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Diff — Euclidean space

Revision #1198 → #1821 · back to history

modifiedEuclidean space (affine)ebb4490a020b
FieldFrom #1198To #1821
mathlib.moduleMathlib.LinearAlgebra.AffineSpace.DefsMathlib.Algebra.AddTorsor.Defs
modifiedTranslation action on a point0a7e279f7c42
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mathlib.moduleMathlib.Algebra.AddTorsor.DefsMathlib.Algebra.Notation.Defs
noteThe notation `v +ᵥ P` (or `P + v` after swapping) is the `VAdd` action used in every `AddTorsor`.The notation `v +ᵥ P` is the `VAdd` action used in every `AddTorsor`.
modifiedVector space as Euclidean space1f8676259c82
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mathlib.declAddGroup.toAddTorsorAddGroup.instAddTorsor
mathlib.moduleMathlib.Algebra.AddTorsor.DefsMathlib.Algebra.Torsor.Defs
modifiedLine through two points0a27977990e0
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mathlib.moduleMathlib.LinearAlgebra.AffineSpace.AffineSubspace.BasicMathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs
addedTwo distinct lines intersect in at most one point7587a5ff88d4
modifiedTriangle inequality593ed4314ab7
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mathlib.moduleMathlib.Topology.MetricSpace.DefsMathlib.Topology.MetricSpace.Pseudo.Defs
modifiedEuclidean space is complete7794488bb1ef
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mathlib.declPiLp.instCompleteSpacePiLp.completeSpace
modifiedOrthogonal vectors3b57ff65009f
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mathlib.declinner_eq_zero_iff_angle_eq_pi_div_twoInnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two
noteOrthogonality is just `⟪x, y⟫ = 0`; the equivalence with `angle = π/2` is `inner_eq_zero_iff_angle_eq_pi_div_two`.Orthogonality is just `⟪x, y⟫ = 0`; the equivalence with `angle = π/2` is `InnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two`.
modifiedPythagorean theoremc2d4391d338b
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mathlib.moduleMathlib.Geometry.Euclidean.TriangleMathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle
modifiedAffine / skew coordinates8d714073842f
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mathlib.declBasis.reprModule.Basis.repr
noteSkew/affine coordinates are realised via `Basis.repr` after picking an origin; not packaged separately.Skew/affine coordinates are realised via `Module.Basis.repr` after picking an origin; not packaged separately.
addedPolar coordinate system7b70dff0b2f9
modifiedIsometry between metric spaces6bb26b88baad
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mathlib.moduleMathlib.Topology.MetricSpace.IsometricSMulMathlib.Topology.MetricSpace.Isometry
modifiedOrigin-preserving isometry preserves norm and inner product1050b0358443
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mathlib.moduleMathlib.Analysis.InnerProductSpace.BasicMathlib.Analysis.InnerProductSpace.LinearMap
modifiedIsometry of Euclidean vector spaces is linearb7327da95a18
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mathlib.moduleMathlib.Analysis.Normed.Affine.MazurUlamMathlib.Analysis.Normed.Affine.AddTorsor
modifiedIsometric Euclidean spaces have same dimension9779d79169f0
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mathlib.moduleMathlib.LinearAlgebra.FiniteDimensional.DefsMathlib.LinearAlgebra.Dimension.Finrank
addedEuclidean topology equals product topologyb4c6dfdff576
modifiedOpen sets via open ballsdc4d2c3c8c11
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mathlib.moduleMathlib.Topology.MetricSpace.DefsMathlib.Topology.MetricSpace.Pseudo.Defs
modifiedPseudo-Euclidean space4b867176565a
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mathlib.declQuadraticForm.NondegenerateQuadraticMap.Nondegenerate
mathlib.moduleMathlib.LinearAlgebra.QuadraticForm.BasicMathlib.LinearAlgebra.QuadraticForm.Radical
noteNon-degenerate quadratic forms exist in Mathlib (`QuadraticForm.Nondegenerate`), but no named `PseudoEuclideanSpace` structure was found.Non-degenerate quadratic forms exist in Mathlib (`QuadraticMap.Nondegenerate`), but no named `PseudoEuclideanSpace` structure was found.