Fix multiplicative_generator predicate: orderOf mult_gen = P - 1 - #10
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LucidSamuel wants to merge 1 commit into
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Fix multiplicative_generator predicate: orderOf mult_gen = P - 1#10LucidSamuel wants to merge 1 commit into
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The emitted predicate was mult_gen ^ P = 1, which is unsatisfiable for actual generators: by Fermat's little theorem g ^ P = g in ZMod P for prime P, so the predicate held only for mult_gen = 1. Since mult_gen models halo2's Field::MULTIPLICATIVE_GENERATOR (a generator of the multiplicative group, order P - 1), any circuit with a real generator made Circuit.isValid unsatisfiable, and root_of_unity / delta lost their intended meaning whenever isValid was used. Emit orderOf mult_gen = P - 1 instead. orderOf resolves with the imports the extraction already emits (verified against Mathlib via Lean: the def compiles, and orderOf (2 : ZMod 5) = 4 = 5 - 1 is kernel-checkable, so the new predicate is satisfiable by a real generator where the old one was not).
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fixes #9
this PR emits
orderOf mult_gen = P - 1.orderOfresolves with the imports the extraction already emits (verified against Mathlib: the definition compiles as-is),orderOf(2 : ZMod 5) = 4 = 5 - 1 is kernel-checkable viaorderOf_eq_iff + decide, while (2 : ZMod 5) ^ 5 = 1 is provably false.