Theorems · Definition · number theory
NumberField.mixedEmbedding.convexBodySum
(K : Type u_1) → [inst : Field K] → [NumberField K] → ℝ → Set (NumberField.mixedEmbedding.mixedSpace K)
The convex body equal to the set of points x : mixedSpace K such that
∑ w real, ‖x w‖ + 2 * ∑ w complex, ‖x w‖ ≤ B.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Set.ofPredproof · cited by 6,101
- NumberFieldstatement and proof · cited by 653
- NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
- NumberField.mixedEmbedding.convexBodySumFunproof · cited by 14
Cited by11
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.convexBodySum_volume_eq_zero_of_le_zerostatement and proof · cited by 2
- NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_lestatement and proof · cited by 2
- NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discrproof · cited by 2
- NumberField.mixedEmbedding.convexBodySum_isBoundedstatement and proof · cited by 1
- NumberField.mixedEmbedding.convexBodySum_memstatement · cited by 1
- NumberField.mixedEmbedding.convexBodySum_neg_memstatement and proof · cited by 1
- NumberField.mixedEmbedding.convexBodySum_volumestatement and proof · cited by 1
- NumberField.mixedEmbedding.convexBodySum_compactstatement and proof · cited by 1
- NumberField.mixedEmbedding.convexBodySum_convexstatement · cited by 1
- NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_lestatement and proof · cited by 0
- NumberField.mixedEmbedding.convexBodySum.congr_simpstatement and proof · cited by 0