FAQ: Using Sage¶
How do I get started?¶
You can try out Sage without downloading anything:
CoCalc™: Go to https://cocalc.com and set up a free account.
If you log in, you will gain access to the latest version of Sage and to many other programs.
Note that this website is an independent commercial service.
Sage cell: A “one-off” version of Sage, available for doing one computation at a time. https://sagecell.sagemath.org/
To download a pre-built binary Sage distribution, visit http://sagemath.org/download.html and click on the link for the binary for your operating system.
The source code of Sage is also available for you to download and use. Go to http://www.sagemath.org/download-source.html to download the tar archive for any release of Sage.
The Sage Jupyter notebook runs within a web browser. To start the notebook,
issue the following command in a terminal, if sage is in your PATH
$ sage -notebook
What are the prerequisites for installing a copy of Sage on my computer?¶
Most of the dependencies of Sage are shipped with Sage itself. In most cases, you can download a pre-built binary and use that without installing any dependencies. If you use Windows, you will need to install VirtualBox, which can be downloaded from the page https://www.virtualbox.org/wiki/Downloads. After installing VirtualBox, you need to download a VirtualBox distribution of Sage available at http://www.sagemath.org/download-windows.html. Ensure you follow the instructions at that page, then start the Sage virtual machine using the VirtualBox software.
You can get the complete source for Sage to compile it on your own
Linux or Mac OS X system. Sage lives in an isolated directory and does
not interfere with your surrounding system. It ships together with
everything necessary to develop Sage, the source code, all its
dependencies and the complete changelog. On Linux systems like
Debian/Ubuntu, you may have to install the build essential
package and the m4 macro processor. Your system
needs to have a working C compiler if you want to compile Sage
from source. On
Debian/Ubuntu, you can install these prerequisites as follows:
$ sudo apt-get install build-essential m4
If you have a multi-core system, you can opt for a parallel build of Sage. The command
$ export MAKE='make -j8'
will enable 8 threads for parts of the build that support parallelism. Change the number 8 as appropriate to suit the number of cores on your system. Some Sage installations may have OpenMP-enabled BLAS (and other) libraries. The amount of OpenMP parallelism is controlled by the environment variable OMP_NUM_THREADS; however, it is known to not play well with Python parallelism, and you might want to
$ export OMP_NUM_THREADS=1
in case of crashes or hangs.
More details may be found in Installation Manual.
How to get Sage’s Python to recognize my system’s Tcl/Tk install?¶
It may be that you have Tcl/Tk installed and that your system’s Python recognizes it but Sage’s Python does not. Normally speaking, there is little need to build Sage’s Python nowadays (anno 2023), but if you do, here it is. Make sure you installed the Tcl/Tk development library. On Ubuntu, this is the command
$ sudo apt-get install tk8.5-dev
or something along that line. Next, reinstall Sage’s Python:
$ make python3-clean python3-uninstall && make python3
This will pick up the Tcl/Tk library automatically. After successfully reinstalling Sage’s Python, from within the Sage command line interface, issue these commands:
import _tkinter
import Tkinter
If they do not raise an ImportError then it worked.
How do I import Sage into a Python script?¶
You can import Sage as a library in a Python script. One caveat is that you need to run that Python script using the version of Python that is bundled with Sage (Sage 9.2 ships with Python 3.7.x). To import Sage, put the following in your Python script:
from sage.all import *
When you want to run your script, you need to invoke Sage with the
option -python which would run your script using the version of
Python that comes with Sage. For example, if Sage is in your PATH
variable then you can do this:
$ sage -python /path/to/my/script.py
Another way is to write a Sage script and run that script using Sage
itself. A Sage script has the file extension .sage and is more or
less a Python script but uses Sage-specific functions and
commands. You can then run that Sage script like so:
$ sage /path/to/my/script.sage
This will take care of loading the necessary environment variables and default imports for you.
How can I reload a Python script in a Sage session?¶
You can load a Python script in a Sage session with the command load. For example, we could use Sage to import a file called simple.py with:
load("simple.py")
and repeat this command every time that we change the file simple.py. However, if we type:
attach("simple.py")
every change applied to the file simple.py will be automatically updated in Sage.
Can I use SageMath with Python 3.x?¶
Since release 9.0 from January 2020, SageMath is running on top of Python 3.
I used XXX to install Sage X.Y and that version is giving lots of errors. What can I do?¶
The version of Sage, i.e. Sage version X.Y, that is available on your XXX system through its package manager, is very old. No one has yet found time to update the XXX version of Sage. Any help is greatly appreciated. You should download the latest version of Sage from the download page. If you would like to help with updating the XXX version of Sage, please email the sage-devel mailing list.
