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Sage

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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

Run

Commandline Interface

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 Interface

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

> sage: notebook()

Introduction

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

Very simple calculation

• Numbers

 > sage: 1+1
 > 2

• Symbolic expression

 > sage: sqrt(2)
 > sqrt(2)

• Evaluate a symbolic expression

 > sage: sqrt(2).n(digits=100)
 > 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573

Arrays

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

Crash Course

Understanding Objects

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