Hi, great idea, but remember that computer algebra systems use
slightly different way than humans to solve problems...

I think than more people work on something like this -- just guessing
from questions like
http://thread.gmane.org/gmane.comp.mathematics.maxima.general/23048/focus=23051
and
http://thread.gmane.org/gmane.comp.mathematics.maxima.general/9291/focus=9292

I am maintainer of MAW, Mathematical Assistant on Web, which *is*
opensource, see
the page at http://user.mendelu.cz/marik/maw/index.php?lang=en&form=main
sources at http://mathassistant.cvs.sourceforge.net/mathassistant/
and perhaps the VMware virtual machine at 
http://user.mendelu.cz/marik/maw/offline.html

MAW can solve selected typical problems like evaluation of integral,
double integral, derivatives etc in steps.
The main idea is that the user input is processed in a worksheet.

So the worksheet for solving quadratic equations could look as folows
1. Get a,b,c
2. Print a*x^2+b*x+c=0
3. If b=0 convert into a*x^=-c, take square roots and finish
4. If c=0 convert into x*(a*x+b)=0, return answers and finish
5. Find b^2-4*a*c
6. Evaluate sqrt(b^2-4*a*c)
7. Find answers x_1,2=.......

However, computers can never emulate the human approach. As an example
consider the problem to differentiate the function sqrt(x)*(x+1). Both
MAW and calc101.com use product rule to find derivative, but much
simpler is to multiply the parenteheses first and continue with sum
rule. The first way is computer way the second one is human way.
Similarly when differentiating something like (x^2+x+2)/(x^3)  ---
quotient rule is far more complicated than algebraic modification and
sum rule for derivatives.

You may be also interested in this post:
http://thread.gmane.org/gmane.comp.mathematics.maxima.general/20007/focus=20068


On 12 Dub, 20:15, mm <haibho...@gmail.com> wrote:
> I am trying to do the same as Mathway, however, with a real step-by-
> step result instead of redirected to a commercial software.  I want to

Steps from mathway were free for few weeks or months. I did not like
their output, it was too long, boring with long explanations for
trivial things.

Robert Marik

> help high school and first year college students to learn math and I
> want it to be based on Open Source technologies.  As long as there is
> some ways to do it with Sage, I don't mind investing the time and
> learn it.

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