Should I use the official version or development version?¶
You are encouraged to use the latest official version of Sage. Development versions are frequently announced on the sage-devel and sage-release mailing lists. An easy way of helping out with Sage development is to download the latest development release, compile it on your system, run all doctests, and report any compilation errors or doctest failures.
Is Sage difficult to learn?¶
Basic features of Sage should be as easy to learn as learning the basics of Python. Numerous tutorials are available online to help you learn Sage. To get the most out of Sage, you are encouraged to learn some features of the Python programming language. Here is an incomplete list of resources on Python. Further resources can be found by a web search.
Building Skills in Python by Steven F. Lott
Dive into Python by Mark Pilgrim
How to Think Like a Computer Scientist by Jeffrey Elkner, Allen B. Downey, and Chris Meyers
Python home page and the Python standard documentation
Can I do X in Sage?¶
You are encouraged to use Sage’s tab autocompletion. Just type a few
characters, hit the Tab key, and see if the command you want appears
in the list of tab autocompletion. If you have a command called
mycmd, then type mycmd. and hit the Tab key to get a list of
functionalities that are supported by that command. To read the
documentation of mycmd, type mycmd? and press the Enter key to
read the documentation for that command. Similarly, type mycmd??
and hit the Enter key to get the source code of that command. You are
also encouraged to search through the source code and documentation of
the Sage library. To search through the source code of the Sage
library, use the command search_src("<search-keyword>") where you
should replace <search-keyword> with the key words you are looking
for. Also, you can search through the documentation of the Sage
library using the command search_doc("<search-keyword>").
What exactly does Sage do when I type “0.6**2”?¶
When you type “0.6**2” in Python, it returns something like 0.35999999999999999. But when you do the same in Sage it returns 0.360000000000000. To understand why Python behaves as it does, see the Python Tutorial, especially the chapter “Floating Point Arithmetic: Issues and Limitations”. What Sage does is “preparse” the input and transforms it like this:
sage: preparse("0.6**2")
"RealNumber('0.6')**Integer(2)"
>>> from sage.all import *
>>> preparse("0.6**2")
"RealNumber('0.6')**Integer(2)"
preparse("0.6**2")
So what is actually run is:
RealNumber('0.6')**Integer(2)
The Sage developers (in fact, Carl Witty) decided that Sage floating
point numbers should by default print only the known correct decimal
digits, when possible, thus skirting the problem that Python has. This
decision has its pros and cons. Note that RealNumber and
Integer are Sage specific, so you would not be able to just type
the above into Python and expect it to work without first an import
statement such as:
from sage.all import RealNumber, Integer, preparse
Why is Sage’s command history different from Magma’s?¶
Using Sage, you are missing a feature of the Magma command line interface. In Magma, if you enter a line found in history using up arrow key and then press down arrow key, then the next line in history is fetched. This feature allows you to fetch as many successive lines in history as you like. However, Sage does not have a similar feature. The IPython command prompt uses the readline library (via pyreadline), which evidently does not support this feature. Magma has its own custom “readline-like” library, which does support this feature. (Since so many people have requested this feature, if anybody can figure out how to implement it, then such an implementation would certainly be welcome!)
I have type issues using SciPy, cvxopt or NumPy from Sage.¶
You are using SciPy or cvxopt or NumPy from Sage and you get type errors, e.g.
TypeError: function not supported for these types, and can't coerce safely to supported types.
When you type in numbers into Sage, the pre-processor converts them to a base ring, which you can see by doing:
sage: preparse("stats.uniform(0,15).ppf([0.5,0.7])")
"stats.uniform(Integer(0),Integer(15)).ppf([RealNumber('0.5'),RealNumber('0.7')])"
>>> from sage.all import *
>>> preparse("stats.uniform(0,15).ppf([0.5,0.7])")
"stats.uniform(Integer(0),Integer(15)).ppf([RealNumber('0.5'),RealNumber('0.7')])"
preparse("stats.uniform(0,15).ppf([0.5,0.7])")
Unfortunately, NumPy support of these advanced Sage types like
Integer or RealNumber is not yet at 100%. As a solution,
redefine RealNumber and/or Integer to change the behavior of
the Sage preparser, so decimal literals are floats instead of Sage
arbitrary precision real numbers, and integer literals are Python
ints. For example:
sage: RealNumber = float; Integer = int
sage: from scipy import stats
sage: stats.ttest_ind([1,2,3,4,5], [2,3,4,5,.6])
Ttest...Result(statistic=...0.0767529..., pvalue=...0.940704...)
sage: stats.uniform(0,15).ppf([0.5,0.7])
array([ 7.5, 10.5])
>>> from sage.all import *
>>> RealNumber = float; Integer = int
>>> from scipy import stats
>>> stats.ttest_ind([Integer(1),Integer(2),Integer(3),Integer(4),Integer(5)], [Integer(2),Integer(3),Integer(4),Integer(5),RealNumber('.6')])
Ttest...Result(statistic=...0.0767529..., pvalue=...0.940704...)
