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Doing Mathematics with CoCalc

by William Stein

Online Colloquium Series

SageMath, Inc.

Feb 24, 2023

What is CoCalc?

Jupyter + SageMath right here

version()
'SageMath version 9.8, Release Date: 2023-02-11'
show(factor(2023))

show(plot(sin(x^2)/x, (x, -2*pi, 2*pi), figsize=[6,2]))
[unavailable png image]
next_prime(randint(0, 10**500), proof=False)
67738145509333003733649862788091607704800095245889089251008505590617536224247195668436723406775803958247420477003979334687776030099290149735328075642194238853615257728640512330483267369878324783564540411776977998475176607011395705404609318879723115992178709742010211239253944921771816155826593150988015472846834633975763870618621546087358125464050309636874474998529182262712567454807949544755041522090093988300769121586548500399755103041866233940011536855253527101644279076284156272427164730820619037

Background

  • Grad school at Berkeley in late 90s: online tables & calculators (cgi-bin, C++)

  • Teaching at Harvard 2000-2005: online calculators using Pari and Magma for my students. Started SageMath in 2004 when threatened by closed Magma.

  • At Univ of Washington in 2006-2007: Wrote first "Mathematica-like" web-based notebook (the Sage Notebook). Jupyter started in 2011 and was similar, so we deprecated the Sage notebook, since wanted to work on math software.

  • Teaching at UW: First release of CoCalc in 2013, so my students could use Sage, LaTeX\LaTeX, R, etc., collaboratively in browser for all homework and final projects. Motivation: Jupyter/Sage notebook too limited; frustration with funding open source math software development.

  • Startup company: fulltime on CoCalc since in 2019.

Writing Mathematics Books

Includes SageMath code

Wrote entirely in CoCalc!

Guided Tour / Live Demo

Slides

That's what we're using right here!

Consider.

You can put sticky notes with math formulas using LaTeX\LaTeX:

y2=x3+αx+βy^2 = x^3 + \alpha x +\beta

Something else

yavg(a,b)=1b−a∫ab ⁣g(x) dxy_\text{avg}(a, b) = \frac{1}{b - a} \int\limits_a^b\! g(x)\,dx
xˉ=2n  ∑i=n4+134n ⁣ ⁣xi\bar{x} = \frac{2}{n} \;\sum_{i = \frac{n}{4} + 1}^{\frac{3}{4}n}\!\! x_i
E = EllipticCurve('37a'); show(E); plot(E, figsize=[3,2])
[unavailable png image]

Jupyter Notebooks

  • realtime collaboration

  • TimeTravel history

  • chat on the side

  • many kernels

  • graphical editor for text between cells

  • multiple views of notebook at once

  • publish to https://cocalc.com/share

You can also use standard JupyterLab and Jupyter Classic from CoCalc via the Servers Page...

LaTeX\LaTeX Editor

  • full collaborative LaTeX\LaTeX environment

  • PDFLaTeX, XeLaTeX, LuaTex

  • use Python and Sage in your document (we also support R via Knitr .rtex files)

  • forward and inverse search

  • high resolution TimeTravel edit history

CoCalc's Interface

  • Projects

  • Files

  • Linux terminals and graphical applications

  • Course management

  • And much more...

Thank You

Questions? There's a lot more to CoCalc...