OAI/LinearAlgebra/MatrixMultiplication/Arithmetic/Complexity.lean

GitHub source file

13 declarations, 0 contain sorry, 0 declared as axioms

Division-free arithmetic programs over a field and their operation counts.

  1. theorem OAI.MatrixMultiplication.Arithmetic.Program.eval_step_zero line 25
  2. theorem OAI.MatrixMultiplication.Arithmetic.Program.eval_step_succ line 29
  3. theorem OAI.MatrixMultiplication.Arithmetic.Program.cost_step line 33
  4. theorem OAI.MatrixMultiplication.Arithmetic.MatrixAlgorithm.correct_iff_entries line 42
  5. def OAI.MatrixMultiplication.Arithmetic.scalarAlgorithm line 55
  6. theorem OAI.MatrixMultiplication.Arithmetic.scalarAlgorithm_correct line 61
  7. theorem OAI.MatrixMultiplication.Arithmetic.scalarAlgorithm_cost line 71
  8. theorem OAI.MatrixMultiplication.Arithmetic.one_le_innerSize line 73
  9. theorem OAI.MatrixMultiplication.Arithmetic.innerSize_zero line 77
  10. theorem OAI.MatrixMultiplication.Arithmetic.innerSize_one line 80
  11. theorem OAI.MatrixMultiplication.Arithmetic.innerSize_mono line 83
  12. theorem OAI.MatrixMultiplication.Arithmetic.innerSize_le_pow line 87
  13. theorem OAI.MatrixMultiplication.Arithmetic.innerSize_cast_le line 98