>>> stats.uniform(Integer(0),Integer(15)).ppf([RealNumber('0.5'),RealNumber('0.7')])
array([ 7.5, 10.5])
RealNumber = float; Integer = int from scipy import stats stats.ttest_ind([1,2,3,4,5], [2,3,4,5,.6]) stats.uniform(0,15).ppf([0.5,0.7])
Alternatively, be explicit about data types, e.g.
sage: from scipy import stats
sage: stats.uniform(int(0),int(15)).ppf([float(0.5),float(0.7)])
array([ 7.5, 10.5])
>>> from sage.all import *
>>> from scipy import stats
>>> stats.uniform(int(Integer(0)),int(Integer(15))).ppf([float(RealNumber('0.5')),float(RealNumber('0.7'))])
array([ 7.5, 10.5])
from scipy import stats stats.uniform(int(0),int(15)).ppf([float(0.5),float(0.7)])
As a third alternative, use the raw suffix:
sage: from scipy import stats
sage: stats.uniform(0r,15r).ppf([0.5r,0.7r])
array([ 7.5, 10.5])
>>> from sage.all import *
>>> from scipy import stats
>>> stats.uniform(0,15).ppf([0.5,0.7])
array([ 7.5, 10.5])
from scipy import stats stats.uniform(0r,15r).ppf([0.5r,0.7r])
You can also disable the preprocessor in your code via
preparser(False). You can start IPython alone from the command
line sage -ipython which does not pre-load anything
Sage-specific. Or switch the Notebook language to “Python”.
How do I save an object so I don’t have to compute it each time I open a worksheet?¶
The save and load commands will save and load an object,
respectively.
Does Sage contain a function similar to Mathematica’s ToCharacterCode[]?¶
You might want to convert ASCII characters such as “Big Mac” to ASCII
numerals for further processing. In Sage and Python, you can use ord,
e.g.
sage: list(map(ord, "abcde"))
[97, 98, 99, 100, 101]
sage: list(map(ord, "Big Mac"))
[66, 105, 103, 32, 77, 97, 99]
>>> from sage.all import *
>>> list(map(ord, "abcde"))
[97, 98, 99, 100, 101]
>>> list(map(ord, "Big Mac"))
[66, 105, 103, 32, 77, 97, 99]
list(map(ord, "abcde")) list(map(ord, "Big Mac"))
How can I write multiplication implicitly as in Mathematica?¶
Sage has a function that enables this:
sage: implicit_multiplication(True)
sage: x 2 x # not tested
2*x^2
sage: implicit_multiplication(False)
>>> from sage.all import *
>>> implicit_multiplication(True)
>>> x Integer(2) x # not tested
2*x^2
>>> implicit_multiplication(False)
implicit_multiplication(True) x 2 x # not tested implicit_multiplication(False)
This is preparsed by Sage into Python code. It may not work in a complicated situation. To see what the preparser does:
sage: implicit_multiplication(True)
sage: preparse("2 x")
'Integer(2)*x'
sage: implicit_multiplication(False)
sage: preparse("2 x")
'Integer(2) x'
>>> from sage.all import *
>>> implicit_multiplication(True)
>>> preparse("2 x")
'Integer(2)*x'
>>> implicit_multiplication(False)
>>> preparse("2 x")
'Integer(2) x'
implicit_multiplication(True)
preparse("2 x")
implicit_multiplication(False)
preparse("2 x")
See https://wiki.sagemath.org/sage_mathematica for more information about Mathematica vs. SageMath.
Can I make Sage automatically execute commands on startup?¶
Yes, just make a file $HOME/.sage/init.sage and it will be
executed any time you start Sage. This assumes that the Sage
environment variable DOT_SAGE points to the hidden directory
$HOME/.sage, which by default is the case.
