Sage/Printable version


Sage

The current, editable version of this book is available in Wikibooks, the open-content textbooks collection, at
https://en.wikibooks.org/wiki/Sage

Permission is granted to copy, distribute, and/or modify this document under the terms of the Creative Commons Attribution-ShareAlike 3.0 License.


First Steps

InstallationEdit

RunEdit

Commandline InterfaceEdit

In Ubuntu terminal:

> ./sage
┌────────────────────────────────────────────────────────────────────┐
 SageMath version 8.1, Release Date: 2017-12-07                     
 Type "notebook()" for the browser-based notebook interface.        
 Type "help()" for help.                                            
└────────────────────────────────────────────────────────────────────┘
> sage:

Notebook InterfaceEdit

Inside Sage type "notebook()" for the browser-based notebook interface.

> sage: notebook()

IntroductionEdit

Sage is based on Python. With some exceptions, all commands are regular Python syntax.

Very simple calculationEdit

  • Numbers
 > sage: 1+1
 > 2
  • Symbolic expression
 > sage: sqrt(2)
 > sqrt(2)
  • Evaluate a symbolic expression
 > sage: sqrt(2).n(digits=100)
 > 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573

ArraysEdit

 > sage: a = [1,2,3]
 > sage: sum(a)
 > 6



Crash Course

Understanding ObjectsEdit

To work with Sage you have to know a little bit of Python, because it is the underlying language Sage is written in and it is the language Sage understands!

  • Objects: An object is a data structure with methods that operate on the data inside an object. In Python - and Sage - everything is an object, even the number "1".
  • You can store objects in variables. That is a string of characters where only a-z, A-Z, digits (digits must not be at the first position) and the sign "_" is allowed (e.g. "abs_1"). To accomplish this, enter "x=1" and indicate with "Shift-Return/Enter" that you have ended your input.
  • To access the data (the object's value) behind the variable, you have to enter it and probably write "print" in front of it.
  • The methods of an object can be accessed via the "." sign and then comes the name and parenthesis "(...)", where they can be empty or have arguments.
  • The data stored inside an object is accessed similarly just by the "." and the name but with no parenthesis.
  • Functions are objects that do not need an object.

Example:

# storing the object "11" in "x"
sage: x = 11

#show me "x"
sage: print x
11

# factorial() is a method of x
sage: x.factorial()
39916800

# sqrt is a function
sage: sqrt(x)
sqrt(11)
  • Objects can be combined with others:
    • using an operator sign like "+", "*", ...
    • inserting them into the argument list of a method or function

Example:

# operator "+" adds the values of "x" and "x"
sage: x+x
22

# function "n" evaluates the numerical value of "sqrt(11)"
sage: n(sqrt(11), digits=50)
3.3166247903553998491149327366706866839270885455894