
OR
x=-.215+.265i and y=1.431-0i and z=-.215-.265i
OR
x=-.215-.265i and y=1.431+0i and z=.215+.265i
OR
x=-.215-.265i and y=.215+.265i and z=1.431

WOW that took a long time to copy down.

note that anywhere I rounded to 0i the calculator results were less than
.00000000001i which seemed like a rounding error within the calculator.

>--- By the way, thanks also to Bill Risher for providing the other
>    suggested approaches to examining the problem at leisure. I
>    expect that it is going to take some time (and a lot of
>    creativity) before commonly-accepted _styles_ of work emerge
>    in this new medium.
Why thank you.

--
Bill Risher        Sparr      UIN:1952775    ._, . . .
Lorenai #44        Makra      FON:9316484164 |_) o | |
Overlord n7hq      Decius                    |_) | | |
mailto://billr1@midsouth.net  FAX:9315526807 ^ ` ^ ^ ^


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