Residue readers: the finite places

A reader that sees an integer only through its residues modulo a few coprime moduli. These pages cover which maps such a reader computes channel by channel, the operations no channel computes alone (sign, comparison and overflow), the least extra structure that restores each, the logic the ring's own operations carry, readers built from gates on words, and words held in a product of fields, bound by multiplication and bundled by addition.

• SIZE — what a residue window cannot read, and what reading it costs
• COORDINATES — which coordinate system reads which operation
• LOGIC — the logic a squarefree ring's own polynomials carry
• GATES — what a reader of words decides, and what it pays
• BINDING — what multiplication keeps of a code, and what a sum costs