Sage

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First Steps

Installation

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