Notes on using sage

To see already prepared worksheets

Worksheets from the lectures are also accessible through the lecture page.

Open a browser at the address http://arcikam.kam.mff.cuni.cz:12080/
Log in by using your own credentials or by using a public account. Id: Guest, pw: 8GxPsCOs. Id is case sensitive. Do not change pw!
You shall also register to receive an account, since the anonymous account will soon be blocked - as soon as most of you will register.
Then just click "New worksheet", give it a name and you may start experimenting.

See also an official tutorial on registering.

The list will be gradually updated. For more commands see a quick reference sheet that covers much more than we will need in our course.

To define a vector or a matrix
b=vector([1,0,5,3]); A=matrix(QQ,[[1,4],[3,4],[5,1]]);
or equivalently. A=matrix(QQ,3,2,[1,4,3,4,5,1]);
The first optional parameter is the field. We will need the following ones:
ZZ - integers, QQ - rationals, RR - real numbers, CC - complex numbers, GF(k) - the unique finite field with k elements.
The optional second and third parameters are the numbers of rows and columns.
To get a reduced row echelon form
A.rref() or A.echelon_form()
To transpose, multiply or invert matrices
transpose(A) A*B A^{-1} or A.inverse()
To combine two matrices together
A.augment(B) - horizontally
A.stack(B, subdivide=True) - vertically
The optional parameter subdivide=True is for aestheticeal purposes only - it draws a line between the parts.