When I compile Sage my computer beeps and shuts down or hangs.¶
Compiling Sage is quite taxing on the CPU. The above behavior usually indicates that your computer has overheated. In many cases this can be fixed by cleaning the CPU fan and assuring proper ventilation of the system. Please ask your system administrator or a professional to do this in case you have never done this. Such hardware maintenance, if not performed by a skilled professional, you can potentially damage your system.
For Linux users, if you suspect that the compilation fails because of
a resource issue, a fix might be to edit your /etc/inittab so that
Linux boots into run level 3. The file /etc/inittab usually
contains something similar to the following snippet:
# 0 - halt (Do NOT set initdefault to this)
# 1 - Single user mode
# 2 - Multiuser, without NFS (The same as 3, if you do not have
# networking)
# 3 - Full multiuser mode
# 4 - unused
# 5 - X11
# 6 - reboot (Do NOT set initdefault to this)
#
id:5:initdefault:
which directs your Linux distribution to boot into a graphical login
screen. Comment out the line id:5:initdefault: and add the line
id:3:initdefault:, so that you now have something like:
# 0 - halt (Do NOT set initdefault to this)
# 1 - Single user mode
# 2 - Multiuser, without NFS (The same as 3, if you do not have
# networking)
# 3 - Full multiuser mode
# 4 - unused
# 5 - X11
# 6 - reboot (Do NOT set initdefault to this)
#
# id:5:initdefault:
id:3:initdefault:
Now if you reboot your system, you will be greeted with a text based login screen. This allows you to log into your system with a text based session from within a virtual terminal. A text based session usually does not consume as much system resources as would be the case with a graphical session. Then build your Sage source distribution from within your text based session. You need to make sure that you can first restore your graphical session, before you attempt to log into a text based session.
When I start Sage, SELinux complains that “/path/to/libpari-gmp.so.2” requires text-relocation. How can I fix it?¶
The problem can be fixed by running the following command:
$ chcon -t textrel_shlib_t /path/to/libpari-gmp.so.2
How do I run sage in daemon mode, i.e. as a service?¶
There are several possibilities. Use screen, nohup or disown.
May I use Sage tools in a commercial environment?¶
Yes! Absolutely! Basically the only constraint is that if you make changes to Sage itself and redistribute this changed version of Sage publicly, then you must make these changes available to us so that we can put them into the standard version of Sage (if we want). Otherwise, you are free to use as many copies of Sage as you want completely for free to make money, etc. without paying any license fees at all.
I want to write some Cython code that uses finite field arithmetic but “cimport sage.rings.finite_field_givaro” fails. What can I do?¶
You need to give hints to Sage so that it uses C++ (both Givaro and NTL are C++ libraries), and it also needs the GMP and STDC C++ libraries. Here is a small example:
# These comments are hints to Cython about the compiler and
# libraries needed for the Givaro library:
#
# distutils: language = c++
# distutils: libraries = givaro gmpxx gmp m
cimport sage.rings.finite_field_givaro
# Construct a finite field of order 11.
cdef sage.rings.finite_field_givaro.FiniteField_givaro K
K = sage.rings.finite_field_givaro.FiniteField_givaro(11)
print("K is a {}".format(type(K)))
print("K cardinality = {}".format(K.cardinality()))
# Construct two values in the field:
cdef sage.rings.finite_field_givaro.FiniteField_givaroElement x
cdef sage.rings.finite_field_givaro.FiniteField_givaroElement y
x = K(3)
y = K(6)
print("x is a {}".format(type(x)))
print("x = {}".format(x))
print("y = {}".format(y))
print("x has multiplicative order = {}".format(x.multiplicative_order()))
print("y has multiplicative order = {}".format(y.multiplicative_order()))
print("x*y = {}".format(x * y))
# Show that x behaves like a finite field element:
for i in range(1, x.multiplicative_order() + 1):
print("{} {}".format(i, x**i))
assert x*(1/x) == K.one()
To find out more, type
sage.rings.finite_field_givaro.FiniteField_givaro.
at the Sage prompt and hit tab, then use ?? to get more
information on each function. For example:
sage.rings.finite_field_givaro.FiniteField_givaro.one??
tells you more about the multiplicative unit element in the finite field.
I’m getting weird build failures on Mac OS X. How do I fix this?¶
Search the build log (install.log) to see if you are getting the following log message:
fork: Resource temporarily unavailable.
If so, try the following. Create (or edit) /etc/launchd.conf and
include the following:
limit maxproc 512 2048
then reboot. See this page for more details.
