OAI/AlgebraicGeometry/AbhyankarSathaye/NonCoordinate.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

Critical points obstruct polynomial coordinates

The polynomial chain rule shows that a coordinate polynomial over a nontrivial commutative ring cannot have a point where every partial derivative vanishes.

  1. theorem OAI.AbhyankarSathaye.polynomial_chain_rule line 16
  2. theorem OAI.AbhyankarSathaye.no_coordinate_of_critical line 35
  3. theorem OAI.AbhyankarSathaye.F_not_coordinate line 48