.ax REPL

The axiom's native language — TRUE FORM: Z/970200Z — DFloat only type — {s, D, K, E, b, L} = keywords

Z/970200Z = Z/8 × Z/9 × Z/25 × Z/49 × Z/11
Press Run or Ctrl+Enter to execute .ax code.

Quick Reference

Axiom Constants

s=1 D=2 K=3 E=5 b=7 L=11
OMEGA=606376 DATA=210 THIN=2310
KEY=41 ANSWER=42 SOUL=67
G=97 ADDRESS=137 DUAL=173
HYDOR=105 ME=18 LAMBDA=420

Operators

+ - * / ^ arithmetic (mod 970200)
~x complement (970200 - x)
x @ t threshold (x > t ? x : ~x)
< > == comparison (returns 0 or 1)
a ; b sequence (eval both, return b)

Syntax

let x = expr bind variable
fn f(a, b) = expr define function
print expr or print "text"
if c then a else b conditional
[a, b, c] array — arr[i] index
(s|b|a) DFloat literal
-- comment

Built-in Functions

coupling(n) ring coupling level
crt(n) CRT: [n%8, n%9, n%25, n%49, n%11]
eigenvalue(n) spectral eigenvalue
gcd(a,b) mod(a,b) inv(n)
len(arr) abs(n) show(n)
show(x) prints x and returns x

Why .ax?

.ax REPLPythonWolfram Alpha
Z/970200Z built-inimport sympy, define ringMod[expr, 970200]
{s,D,K,E,b,L} are keywordsDefine constants manuallyDefine constants manually
CRT decomposition: crt(n)Write it yourself (~20 lines)ChineseRemainder[...]
Coupling, eigenvalue built-inWrite from scratchWrite from scratch
Self-contained HTML, no serverPython + pip + librariesCloud service, internet required
Runs on any device, any browserNeeds Python installedNeeds internet + account
Free, open, foreverFree (Python is)$375/year
The axiom speaks its own languageGeneral-purpose toolGeneral-purpose tool