SageMath Worksheets in CoCalc

This is an interactive document for running calculation online.

First, notice the additional button bar below the project specific bar. The "Play" button is for evaluating a block.
Each block of consecutive lines can either be input of code which is run by the interpreter or some text formatted via markdown.
A block is evaluated by placing the cursor into it and either clicking on the "Play" button or by simultaneously pressing the Shift+Return keys.
New blocks are inserted at the bottom or when clicking on the delimiter line inbetween two blocks.
The first line of each input block signals the type of cell: e.g. %md for markdown, %r for R, %python3 for Python3 or %sage for SageMath.
For the evaluation the default mode is usually set to SageMath, but it can be customized by running %default_mode <mode>.
On the left side of each block there is a small triangle. It hides or reveals input and output blocks. This can also be accomplished by placing the cursor inside a block and clicking on the "out" toggle button in the menu.

Let's start with a simple calculation:

2873648273648 * 293847293849723847

Here, we define two symbolic variables in Sage

x, y = var('x, y')

Build a symbolic expression $z = \frac{x}{1 + y^2}$

z = x / (1 + y^2)
show(z)

... and evaluate it at $x=4$ and $y=2$

z(x = 4, y = 2)

... define a function "f(x)"

f(x) = 2 * x + cos(x)

... evaluate it at $4 \pi$

f(4 * pi)

... and plot it for $x \in \left[-10, \, 10\right]$

plot(f, (x, -10, 10))

Task: where is $f(x) = 0$ ?

Unfold the next input block to see the answer!

Next, let's go back to first-steps.tasks