OAI/GroupTheory/PolycyclicRecognition/Algebra/PolynomialCoordinateEvaluation.lean

GitHub source file

7 declarations, 0 contain sorry, 0 declared as axioms

Polynomial maps detected by point evaluations

A finite-dimensional function space is separated by evaluations. Their span is the whole dual, so polynomiality at every point gives polynomial coordinates.

  1. def OAI.PolycyclicRecognition.multivariatePolynomialEvaluation line 15
  2. def OAI.PolycyclicRecognition.multivariatePolynomialFunctions line 24
  3. theorem OAI.PolycyclicRecognition.mem_multivariatePolynomialFunctions line 27
  4. theorem OAI.PolycyclicRecognition.coordinatePolynomial_iff_components line 34
  5. theorem OAI.PolycyclicRecognition.IsCoordinatePolynomial.linear_pi line 41
  6. theorem OAI.PolycyclicRecognition.polynomial_of_multivariate_evaluations line 52
  7. theorem OAI.PolycyclicRecognition.coordinatePolynomial_of_evaluations line 69