OAI/MathematicalPhysics/DefocusingNLS/Linear/HomogeneousPolynomialCalculus.lean

GitHub source file

11 declarations, 0 contain sorry, 0 declared as axioms

Cartesian realization of the algebraic polynomial Laplacian

This identifies the algebraic harmonic polynomials used in the sphere-density argument with smooth Cartesian harmonic functions.

  1. def OAI.DefocusingNLS.physicalPolynomialFunction line 19
  2. theorem OAI.DefocusingNLS.physicalPolynomialFunction_C line 22
  3. theorem OAI.DefocusingNLS.physicalPolynomialFunction_X line 26
  4. theorem OAI.DefocusingNLS.physicalPolynomialFunction_C_eq line 30
  5. theorem OAI.DefocusingNLS.physicalPolynomialFunction_X_eq line 35
  6. theorem OAI.DefocusingNLS.physicalPolynomialFunction_eval line 40
  7. theorem OAI.DefocusingNLS.physicalPolynomialFunction_contDiff line 49
  8. theorem OAI.DefocusingNLS.physicalPolynomialFunction_fderiv_basis line 72
  9. theorem OAI.DefocusingNLS.physicalPolynomialFunction_laplacian line 102
  10. theorem OAI.DefocusingNLS.physicalPolynomialFunction_euler line 114
  11. theorem OAI.DefocusingNLS.physicalPolynomialFunction_smul line 124