Theorems · Theorem · number theory
Complex.isAlgebraic_sin_rat_mul_pi
∀ (q : ℚ), IsAlgebraic ℤ (Complex.sin (↑q * ↑Real.pi))
sin(q * π) for q : ℚ is algebraic over ℤ, using the complex sin function.
- Defined in
- Mathlib.NumberTheory.Niven
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- Real.pistatement · cited by 1,774
- Complex.ofRealstatement · cited by 1,654
- nonZeroDivisorsproof · cited by 895
- Complex.sinstatement · cited by 258
- Int.castRingHomproof · cited by 254
- IsAlgebraicstatement · cited by 163
- eq_intCastproof · cited by 127
- Int.cast_ofNatproof · cited by 86
- isAlgebraic_algebraMapproof · cited by 19
- IsIntegral.isAlgebraicproof · cited by 18
- IsAlgebraic.of_mulproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Complex.isAlgebraic_tan_rat_mul_piproof · cited by 0