Theorems · Theorem · harmonic analysis
ZMod.dft_apply
∀ {N : ℕ} [inst : NeZero N] {E : Type u_1} [inst_1 : AddCommGroup E] [inst_2 : Module ℂ E] (Φ : ZMod N → E)
(k : ZMod N), ZMod.dft Φ k = ∑ j, ZMod.stdAddChar (-(j * k)) • Φ j- Defined in
- Mathlib.Analysis.Fourier.ZMod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZeroAddCommGroupModule
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Complexstatement and proof · cited by 5,565
- Finset.sumstatement · cited by 5,195
- Finset.univstatement · cited by 3,473
- LinearEquivstatement · cited by 3,317
- ZModstatement and proof · cited by 1,024
- AddCharstatement · cited by 286
- ZMod.dftstatement · cited by 25
- ZMod.stdAddCharstatement · cited by 19
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