****************
Interface Issues
****************
.. index::
single: background, running Sage in
.. _section-background:
Background jobs
===============
Yes, a Sage job can be run in the background on a
UNIX system. The canonical thing to do is type
::
nohup sage < command_file > output_file &
The advantage of nohup is that Sage will continue running after you
log out.
Currently Sage will appear as "sage-ipython" or "python" in the output
of the (unix) ``top`` command, but in future versions of Sage it will
appears as ``sage``.
.. index::
pair: referencing; Sage
Referencing Sage
================
To reference Sage, please add the following to your
bibliography:
::
\bibitem[Sage]{sage}
Stein, William, \emph{Sage: {O}pen {S}ource {M}athematical {S}oftware
({V}ersion 2.10.2)}, The Sage~Group, 2008, {\tt http://www.sagemath.org}.
Here is the bibtex entry:
::
@manual{sage,
Key = {Sage},
Author = {William Stein},
Organization = {The Sage~Group},
Title = {{Sage}: {O}pen {S}ource {M}athematical {S}oftware ({V}ersion 2.10.2)},
Note= {{\tt http://www.sagemath.org}},
Year = 2008
}
If you happen to use the Sage interface to PARI, GAP or Singular,
you should definitely reference them as well. Likewise, if you use
code that is implemented using PARI, GAP, or Singular, reference
the corresponding system (you can often tell from the documentation
if PARI, GAP, or Singular is used in the implementation of a
function).
.. index::
pair: referencing; PARI
For PARI, you may use
::
@manual{PARI2,
organization = "{The PARI~Group}",
title = "{PARI/GP, version {\tt 2.1.5}}",
year = 2004,
address = "Bordeaux",
note = "available from \url{http://pari.math.u-bordeaux.fr/}"
}
or
::
\bibitem{PARI2} PARI/GP, version {\tt 2.1.5}, Bordeaux, 2004,
\url{http://pari.math.u-bordeaux.fr/}.
(replace the version number by the one you used).
.. index::
pair: referencing; GAP
For GAP, you may use
::
[GAP04] The GAP Group, GAP -- Groups, Algorithms, and Programming,
Version 4.4; 2005. (http://www.gap-system.org)
or
::
@manual{GAP4,
key = "GAP",
organization = "The GAP~Group",
title = "{GAP -- Groups, Algorithms, and Programming,
Version 4.4}",
year = 2005,
note = "{\tt http://www.gap-system.org}",
keywords = "groups; *; gap; manual"}
::
\bibitem[GAP]{GAP4}
The GAP~Group, \emph{GAP -- Groups, Algorithms, and Programming, Version 4.4}; 2005,
{\tt http://www.gap-system.org}.
.. index::
pair: referencing; Singular
For Singular, you may use
::
[GPS05] G.-M. Greuel, G. Pfister, and H. Sch\"onemann.
{\sc Singular} 3.0. A Computer Algebra System for Polynomial
Computations. Centre for Computer Algebra, University of
Kaiserslautern (2005). {\tt http://www.singular.uni-kl.de}.
or
::
@TechReport{GPS05,
author = {G.-M. Greuel and G. Pfister and H. Sch\"onemann},
title = {{\sc Singular} 3.0},
type = {{A Computer Algebra System for Polynomial Computations}},
institution = {Centre for Computer Algebra},
address = {University of Kaiserslautern},
year = {2005},
note = {{\tt http://www.singular.uni-kl.de}},
}
or
::
\bibitem[GPS05]{GPS05}
G.-M.~Greuel, G.~Pfister, and H.~Sch\"onemann.
\newblock {{\sc Singular} 3.0}. A Computer Algebra System for Polynomial Computations.
\newblock Centre for Computer Algebra, University of Kaiserslautern (2005).
\newblock {\tt http://www.singular.uni-kl.de}.
.. index:: logging Sage
Logging your Sage session
=========================
Yes you can log your sessions.
(a) Modify line 186 of the .ipythonrc file (or open .ipythonrc into
an editor and search for "logfile"). This will only log your input
lines, not the output.
(b) You can also write the output to a file, by running Sage in the
background ( :ref:`section-background` ).
(c) Start in a KDE konsole (this only work in linux). Go to
``Settings`` :math:`\rightarrow` ``History ...`` and select
unlimited. Start your session. When ready, go to ``edit``
:math:`\rightarrow` ``save history as ...``.
Some interfaces (such as the interface to Singular or that to GAP)
allow you to create a log file. For Singular, there is a logfile
option (in ``singular.py``). In GAP, use the command ``LogTo``.
.. index:: LaTeX output
LaTeX conversion
================
Yes, you can output some of your results into LaTeX.
::
sage: M = MatrixSpace(RealField(),3,3)
sage: A = M([1,2,3, 4,5,6, 7,8,9])
sage: print latex(A)
\left(\begin{array}{rrr}
1.00000000000000 & 2.00000000000000 & 3.00000000000000 \\
4.00000000000000 & 5.00000000000000 & 6.00000000000000 \\
7.00000000000000 & 8.00000000000000 & 9.00000000000000
\end{array}\right)
.. skip
::
sage: view(A)
At this point a dvi preview should automatically be called to
display in a separate window the LaTeX output produced.
