This is a test of Sage
in MathAction.

Sage stands for:
  Software for Algebra and Geometry Experimentation


Sage has native computer algebra capabilities as well as
interfaces to other systems such as
GAP ,
PARI ,
Singular
and Maxima.
Sage was recently extended (version 1.4.1.2) to include support
for Axiom.
Here is a summary of features

This is how to enter Sage commands:
  Commands can be used inline, for example: $1+2=\sage{1+2}$ and $\sqrt{1+2}=\sage{sqrt(1+2)}$.
  Or we can evaluate a block of Sage commands:
  \begin{sageblock}
  # do some stuff
  E = EllipticCurve("37a")
  # more stuff
  \end{sageblock}

  Now the elliptic curve $E$ given by $\sage{E}$
  has discriminant $\sage{E.discriminant()}$.


To get this:
Commands can be used inline, for example: $1+2=\sage{1+2}$ and $\sqrt{1+2}=\sage{sqrt(1+2)}$.
Or we can evaluate a block of Sage commands:
\begin{sageblock}
# do some stuff
E = EllipticCurve?("36a")
# more stuff
\end{sageblock}
Now the elliptic curve $E$ given by $\sage{E}$
has discriminant $\sage{E.discriminant()}$.
Maxima commands in Sage look like this:
\begin{sageblock}
f = maxima(sin(x)^2*cos(x)*exp(x)+a*y)
g = f.integrate("x")
\end{sageblock}
The \sage commands can occur in other LaTeX contexts such
as:
  \begin{equation}
     \int \sage{f} dx = \sage{g}.
  \end{equation}


This produces:
\begin{equation}
\label{eq1}
  \int \sage{f} dx = \sage{g}.
\end{equation}
---------
Axiom commands in Sage look like this:
\begin{sageblock}
fAxiom = axiom(sin(x)^2*cos(x)*x)
gAxiom = fAxiom.integrate("x")
\end{sageblock}
The \sage commands can occur in other LaTeX contexts such
as:
  \begin{equation}
     {\int \sage{fAxiom} dx} = {\sage{gAxiom}}.
  \end{equation}


This produces:
\begin{equation}
\label{eq2}
  {\int \sage{fAxiom} dx} = {\sage{gAxiom}}.
\end{equation}
Using Axiom to guess integer sequences:
\begin{sageblock}
f = axiom('(guess [2,4,6]?).1.function')
\end{sageblock}
Gives:
$$
\sage{f}
$$
---------


Sage and literate programming --Bill Page,  Wed, 16 Aug 2006 08:17:56 -0500 reply
Sage also works in pamphlet files. See SandBoxSagePamphlet

sage: unset PYTHONPATH; PATH=/usr/local/bin:$PATH HOME=/var/lib/zope sage 1433308504340526167-18.0px.sage
Traceback (most recent call last):
  File "1433308504340526167-18.0px.py", line 24, in <module>
    fAxiom = axiom(sin(x)^2*cos(x)*x)
  File "/home/server2/sage/local/lib/python2.5/site-packages/sage/interfaces/expect.py", line 963, in __call__
    return cls(self, x, name=name)
  File "/home/server2/sage/local/lib/python2.5/site-packages/sage/interfaces/expect.py", line 1281, in __init__
    raise TypeError, x
TypeError: Unable to start axiom

Timeout exceeded in read_nonblocking().
<pexpect.spawn instance at 0x2ade2b7d8320>
version: 2.0 ($Revision: 1.151 $)
command: /home/server2/sage/local/bin/axiom
args: [/home/server2/sage/local/bin/axiom, -nox, '-noclef']
patterns:
    \([0-9]+\) -> 
buffer (last 100 chars): 
before (last 100 chars): ad.so"
foreign routines found
*** - invalid byte #xC3 in CHARSET:ASCII conversion
Break 1 [1]> 
after: <class pexpect.TIMEOUT>
match: None
match_index: None
exitstatus: None
flag_eof: 0
pid: 19875
child_fd: 7
timeout: 30
delimiter: <class pexpect.EOF>
logfile: None
maxread: 10
searchwindowsize: None
delaybeforesend: 0