How do I plot the cube root (or other odd roots) for negative input?¶
This is one of the most frequently asked questions. There are several methods mentioned in the plot documentation, but this one is easiest:
sage: plot(real_nth_root(x, 3), (x, -1, 1))
Graphics object consisting of 1 graphics primitive
>>> from sage.all import *
>>> plot(real_nth_root(x, Integer(3)), (x, -Integer(1), Integer(1)))
Graphics object consisting of 1 graphics primitive
plot(real_nth_root(x, 3), (x, -1, 1))
On the other hand, note that the straightforward
sage: plot(x^(1/3), (x, -1, 1)) # not tested
>>> from sage.all import *
>>> plot(x**(Integer(1)/Integer(3)), (x, -Integer(1), Integer(1))) # not tested
plot(x^(1/3), (x, -1, 1)) # not tested
produces the expected plot only for positive \(x\). The reason is that Sage returns complex numbers for odd roots of negative numbers when numerically approximated, which is a standard convention.
sage: numerical_approx( (-1)^(1/3) )
0.500000000000000 + 0.866025403784439*I
>>> from sage.all import *
>>> numerical_approx( (-Integer(1))**(Integer(1)/Integer(3)) )
0.500000000000000 + 0.866025403784439*I
numerical_approx( (-1)^(1/3) )
How do I use the bitwise XOR operator in Sage?¶
The exclusive or operator in Sage is ^^. This also works for
the inplace operator ^^=:
sage: 3^^2
1
sage: a = 2
sage: a ^^= 8
sage: a
10
>>> from sage.all import *
>>> Integer(3)^Integer(2)
1
>>> a = Integer(2)
>>> a ^= Integer(8)
>>> a
10
3^^2 a = 2 a ^^= 8 a
If you define two variables and then evaluate as follows:
sage: a = 5; b = 8
sage: a.__xor__(b), 13
(13, 13)
>>> from sage.all import *
>>> a = Integer(5); b = Integer(8)
>>> a.__xor__(b), Integer(13)
(13, 13)
a = 5; b = 8 a.__xor__(b), 13
You can also do
sage: (5).__xor__(8)
13
>>> from sage.all import *
>>> (Integer(5)).__xor__(Integer(8))
13
(5).__xor__(8)
The parentheses are necessary so that Sage does not think you have a real number. There are several ways to define a function:
sage: xor = lambda x, y: x.__xor__(y)
sage: xor(3, 8)
11
>>> from sage.all import *
>>> xor = lambda x, y: x.__xor__(y)
>>> xor(Integer(3), Integer(8))
11
xor = lambda x, y: x.__xor__(y) xor(3, 8)
Another option, which sneaks around the Sage preparser, is
sage: def xor(a, b):
....: return eval("%s^%s" % (a, b))
sage: xor(3, 8)
11
>>> from sage.all import *
>>> def xor(a, b):
... return eval("%s^%s" % (a, b))
>>> xor(Integer(3), Integer(8))
11
def xor(a, b):
return eval("%s^%s" % (a, b))
xor(3, 8)
You can also turn off the Sage preparser with preparser(False),
then ^ will work just like in Python. You can later turn on the
preparser with preparser(True). That only works in command line
Sage. In a notebook, switch to Python mode.
With objects a and b and a function f, I accidentally typed f(a) = b instead of f(a) == b. This returned a TypeError (as expected), but also deleted the object a. Why?¶
It is because of how functions are defined in Sage with the
f(x) = expr notation using the preparser. Also notice that if you
make this mistake inside of an if statement, you will get a
SyntaxError before anything else goes wrong. So in this case,
there is no problem.
How do I use a different browser with the Sage notebook?¶
You will need to do this from the command line. Just run a command like this.
Linux (assuming you have Sage in
/usr/bin):$ env BROWSER=opera /usr/bin/sage --notebook
Mac (assuming you are in the directory of your downloaded Sage). With the Jupyter notebook:
$ BROWSER='open -a Firefox %s' ./sage --notebook jupyter $ BROWSER='open -a Google\ Chrome %s' ./sage --notebook jupyter
Where is the source code for <function>?¶
Functions and classes written in Python or Cython are in general accessible
on the IPython command line with the ?? shortcut:
sage: plot?? # not tested
Signature: plot(*args, **kwds)
Source:
...
>>> from sage.all import *
>>> plot?? # not tested
Signature: plot(*args, **kwds)
Source:
...
plot?? # not tested
Objects that are built into Python or IPython are compiled and will not show, however. There are many functions in Sage implemented as symbolic functions, i.e., they can be used unevaluated as part of symbolic expressions. Their source code may also not be accessible from the command line, especially with elementary functions, because they are coded in C++ for efficiency reasons.