OAI/NumberTheory/DukePrimeDegree/Geometry/RowReducedChart.lean
2 declarations, 0 contain sorry, 0 declared as axioms
Compatibility of row charts and one-root charts
Removing one coordinate from the row time space gives precisely the transversal of the existing one-root chart. The parameterizations agree pointwise, so their disintegrations refer to the same actual root leaves.
- def
OAI.DukePrimeDegree.rowReducedHomeomorphline 21 - theorem
OAI.DukePrimeDegree.row_one_root_parametrizationline 53Source documentation
The single-root and simultaneous-row parameterizations agree, with the selected real parameter occupying the last factor.
theorem row_one_root_parametrization {n : ℕ} {i j : Fin n} (hij : i ≠ j) (k : Fin n) (s : RowRootSlice i k) (w : RowRemainingTime i j) (t : ℝ) : rootQuotientParametrization hij ((rowReducedHomeomorph hij k).symm (s, w), t) = rowQuotientParametrization i k (s, w.val + t • rowUnit hij) := by …Mentions: OAI.DukePrimeDegree.RowRootSlice, OAI.DukePrimeDegree.RowRemainingTime, OAI.DukePrimeDegree.rowReducedHomeomorph, OAI.DukePrimeDegree.rowQuotientParametrization, OAI.DukePrimeDegree.rowUnit