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Python 3.14 in the page: exact big integers, fractions, a prime sieve and Markdown cells.

notebook · Python · intro · by Sagebrush · MIT license

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Welcome to Sagebrush

Python 3.14, compiled to JavaScript, runs in this page: nothing is sent anywhere. Press Shift+Enter to run a cell (or Run all above). This is a Markdown cell: double-click it to edit. It can have lists, tables, code, links and math:

e^{iπ} + 1 = 0, n = 1 \sum \infty \frac{1}{n ^{2}} = \frac{π ^{2}}{6} .

How it is built: articles on the open-source (MIT/Apache) engines behind this page, from Gröbner bases and FGLM to modular symbols, Galois groups and class groups: how each algorithm works, what worked, what did not.

# Big integers are exact
2**200

1606938044258990275541962092341162602522202993782792835301376

from fractions import Fraction
H = sum(Fraction(1, n) for n in range(1, 31))
H, float(H)

(Fraction(9304682830147, 2329089562800), 3.994987130920391)

def primes(n):
    sieve = bytearray([1]) * (n + 1)
    sieve[:2] = b'\x00\x00'
    for p in range(2, int(n**0.5) + 1):
        if sieve[p]:
            sieve[p*p::p] = bytes(len(range(p*p, n + 1, p)))
    return [i for i, ok in enumerate(sieve) if ok]

ps = primes(10**5)
print(len(ps), ps[-5:])

9592 [99929, 99961, 99971, 99989, 99991]

import cmath
[cmath.exp(2j * cmath.pi * k / 6) for k in range(3)]

[(1+0j), (0.5000000000000001+0.8660254037844386j), (-0.4999999999999998+0.8660254037844387j)]

Files

main.ipynb (2491 bytes)

Open the ZIP's notebook in Sagebrush (File, Open) to run and change it.