Source-pinned research
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This index contains 2,569 curated research declarations and 119,070 complete package declarations. Search 10,000 more complete Mathlib declarations.
Showing 1,237 to 1,242 of 2,569 results.
GuruswamiSudan.rootMultiplicity_ge_of_shift_zero
Mathematical statement
If the shifted polynomial has no non-zero coefficients of total degree less than m, then the root multiplicity is at least m.
Source project: ArkLib
Person-level attribution pending.
GuruswamiSudan.rootMultiplicity_le_of_coeff_ne_zero
Mathematical statement
If the (s, t)-coefficient of shift Q x y is non-zero, then the root multiplicity of Q at (x, y) is at most s + t.
Source project: ArkLib
Person-level attribution pending.
GuruswamiSudan.roots_le_degree_of_deg_lt_roots
Mathematical statement
If a polynomial R has roots at points indexed by A with multiplicity at least m, and its degree is strictly less than m * |A|, then R must be the zero polynomial.
Source project: ArkLib
Person-level attribution pending.
GuruswamiSudan.sufficient_multiplicity_bound
Mathematical statement
The degree bound is strictly less than m times the number of agreement points, provided the distance is within the Johnson radius.
Source project: ArkLib
Person-level attribution pending.
GuruswamiSudan.toPolynomial_degree_le
Mathematical statement
The polynomial corresponding to a codeword has degree at most k-1.
Source project: ArkLib
Person-level attribution pending.
H_hat_conj_sigma
Project documentation
Sub-lemma for Step 1b: the conj of H_hat by σ^{−γ} simplifies to (ρ.M.conj (σ^γ).mat)^{α−1}. This uses σ^{−γ} · σ^γ = identity (on support) to cancel the outer σ^γ factors.
Source project: quantumInfo
Person-level attribution pending.