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Commit 2020-10-17 18:25 688157f8

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feat(ring_theory/polynomial/content): definition of content + proof that it is multiplicative (#4393) Defines polynomial.content to be the gcd of the coefficients of a polynomial Says a polynomial is_primitive if its content is 1 Proves that `(p * q).content = p.content * q.content

Estimated changes

Modified src/algebra/ordered_group.lean

added theorem with_bot.add_lt_add_iff_left

added theorem with_bot.add_lt_add_iff_right

Modified src/data/polynomial/erase_lead.lean

added theorem polynomial.erase_lead_nat_degree_lt_or_erase_lead_eq_zero

Created src/ring_theory/polynomial/content.lean

added theorem polynomial.C_content_dvd

added def polynomial.content

added theorem polynomial.content_C

added theorem polynomial.content_C_mul

added theorem polynomial.content_X

added theorem polynomial.content_X_mul

added theorem polynomial.content_X_pow

added theorem polynomial.content_dvd_coeff

added theorem polynomial.content_eq_gcd_leading_coeff_content_erase_lead

added theorem polynomial.content_eq_gcd_range_of_lt

added theorem polynomial.content_eq_gcd_range_succ

added theorem polynomial.content_eq_zero_iff

added theorem polynomial.content_monomial

added theorem polynomial.content_mul

added theorem polynomial.content_mul_aux

added theorem polynomial.content_one

added theorem polynomial.content_zero

added theorem polynomial.dvd_content_iff_C_dvd

added theorem polynomial.eq_C_mul_primitive

added theorem polynomial.gcd_content_eq_of_dvd_sub

added theorem polynomial.is_primitive.content_eq_one

added theorem polynomial.is_primitive.ne_zero

added def polynomial.is_primitive

added theorem polynomial.is_primitive_iff_is_unit_of_C_dvd

added theorem polynomial.is_primitive_one

added theorem polynomial.normalize_content