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== Solution for polynoms == == A bad solution for polynoms ==
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The version with unknown returns algebraic elements when asking for roots:
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sage: a,b,c = var('a,b,c')
sage: X, Y = unknown('X')
(X,Y)
sage: P = a*X^2 + b*X + c		 sage: unknown('X')
X
sage: P = X^2 - X - 1
sage: roots(P)
[(-0.618033988749895?, 1), (1.618033988749895?, 1)]
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== An interactive trigonometric circle ==


== 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 var returns symbolic expression when asking for roots:
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sage: a,b,c = var('a,b,c')
sage: X, Y = unknown('X')
(X,Y)
sage: P = a*X^2 + b*X + c		 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)]
Line 35: Line 33:

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.

  • Sage patch

  • 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 ?

  • latex "bug" for rational fractions : http://groups.google.com/group/sage-devel/browse_thread/thread/9d58693356e11947 and the corresponding (minor) trac ticket http://trac.sagemath.org/sage_trac/ticket/7363