Tools: programs to call on your own input

Most programs here check the claims of the page that cites them. These four are written to be called on a reader's own input: residue arithmetic and the residue code, an exact comparator of two residue words through the key of least range, the lookahead of an on-line arithmetic unit, and the class group of a complex cubic field. Each program opens with its calls and what they print, and every shown call is run whenever the site is built, which fails if a call prints anything else. Save a program by the link in its page's opening lines, with the programs its page lists, install the outside packages it names, start Python in that folder, and type each line shown after >>>. The build runs them under Python 3.12; crt.py is written for Python 3.9 or later, but no version below 3.12 is tested.

• crt.py -- residue arithmetic on Z/N for N a product of coprime prime powers, with the primorial rungs Z/p_k# as the canonical family.
• size.py -- what a residue window cannot read about size, and what the cheapest exact read of size costs.
• delays.py -- the delay of an on-line unit, read by one entry point: pass a unit's box, as its width rate (the sup of its gradient's L1 norm over the box) and its range, or its pieces, or a chain, at a signed digit system, and read its lead, its delay L* and its lookahead.
• cubic.py -- complex cubic fields read through binary cubic forms: the ring of integers, the prime places, a class group checked against the analytic class number formula, and the class of a degree-1 place.