LaTeX previewing for multivariate polynomials and rational functions
is also available:
::
sage: x = PolynomialRing(QQ,3, 'x').gens()
sage: f = x[0] + x[1] - 2*x[1]*x[2]
sage: h = f /(x[1] + x[2])
sage: print latex(h)
\frac{-2 x_{1} x_{2} + x_{0} + x_{1}}{x_{1} + x_{2}}
Sage and other computer algebra systems
=======================================
If ``foo`` is a Pari, GAP ( without ending semicolon), Singular,
Maxima command, resp., enter ``gp("foo")`` for Pari,
``gap.eval("foo")}`` ``singular.eval("foo")``, ``maxima("foo")``, resp..
These programs merely send the command string to the external
program, execute it, and read the result back into Sage. Therefore,
these will not work if the external program is not installed and in
your PATH.
.. index:: help in Sage
Command-line Sage help
======================
If you know only part of the name of a Sage command and want to
know where it occurs in Sage, a new option for 0.10.11 has been
added to make it easier to hunt it down. Just type
``sage -grep `` to find all occurences of ```` in the
Sage source code. For example,
::
was@form:~/s/local/bin$ sage -grep berlekamp_massey
matrix/all.py:from berlekamp_massey import berlekamp_massey
matrix/berlekamp_massey.py:def berlekamp_massey(a):
matrix/matrix.py:import berlekamp_massey
matrix/matrix.py: g =
berlekamp_massey.berlekamp_massey(cols[i].list())
Type ``help(foo)`` or ``foo??`` for help and ``foo.[tab]`` for searching
of Sage commands. Type ``help()`` for Python commands.
For example
::
help(Matrix)
returns
::
Help on function Matrix in module sage.matrix.constructor:
Matrix(R, nrows, ncols, entries = 0, sparse = False)
Create a matrix.
INPUT:
R -- ring
nrows -- int; number of rows
ncols -- int; number of columns
entries -- list; entries of the matrix
sparse -- bool (default: False); whether or not to store matrices as sparse
OUTPUT:
a matrix
EXAMPLES:
sage: Matrix(RationalField(), 2, 2, [1,2,3,4])
[1 2]
[3 4]
sage: Matrix(FiniteField(5), 2, 3, range(6))
[0 1 2]
[3 4 0]
sage: Matrix(IntegerRing(), 10, 10, range(100)).parent()
Full MatrixSpace of 10 by 10 dense matrices over Integer Ring
sage: Matrix(IntegerRing(), 10, 10, range(100), sparse = True).parent()
Full MatrixSpace of 10 by 10 sparse matrices over Integer Ring
in a new screen. Type q to return to the Sage screen.
.. index:: importing into Sage
Reading and importing files into Sage
=====================================
A file imported into Sage must end in ``.py``, e.g., ``foo.py`` and
contain legal Python syntax. For a simple example see :ref:`section-permutation`
with the Rubik's cube group example above.
Another way to read a file in is to use the ``load`` or ``attach``
command. Create a file called ``example.sage`` (located in the home
directory of Sage) with the following content:
.. skip
::
print "Hello World"
print 2^3
.. index:: load into Sage
Read in and execute ``example.sage`` file using the ``load`` command.
.. skip
::
sage: load("example.sage")
Hello World
8
.. index:: attach into Sage
You can also ``attach`` a Sage file to a running session:
.. skip
::
sage: attach("example.sage")
Hello World
8
Now if you change ``example.sage`` and enter one blank line into
Sage, then the contents of ``example.sage`` will be automatically
reloaded into Sage:
.. skip
::
sage: !emacs example.sage& #change 2^3 to 2^4
sage: #hit return
***************************************************
Reloading 'example.sage'
***************************************************
Hello World
16
.. index:: installation of Sage
.. _section-installALL:
Installation for the impatient
==============================
We shall explain the basic steps for installing the most recent
version of Sage (which is the "source" version, not the "binary").
#. Download ``sage-*.tar`` (where ``*`` denotes the version number)
from the website and save into a directory, say ``HOME``. Type
``tar zxvf sage-*.tar`` in ``HOME``.
#. cd ``sage-*`` (we call this ``SAGE_ROOT``) and type ``make``. Now be
patient because this process make take 2 hours or so.
#. Optional: When the compilation is finished, type on the command
line in the Sage home directory:
::
./sage -i database_jones_numfield
./sage -i database_gap-4.4.8
./sage -i database_cremona_ellcurve-2005.11.03
./sage -i gap_packages-4.4.8_1
This last package loads the GAP GPL'd packages braid, ctbllib,
DESIGN, FactInt, GAPDoc, GRAPE, LAGUNA, SONATA 2.3, and TORIC . It
also compiles (automatically) the C programs in GUAVA and GRAPE.
Other optional packages to install are at
http://modular.math.washington.edu/sage/packages/optional/.
.. index:: installation of packages
Another way: download packages from
http://sage.scipy.org/sage/packages/optional/ and save to the
directory ``SAGE_ROOT``. Type
::
/sage -i sage-package.spkg
for each ``sage-package`` you download (use ``sage -f`` if you are
reinstalling.) This might be useful if you have a CD of these
packages but no (or a very slow) internet connection.
