Examples: number theory
- The Collatz map, live
Python code items, run reactively in reading order, with their output under their code.
number theoryprogramming - Three proofs that there are infinitely many primes
Euclid, Euler and Fürstenberg, a page each, with tours: pages, math, and printing (or saving as PDF) a sheet per page or per step.
number theoryproofs - Museum tour: how do you solve polynomial equations? (after Bianca Viray)
A tour in rooms: solving polynomial equations by Newton's method, number fields, Galois groups and rational points.
polynomialsnumber theory - Number theory in Sage
Sage code items: primes, a Fermat number factored, the Chinese remainder theorem, and arithmetic functions.
number theory - How do you solve polynomial equations over Q? A museum tour
Rational roots, Galois groups, rational points on a circle and on an elliptic curve, in Sage code items.
polynomialsnumber theory - A paper with its own helper code
SageTeX whose code imports helper.py beside the .tex: Pell's equation for 61 and the longest Collatz run below 1000. A document is a folder.
writingnumber theorysagebrush - A notebook with its own helper code
A notebook that imports its longer functions from _code/helpers.py beside it, and reads a data file: a document is a folder.
programmingnumber theorysagebrush - A notebook that hides its setup
Continued fractions of the square root of 2 and of pi, with the setup code hidden and a long check's output hidden (Jupyter's own flags).
number theoryprogramming - Number theory
The extended Euclidean algorithm, Fermat numbers, RSA in a few lines and Pell's equation, in plain Python.
number theory - Algebraic number theory (Sage)
Number fields: discriminants, maximal orders, units, regulators and how primes split.
number theoryalgebra - Sage
Sage mode: ^ is a power, division is exact; harmonic numbers, factoring and primes.
basicsnumber theory - Galois groups (Sage)
Galois groups of polynomials over the rationals, and how the descent found them.
group theorypolynomialsnumber theory - Modular forms (Sage)
Modular symbols, Hecke polynomials, spaces with a character and dimensions of cusp forms.
modular formsnumber theory