eigenMath

When I do these tutorials I often have to take out pencil and paper and do some calculations. It's painful and ..

>Aah, poor guy. I feel so sorry for you.
At one time I thought I'd buy symbolic algebra software, like Maple, but it's a few hundred dollars so ...

>Aah, poor guy.
Then I discover that there's this really neat program called eigenMath.

>Is it any good?
It has three things going for it:

  1. It does some calculus, finds roots, sums series, plots curves ... and a host of other neat things.
  2. It's very easy to use.
  3. It's less than 600 kB in size !
  4. It's free!!
>That's four things!
For example ...
You ask for thisand you get this display
S = sum(k,0,10,(1.01)^k) --- sums 1.01^k from k = 0 to k = 10
S --- this just displays the value of S		S = 11.5668
roots(x^3-2*x^2+2*x-1)
y = x*sin(x)
draw
integral(pi*sqrt(1-x^2),x)
eval(last,x,0.5)
M=0.1 -- Mean is 10%
S=0.3 -- Standard Deviation is 30%
f=(1/S/(2*pi)^(1/2))*(1/sqrt(2*pi))*exp(-(x-M)^2/(2*S^2))
yrange=(0,1)
xrange=(-1,1)
draw(f) --- the Normal Distribution :^)
>Wait! How do you ask for things?
When you open fire up the software, you get a window like so
That's where you type in your script request,
Then you click on a button: Run Script and get ...

.

.

.

.

... surprise!

>It says simplify?
Yeah, ask for:

1/(x-a) - 1/(x+a)

and get:

Then click Simplify and get:


>What else does it do?
Check out the functions it's got:
| abs | adj | and | arccos | arccosh | arcsin | arcsinh | arctan | arctanh | arg | binomial | ceiling | check | coeff | cofactor | condense | conj | contract | cos | cosh | d | deg | denominator | det | dim | display | do | dot | draw | eigen | erf | erfc | eval | exp | expcos | expsin | factor | factorial | filter | float | floor | for | gcd | hermite | hilbert | imag | inner | integral | inv | isprime | laguerre | lcm | legendre | log | mag | mod | not | numerator | or | outer | polar | prime | product | quote | quotient | rank | rationalize | real | rect | roots | simplify | sin | sinh | sqrt | stop | subst | sum | tan | tanh | taylor | test | trace | transpose | unit | zero

>Taylor? Who's he?
Just download a copy, using this link, and try:     taylor(x*exp(-x))
then Derivative and/or Integral and/or Draw and/or ...

>Hold on! I'm getting my own copy ...

You might also try:

taylor(sin(x),x,9) --- asking for powers up to the 9th
draw

and get:

See how it tries to mimic the sine curve?
Then try higher powers and ...

>Hold on! I'm getting my own copy ...

Then, too, you can do some financial stuff:

Write:
r = 0.1 -- Mean Return is 10%
s = 0.25 -- Standard Deviation is 25%
T = 3.0 -- Time is 3 years into the future
Po = 10 --- current stock price is $10
f = (1/s/x/(2*pi*T)^(1/2))*exp(-(ln(x/Po)-(r-s^2/2)*T)^2/2/T/s^2)
xrange=(0,40)
yrange=(0,0.1)
draw(f)

and get the Ito probability distribution for stock prices T = 3 years into the future:

   

See also Maxima.