Sage/Crash Course
< Sage
Understanding Objects
[edit | edit source]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