.. index:: Python and Sage
Python language program code for Sage commands
==============================================
Let's say you want to know what the Python program is for the Sage
command to compute the center of a permutation group. Use Sage's
help interface to find the file name:
.. skip
::
sage: PermutationGroup.center?
Type: instancemethod
Base Class:
String Form:
Namespace: Interactive
File: /home/wdj/sage/local/lib/python2.4/site-packages/sage/groups/permgroup.py
Definition: PermutationGroup.center(self)
Now you know that the command is located in the ``permgroup.py`` file
and you know the directory to look for that Python module. You can
use an editor to read the code itself.
.. index:: special functions in Sage
"Special functions" in Sage
===========================
Sage has several special functions:
- Bessel functions and Airy functions
- spherical harmonic functions
- spherical Bessel functions (of the 1st and 2nd kind)
- spherical Hankel functions (of the 1st and 2nd kind)
- Jacobi elliptic functions
- complete/incomplete elliptic integrals
- hyperbolic trig functions (for completeness, since they are
special cases of elliptic functions)
and orthogonal polynomials
- chebyshev\_T (n, x), chebyshev\_U (n, x) - the Chebyshev
polynomial of the first, second kind for integers
:math:`n > -1`.
- laguerre (n, x), gen\_laguerre (n, a, x) - the (generalized)
Laguerre poly. for :math:`n > -1`.
- legendre\_P (n, x), legendre\_Q (n, x), gen\_legendre\_P (n, x),
gen\_legendre\_Q (n, x) - the (generalized) Legendre function of
the first, second kind for integers :math:`n > -1`.
- hermite (n,x) - the Hermite poly. for integers
:math:`n > -1`.
- jacobi\_P (n, a, b, x) - the Jacobi polynomial for integers
:math:`n > -1` and :math:`a` and :math:`b` symbolic or
:math:`a > -1` and :math:`b > -1`.
- ultraspherical (n,a,x) - the ultraspherical polynomials for
integers :math:`n > -1`. The ultraspherical polynomials are also
known as Gegenbauer polynomials.
In Sage, these are restricted to numerical evaluation and plotting but
via maxima, some symbolic manipulation is allowed:
::
sage: maxima.eval("f:bessel_y (v, w)")
'bessel_y(v,w)'
sage: maxima.eval("diff(f,w)")
'(bessel_y(v-1,w)-bessel_y(v+1,w))/2'
sage: maxima.eval("diff (jacobi_sn (u, m), u)")
'jacobi_cn(u,m)*jacobi_dn(u,m)'
sage: jsn = lambda x: jacobi("sn",x,1)
sage: P = plot(jsn,0,1, plot_points=20); Q = plot(lambda x:bessel_Y( 1, x), 1/2,1)
sage: show(P)
sage: show(Q)
In addition to ``maxima``, ``pari`` and ``octave`` also have special
functions (in fact, some of ``pari``'s special functions are wrapped
in Sage).
Here's an example using Sage's interface (located in
sage/interfaces/octave.py) with ``octave``
(http://www.octave.org/doc/index.html).
::
sage: octave("atanh(1.1)") ## optional - octave
(1.52226,-1.5708)
Here's an example using Sage's interface to ``pari``'s special
functions.
::
sage: pari('2+I').besselk(3)
0.0455907718407551 + 0.0289192946582081*I
sage: pari('2').besselk(3)
0.0615104584717420
What is Sage?
=============
Sage is a framework for number theory, algebra, and geometry
computation that is initially being designed for computing with
elliptic curves and modular forms. The long-term goal is to make it
much more generally useful for algebra, geometry, and number
theory. It is open source and freely available under the terms of
the GPL. The section titles in the reference manual gives a rough
idea of the topics covered in Sage.
.. index::
pair: Sage; history
History of Sage
---------------
Sage was started by William Stein while at Harvard University in
the Fall of 2004, with version 0.1 released in January of 2005.
That version included Pari, but not GAP or Singular. Version 0.2
was released in March, version 0.3 in April, version 0.4 in July.
During this time, support for Cremona's database, multivariate
polynomials and large finite fields was added. Also, more
documentation was written. Version 0.5 beta was released in August,
version 0.6 beta in September, and version 0.7 later that month.
During this time, more support for vector spaces, rings, modular
symbols, and windows users was added. As of 0.8, released in
October 2005, Sage contained the full distribution of GAP, though
some of the GAP databases have to be added separately, and
Singular. Adding Singular was not easy, due to the difficulty of
compiling Singular from source. Version 0.9 was released in
November. This version went through 34 releases! As of version
0.9.34 (definitely by version 0.10.0), Maxima and clisp were
included with Sage. Version 0.10.0 was released January 12, 2006.
The release of Sage 1.0 was made early February, 2006. As of
February 2008, the latest release is 2.10.2.
Many people have contributed significant code and other expertise,
such as assistance in compiling on various OS's. Generally code
authors are acknowledged in the AUTHOR section of the Python
docstring of their file and the credits section of the Sage
website.