## What goes wrong in the SAGE notebook interface for secondary school usage

Some of (nice) sage features are not well adapted at an elementary level. In particular:

- the oriented object syntax should sometimes be avoided: the interface must be intuitive from the mathematic *standard* syntax point of vue; on the other side we must keep all python features of list, tuple, dict as they are (ask teachers).
- the algebra under polynoms must be hided a little bit. QQbar, Number fields and symbolic rings must stay in backend;
- the namespace is huge (a general problem of SAGE)
- the help on elementary functions is not well adapted

Supplementary:

- do a french translation of commmands (?)
- write some help files and a really basic tutorial mixing Sage and python.

## A bad solution for polynoms

The high school interface provides two basics functions for creating variables : the var (a symbolic variables for functions) and unknowns (exclusively for polynoms).

The version with unknown returns algebraic elements when asking for roots:

sage: unknown('X') X sage: P = X^2 - X - 1 sage: roots(P) [(-0.618033988749895?, 1), (1.618033988749895?, 1)]

The version with var returns symbolic expression when asking for roots:

sage: var('x') sage: P = x^2 - x - 1 sage: roots(P) [(-1/2*sqrt(5) + 1/2, 1), (1/2*sqrt(5) + 1/2, 1)]

## Patches

Following the development model of Sage, we will use mercurial patches here.

- a patch for the documentation will come soon

## Program of high school in France

In bracket are the corresponding levels.

- second degree polynom [1e S]
- sequences in particular recursive ones [1e S]
- sequences and approximations : pi, e, sqrt(2), ... [1e S]
- continuity and derivation [Tale S]
- functions study and graphics [Ta1e S]
- integration[Tale S]
- elementary graph theory [Tale ES]

## Object or not

The python list usage must be kept as it is. But we have the choice to use or not (explicitely) some methods.

Starting from a list:

python: l = [1,2,3]

We can use the standard append:

python: l.append(4)

or the += concatenation:

python: l += [4]

## TODO

There is still a lot of problems:

- clearing the namespace causes some crashes (there are some general memory initialization). I make research to do it properly. For now, I use a "do it, if it works it's good" method.
- sqrt(n) (log(n), exp(n), ...) returns a symbolic expression which does not evaluate correctly as boolean expression.
- help topics in the rest documentation
latex rendering in plot is not easy to have :

`sage: text("$" + latex(my_object) + "$", (0,0))`. Is there a better way ?