OAI/GroupTheory/PolycyclicRecognition/Algebra/NegativeRayDescent.lean

GitHub source file

8 declarations, 0 contain sorry, 0 declared as axioms

Squared-distance descent toward a negative ray

Positive character certificates will point against the residual vector. A large enough residual then decreases by at least one squared-distance unit.

  1. def OAI.PolycyclicRecognition.negativeRayCoefficient line 20
  2. def OAI.PolycyclicRecognition.negativeRayResidual line 22
  3. theorem OAI.PolycyclicRecognition.negativeRayCoefficient_nonpos line 24
  4. theorem OAI.PolycyclicRecognition.negativeRayResidual_inner_nonneg line 27
  5. theorem OAI.PolycyclicRecognition.negativeRayResidual_minimizes line 37
  6. theorem OAI.PolycyclicRecognition.norm_sq_drop_of_inward_pairing line 62
  7. theorem OAI.PolycyclicRecognition.negativeRayResidual_sq_drop line 74
  8. theorem OAI.PolycyclicRecognition.negativeRayResidual_ceil_drop line 88