p vs Boolean Builder by ChatStick

Every rational number lives simultaneously in infinitely many completions of Q: the real line at infinity, and the p-adic fields Q_2, Q_3, Q_5, and so on. Most of modern number theory's deepest theorems are statements about how these completions fit together. p-adelic puts all of them on one screen. THE ADELIC STRIP Type a number - rational, algebraic radical, polynomial, Hilbert pair, special-function value - and a horizontal strip materializes with one column per place: infinity on the left, then 2, 3, 5, 7, and so on. There is no "p-adic mode": you see all completions at once. Tap a column to expand; toggle between digit-string and Laurent series; long-press to copy as plain text or LaTeX. ARBITRARY PRECISION Every computation runs through arbitrary-precision BigInt. Type 2^60 / 3 and the parser hands the engine a real BigInt - no Int.max ceilings, no silent truncation. The precision dial at the bottom of every screen is the canonical gesture: drag it and digits stream in across every place, lazily extended via long division, Hensel lifting, or whichever generator the source warrants. ALGEBRAIC NUMBERS sqrt(17) lifts via Hensel iteration at every prime where it splits, and renders 4.12310562 at infinity to dial-controlled depth. algebraic(x^3 - 2) triggers the algebraic engine: Newton polygon partitions roots by valuation, F_p[x] factorization splits the unramified part, Hensel lifts each factor to Z_p[x] mod p^N. The Galois toggle cycles three roots at p = 31 (fully split), one totally-ramified root at p = 2 (Eisenstein), one inert F_343 lift at p = 7. CYCLOTOMIC IN FULL zeta_n at every prime: split, inert with residue degree greater than 1 (zeta_7 at p = 2 with F_8 digits per level), ramified (zeta_4 at p = 2 with uniformizer 1 - zeta_4). The strip's per-prime (e, f) metadata is correct; the Galois row lets you walk embeddings. THREE VISUALIZATIONS Nested balls: the canonical Z_p picture as a tangent-circle packing. Pinch-zoom drills into the on-path sub-ball, which becomes the new outer disk; a breadcrumb shows descended digits. Bruhat-T**s tree: the (p^f + 1)-regular tree of PGL_2 over the local field. Tap any node for its coordinates. Berkovich line: the analytic refinement. Type II vertices at rational radii along the geodesic from the Gauss point to the Type I leaf. SPECIAL FUNCTIONS exp_p, log_p, Artin-Hasse E_p with proper convergence checks. Morita's p-adic Gamma_p including Wilson's theorem at every prime. fact(n) via Legendre's formula: fact(1000) at p = 2 reports v_2 = 994 instantly without materializing 1000 factorial.

Boolean Builder helps you understand digital logic through hands-on learning. Whether you're a student, a beginner in electronics, or preparing for computer engineering topics, this app makes Boolean logic visual, practical, and easy to remember. ### What you can do - Learn core concepts from binary basics to Boolean identities and De Morgan's Laws - Explore gate behavior with live input/output simulation - Generate and inspect truth tables instantly - Build your own circuits by connecting logic gates on a visual canvas - Test your knowledge with quizzes and timed logic challenges - Track your progress with completion stats, XP, streaks, and achievements ### Core topics covered - AND, OR, NOT, XOR - NAND, NOR, XNOR, BUFFER - Boolean expressions - Truth tables (2-input and advanced 3-input mode) - Circuit composition and logic flow ### Great for - High school and university students - Self-learners in coding, electronics, and computer science - Teachers who want a visual companion for logic lessons ### Premium A one-time Premium upgrade unlocks advanced lessons, advanced quizzes/challenges, and premium gates. ### Free experience The free version includes substantial learning content and core tools. Ads may be shown in free mode. Build real intuition for Boolean logic - one gate at a time.