Rabin's irreducibility test for polynomials over finite fields#153
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finite fields. The development, both statements and proofs, was
entirely written by Claude Code (Opus 4.6, running on AWS Bedrock). A
few lemmas have been slightly tweaked manually and placed in the ring
theory file, since they seem more broadly applicable:
POLY_DEG_1_IMP_IRREDUCIBLE
POLY_DEG_EQ_0_UNIT
POLY_DEG_UNIT
RING_DIVIDES_SUB_POW
RING_PRODUCT_CONST
RING_PRODUCT_LMUL
RING_SUB_TELESCOPE
These are the theorems in the main Library/rabin_test.ml file
culminating in RABIN_IRREDUCIBILITY_TEST:
FIELD_NONZERO_PRODUCT_PERMUTE
FIELD_ROOTS_BOUND
FINITE_FIELD_ELEMENT_POW
FINITE_FIELD_POW_ITERATE
ING_DIVIDES_POW_ITERATE
IRREDUCIBLE_DIVIDES_DEGREE
IRREDUCIBLE_DIVIDES_DEGREE_BOUND
IRREDUCIBLE_DIVIDES_XQ_MINUS_X
IRREDUCIBLE_DIVIDES_XQ_MINUS_X_GEN
IRRED_DIVIDES_POLY_EVAL_MINUS
POLY_NONUNIT_DEGREE_GE_1
QUOTIENT_POLY_RING_FINITE_CARD
RABIN_IRREDUCIBILITY_NECESSARY
RABIN_IRREDUCIBILITY_SUFFICIENT
RABIN_IRREDUCIBILITY_TEST
RING_DIVIDES_REDUCE
RING_ENDOMORPHISM_FROBENIUS_ITERATE
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