Theorems · Theorem · number theory
Polynomial.cyclotomic_zero
∀ (R : Type u_1) [inst : Ring R], Polynomial.cyclotomic 0 R = 1
The zeroth cyclotomic polynomial is 1.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Polynomialstatement · cited by 5,681
- Polynomial.mapproof · cited by 806
- Int.castRingHomproof · cited by 254
- Polynomial.cyclotomicstatement · cited by 130
Cited by11
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_eq_prod_X_sub_primitiveRootsproof · cited by 5
- Polynomial.cyclotomic_pos_and_nonnegproof · cited by 2
- Polynomial.cyclotomic.dvd_X_pow_sub_oneproof · cited by 2
- Polynomial.cyclotomic_expand_eq_cyclotomicproof · cited by 2
- Polynomial.cyclotomic_expand_eq_cyclotomic_mulproof · cited by 2
- Polynomial.eval_one_cyclotomic_not_prime_powproof · cited by 1
- Polynomial.cyclotomic_injectiveproof · cited by 1
- Polynomial.sub_one_pow_totient_le_cyclotomic_evalproof · cited by 0
- Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebiusproof · cited by 0
- Polynomial.cyclotomic_eval_le_add_one_pow_totientproof · cited by 0
- Polynomial.cyclotomic_mahlerMeasure_eq_oneproof · cited by 0