Update LinearMaps.lean
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@ -9,7 +9,7 @@ import Mathlib.Algebra.BigOperators.Fin
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/-!
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/-!
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# Linear maps
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# Linear maps
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Some definitions and properites of linear, bilinear, and trilinear maps, along with homogeneous
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Some definitions and properties of linear, bilinear, and trilinear maps, along with homogeneous
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quadratic and cubic equations.
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quadratic and cubic equations.
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## TODO
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## TODO
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@ -62,7 +62,7 @@ instance instFun (V : Type) [AddCommMonoid V] [Module ℚ V] :
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cases g
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cases g
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simp_all
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simp_all
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/-- The construction of a symmetric bilinear map from smul and map_add in the first factor,
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/-- The construction of a symmetric bilinear map from `smul` and `map_add` in the first factor,
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and swap. -/
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and swap. -/
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@[simps!]
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@[simps!]
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def mk₂ (f : V × V → ℚ) (map_smul : ∀ a S T, f (a • S, T) = a * f (S, T))
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def mk₂ (f : V × V → ℚ) (map_smul : ∀ a S T, f (a • S, T) = a * f (S, T))
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@ -196,7 +196,7 @@ instance instFun : FunLike (TriLinearSymm V) V (V →ₗ[ℚ] V →ₗ[ℚ] ℚ
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cases g
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cases g
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simp_all
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simp_all
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/-- The construction of a symmetric trilinear map from smul and map_add in the first factor,
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/-- The construction of a symmetric trilinear map from `smul` and `map_add` in the first factor,
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and two swap. -/
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and two swap. -/
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@[simps!]
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@[simps!]
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def mk₃ (f : V × V × V→ ℚ) (map_smul : ∀ a S T L, f (a • S, T, L) = a * f (S, T, L))
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def mk₃ (f : V × V × V→ ℚ) (map_smul : ∀ a S T L, f (a • S, T, L) = a * f (S, T, L))
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