Re: Some questions about simplification
- From: "Veli-Pekka Nousiainen" <velipekka.nousiainen@xxxxxxxxxxxxx>
- Date: Sun, 10 May 2009 06:17:25 +0300
"Dima" <Iosaaris@xxxxxxxxx> kirjoitti
viestissä:24e6421c-f4db-4608-82c4-009b05eb3752@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
I use HP 49G+/50G for about half a year for my studies. There are some
issues with simplification, that I'd like to understand.
1. Trigonometric functions in series. When I try to calculate sum of
sines or cosines, the calculator makes calculation in approximation
mode even when exact mode is selected.
For example, if I enter
Sum(n=0,5,(n-1)*x)
the result is
9*x
But if (without changing any preferences) I enter
Sum(n=0,5,SIN((n-1)*(Pi/4))
the result is
1.70710678119
which is numerical result and not algebraic expression with sum of
sines. If I add there other variables, I still get results with
decimal points, like in approx. mode. This occurs both in real and
complex modes.
Is there any way to change this in order to get the results as
algebraic expressions with integers?
I tried also, but it seems you need to program your own sum
COMP-> is in 256 MENU (or rather 256.03 MENU)
or
if you have the Development lib attached
To do that automagically you just need
at Home directory a variable called
'STARTUP'
<< 256 ATTACH >>
Sigma is the summation, the Greek S
SigmaLIST is then 5 characters long command name
You will find that command in the CAT (above SYMB key)
by pressing the summation key (above SIN key)
So your own SUM that takes the Greek S function
as a single parameter, eg, evaluates it - is:
'SUM'
<< COMP-> DROP2 4 ROLL EVAL 4 ROLL 4 ROLL
1 SEQ SigmaLIST SIMPLIFY >>
2. Simplification of powers to exponentials. If I enter
1/X^N
the result is displayed as
1/EXP(N*LN(X))
run EXPAND()
3. Entering EXP(X)+EXP(-X) gives as result:
(EXP(x)^2+1)/EXP(X)
run LIN()
4. Simplification in series. I tried to calculate sum of geometric
series. I entered:
Sum(n=1,N,a1*q^(n-1))
The result was:
(a1*EXP((N+1)*LN(q))-q*a1)/(q^2-q)
The question is the same: are there any settings that allow to get rid
of EXP() and LN() functions where they are really non needed?
run EXPAND then SIMPLIFY and then EXPAND
(a1*q^N-a1)/(q-1)
Thank you for your response.
Your welcome
You can also have your own CUSTOM menu
for the Equation Writer - use the search at
www.hpcalc.org
for
Veli-Pekka Nousiainen
or
STARTEQW.VPN
Look that code, experiment...and have fun!
--
VPN
.
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- Some questions about simplification
- From: Dima
- Some questions about simplification
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