Matlab Editor : Rapid programming

Matlab has introduced something called "cells" to speed up writing/testing programs. Just go through this Flash animation to know more about cells.

http://www.mathworks.com/support/2007a/matlab/7.4/demos/RapidCodeIterationUsingCells_viewlet_swf.html


I had been avoiding Matlab for a long time. Its being a proprietory software. But I must admit, its simply great. They just need to reduce the price.

CAS: Roots of a polynomial

Maxima
---------------------------
(%i1) eq1: x^5-x+x*(1-x)^4*(5*a)+x^2*(1-x)^3*(10*b)+
x^3*(1-x)^2*10*(1-b)+x^4*(1-x)*5*(1-a)=0;
(%o1)

(%i2) solve(eq1,x);
(%o2)

(%i3) f1:rhs(%[1] );
(%o3)

(%i4) radcan(f1);
(%o4)

(%i5) ratexpand(%);
(%o5)

(%i6) d1:part(%,1);
(%o6)

(%i7) d2:part(%o5,[2,3,4]);
(%o7)

(%i8) ratsimp(%);
(%o8)

Roots in simplified format is given by

x = 0.5 +/- sqrt((b+1.5a-0.7)/(4b-2a-1.2))


Matlab
-----------------
syms a b x
f = x^5-x+x*(1-x)^4*(5*a)+x^2*(1-x)^3*(10*b)+
x^3*(1-x)^2*10*(1-b)+x^4*(1-x)*5*(1-a);
soln = solve(f,x);
f4 = soln(4,1);
f5 = soln(5,1);

f4 =
1/2/(5*a-10*b+3)*(5*a-10*b+3+(-75*a^2+
100*a*b-10*a+100*b^2-100*b+21)^(1/2))

f5 =
1/2/(5*a-10*b+3)*(5*a-10*b+3-(-75*a^2+
100*a*b-10*a+100*b^2-100*b+21)^(1/2))

It does not simplify roots any further. I tried all sorts of other commands like 'simplify', 'factor' etc. Is it possible to get the simplified form of roots as shown above?

Now scilab comes with its own symbolic toolbox and interface with 'maxima'. Check following link for details.
http://www.cert.fr/dcsd/idco/perso/Magni/s_sym/functions.html