OAI/NumberTheory/DukePrimeDegree/Geometry/FiniteProjectionFrames.lean

GitHub source file

23 declarations, 0 contain sorry, 0 declared as axioms

Finite frame selection by Gram determinants

The projected coordinate vectors form a finite measurable spanning family. Maximal nonzero Gram minors select a basis from that family. All tests used in the selection are measurable real determinants, so this does not assume a measurable tangent-frame theorem.

  1. def OAI.DukePrimeDegree.finiteGramDet line 29
  2. def OAI.DukePrimeDegree.IsMaximalGramFrame line 32
  3. theorem OAI.DukePrimeDegree.exists_maximalGramFrame line 36
  4. theorem OAI.DukePrimeDegree.IsMaximalGramFrame.linearIndependent line 53
  5. theorem OAI.DukePrimeDegree.IsMaximalGramFrame.span_eq line 58
  6. def OAI.DukePrimeDegree.frameEnumeration line 89
  7. theorem OAI.DukePrimeDegree.frameEnumeration_surjective line 94
  8. theorem OAI.DukePrimeDegree.exists_maximalGramFrameIndex line 101
  9. def OAI.DukePrimeDegree.maximalGramFrameIndex line 107
  10. def OAI.DukePrimeDegree.maximalGramFrame line 111
  11. theorem OAI.DukePrimeDegree.maximalGramFrame_spec line 114
  12. def OAI.DukePrimeDegree.finiteFrameVector line 119
  13. def OAI.DukePrimeDegree.selectedFrameVector line 122
  14. theorem OAI.DukePrimeDegree.selectedFrameVector_linearIndependent line 125
  15. theorem OAI.DukePrimeDegree.selectedFrameVector_span line 136
  16. theorem OAI.DukePrimeDegree.maximalGramFrame_card line 156
  17. theorem OAI.DukePrimeDegree.maximalGramFrame_card_of_span_transport line 162
  18. theorem OAI.DukePrimeDegree.measurable_finiteGramDet line 177
  19. theorem OAI.DukePrimeDegree.measurableSet_isMaximalGramFrame line 188
  20. theorem OAI.DukePrimeDegree.measurable_maximalGramFrameIndex line 203
  21. theorem OAI.DukePrimeDegree.measurableSet_maximalGramFrame_eq line 210
  22. theorem OAI.DukePrimeDegree.measurable_selectedFrameVector line 217
  23. theorem OAI.DukePrimeDegree.measurable_selectedFrameCard line 232