Project-declaredLean 4.31.0
Ps sylvester map
ps_sylvester_map
Mathematical statement
The Sylvester matrix commutes with ring homomorphisms.
cryptographyproof systemscoding theory
Source project: ArkLib
Person-level attribution pending.
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Project-declaredLean 4.31.0
Ps sylvester mul vec eq coeff add
ps_sylvester_mul_vec_eq_coeff_add
Mathematical statement
The Sylvester matrix–vector product gives coefficients of A * P + B * Q.
cryptographyproof systemscoding theory
Source project: ArkLib
Person-level attribution pending.
Project-declaredLean 4.32.0
Line In Cubic expand
PureU1.Odd.lineInCubic_expand
Mathematical statement
The condition that a linear solution sits on a line between the two planes within the cubic expands into a on accCubeTriLinSymm applied to the points within the planes.
physicsquantum field theoryrelativity
Source project: Physlib
Person-level attribution pending.
Project-declaredLean 4.32.0
Parameterization Charge cube
PureU1.Odd.parameterizationCharge_cube
Mathematical statement
The parameterization satisfies the cubic ACC.
physicsquantum field theoryrelativity
Source project: Physlib
Person-level attribution pending.
Project-declaredLean 4.32.0
P P P! acc Cube
PureU1.VectorLikeEvenPlane.P_P_P!_accCube
Project documentation
Swapping the elements evenShiftFst j and evenShiftSnd j is equivalent to adding a vector basis!AsCharges j. -/ lemma swap!_as_add {S S' : (PureU1 (2 * n.succ)).LinSols} (j : Fin n) (hS : ((FamilyPermutations (2 * n.succ)).linSolRep (Equiv.swap (evenShiftFst j) (evenShiftSnd j))) S = S') : S'.val = S.val + (S.val (evenShiftSnd j) - S.val (evenShiftFst j))...
physicsquantum field theoryrelativity
Source project: Physlib
Person-level attribution pending.
Project-declaredLean 4.32.0
Pa zero
PureU1.VectorLikeEvenPlane.Pa_zero
Project documentation
A point in the span of the basis as a charge. -/ def Pa (f : Fin n.succ → ℚ) (g : Fin n → ℚ) : (PureU1 (2 * n.succ)).Charges := P f + P! g /-! ### E.3. Components of the inclusion into charges -/ lemma Pa_evenShiftFst (f : Fin n.succ → ℚ) (g : Fin n → ℚ) (j : Fin n) : Pa f g (evenShiftFst j) = f j.succ + g j := by rw [Pa] simp only [ACCSystemCharges.charg...
physicsquantum field theoryrelativity
Source project: Physlib
Person-level attribution pending.