Hi,

While browsing the

http://sage.math.washington.edu/home/wdj/teaching/index.html

(btw which is the best tutorial for sage I ever found), I was looking at this

http://sage.math.washington.edu/home/wdj/teaching/granville-calculus/granville-calculus.pdf

page 75. compare figure 5.9 (original hand made?), and 5.10 (Sage).

I prefer the original one. The Sage one looks too computer made and
ugly. And this reminded me,
that one reason (of many) while I started sympy was that I wanted to
make such plots fully automatic.
i.e. you would write:

Plot(arcsec(x))

and it will plot you the figure 5.9 (instead of 5.10), including all
those titles, like Pi, Pi/2 etc. Using
matplotlib latex engine, etc, etc.

At first sight, it maybe sounds too difficult or vague, but I don't
think so. If a man can do this, than
a computer can do this too. One needs to find singularities first -
arcsec is a difficult example.

Let's take tan(x)=sin(x)/cos(x). So first one would look at the
denominator, finds all zero points.
(symbolically). Then it finds asymptotics, using limits. Plot lines
for asymptotics. Etc., and so on.

I don't think any CAS system can do this, so Sage could be the first.
Just another GSOC idea.

Ondrej

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