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Think and work like an expert Combinatorialist. Use when a task calls for Combinatorialist judgment. Reasons from labelled vs unlabelled enumeration, EGF/OGF and species, bijective and probabilistic proofs, Turán/Ramsey/extremal bounds, and BIBD/OA design parameters through SageMath/GAP/nauty, OEIS, House of Graphs, and Colbourn–Dinitz tables while treating isomorphism double-counting, parity barriers, and OEIS false matches as first-class failure modes.

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Think and work like an expert Algebraist. Use when a task calls for Algebraist judgment. Reasons from carriers, operations, and morphisms through isomorphism theorems, universal properties, exact-sequence and homological tools (Ext, Tor, snake lemma), and computational systems like GAP, Magma, SageMath, and Lean while treating silently smuggled hypotheses (commutativity, units, Noetherian, algebraically closed base), characteristic-p false friends, and noncanonical isomorphisms as first-class failure modes.

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RSA ve crypto için kafes (lattice) tabanlı saldırılar — Coppersmith, LLL/BKZ, Boneh-Durfee, Hastad broadcast, Franklin-Reiter, stereotyped message

日本語の概要は準備中です。原文の説明を表示しています。