SageMath, R, Maxima

macbook-air-de-annick-valibouze:~ avb$ sage
----------------------------------------------------------------------
| SAGE Version 3.0.5, Release Date: 2008-07-11                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------

%%% Déclarer un anneau de polynômes en la variable x sur le corps des rationnels 
sage: R.<x> = PolynomialRing(QQ)

%% DECLARER UN LE CORPS de rupture K=Q(a)=Q[x]/<x^3 + x^2 - 2*x + 8> extension du corps Q
sage: K = NumberField(x^3 + x^2 - 2*x + 8, 'a')

%%% AFFECTER un polynôme f dans K :
sage: f=x^8 - 4*x^7 - x^6 + 15*x^5 - 3*x^4 - 16*x^3 + 4*x^2 + 4*x - 1

%%% APPELER UNE FONCTION MAXIMA SOUS SAGE :
sage: g=maxima.subst('x1','x',f)
sage: g
x1^8-4*x1^7-x1^6+15*x1^5-3*x1^4-16*x1^3+4*x1^2+4*x1-1

%%% MATRICES
sage: m1=matrix([[1,2],[4,6]])
sage: m2=matrix([[1,3],[4,8]])
sage: m1*m2

[ 9 19]
[28 60]

%%% GROUPES 
sage: SymmetricGroup(4)
Symmetric group of order 4! as a permutation group

%%% APPELER UNE FONCTION GAP SOUS SAGE :
sage: gap.SymmetricGroup(4)
SymmetricGroup( [ 1 .. 4 ] )

sage: s=SymmetricGroup(4);

%%%%%%%%%
R sous Sage
%%%%%%%%%

sage: r_console()
R version 2.6.1 (2007-11-26)
Copyright (C) 2007 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

> quit();

%%%%%%%%%
MAXIMA SOUS SAGE :
%%%%%%%%
sage: maxima_console()

Maxima 5.13.0 http://maxima.sourceforge.net
Using Lisp CLISP 2.46 (2008-07-02)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report()
provides bug reporting information.

(%i1) f(x):= x+1;
(%o1)                            f(x) := x + 1

(%i2) f(3);
(%o2)                                  4

(%i13) g(x):=block([VariablesLocales, u],u:x+1,u);
(%o13)        g(x) := block([VariablesLocales, u], u : x + 1, u)

(%i14) g(4);
(%o14)                                 5

(%i15) quit();


%%%%%
 Maxima Mini Doc pour Hopfield
%%%%%

W: matrix([..],,[])  

transpose(W)   

W.M  

W[5]  W[3,6]

not(test)  

true  false

if test then AV else  AF

for i:1 thru 4 do

cons(tete,liste) first(liste) rest(liste)

append(liste1, liste2, , listen)

 sum(...,j,1,4)

 maplist(fonction, liste)