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chore(linear_algebra): rename type variables #1521

Merged
merged 18 commits into from
Oct 10, 2019
Merged

chore(linear_algebra): rename type variables #1521

merged 18 commits into from
Oct 10, 2019

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abentkamp
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@abentkamp abentkamp commented Oct 8, 2019

Rename the type variables in linear algebra from greek letters to

  • R for rings
  • 𝕜 for fields
  • M for modules
  • V / E for vector spaces
  • etc
  • basic.lean
  • basis.lean
  • bilinear_form.lean
  • determinant.lean
  • dimension.lean
  • direct_sum_module.lean
  • dual.lean
  • finite_dimensional.lean
  • finsupp.lean
  • finsupp_vector_space.lean
  • matrix.lean
  • sesquilinear_form.lean
  • tensor_product.lean

@abentkamp abentkamp added help-wanted The author needs attention to resolve issues WIP Work in progress labels Oct 8, 2019
@rwbarton rwbarton changed the title Linear_algebra: rename type variables chore(linear_algebra): rename type variables Oct 8, 2019
@robertylewis
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I've just updated basic, hopefully correctly. This is indeed more annoying than I'd hope.

@@ -56,303 +56,305 @@ open function lattice
reserve infix ` ≃ₗ `:25

universes u v w x y z
variables {α : Type u} {β : Type v} {γ : Type w} {δ : Type y} {ε : Type z} {ι : Type x}
variables {R κ : Type u} {M V : Type v} {M₂ V₂ : Type w} {M₃ V₃ : Type y} {M₄ : Type z} {ι : Type x}
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Why are there variables in the same universe, instead of one universe for each variable? This seems to be calling for trouble...

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They should never mix. R replaced α in module defs/theorems, κ for vector spaces.

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Until someone writes in this file a statement with R and κ and doesn't pay attention to the fact that they belong to the same universe...

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Oh, fair enough. I was thinking in terms of faithfully translating the old file. Updated -- this should be safe in both respects.

@robertylewis robertylewis added awaiting-review The author would like community review of the PR and removed WIP Work in progress help-wanted The author needs attention to resolve issues labels Oct 9, 2019
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I think the only outstanding issue here is that we're not standardized on K vs 𝕜 for fields. Do we care?

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digama0 commented Oct 9, 2019

FWIW I prefer K. I would rather reserve blackboard bold for notations like real, and K is not an uncommon name for a field either. (Indeed I see K or k primarily; I can't say I've ever seen 𝕜 used to mean an arbitrary field.) k is slightly problematic as it's more likely to conflict with element names (particularly integer variables), and I like the idea of sticking to some general naming convention re: types vs elements, and if greek didn't stick then capital letters will suffice as well.

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sgouezel commented Oct 9, 2019

I don't think we really care. In the analysis folder, switching to 𝕜 has really helped a lot for readability as k and K can mean something else. If K is not ambiguous in the algebra folder, let's go for it.

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https://leanprover.zulipchat.com/#narrow/stream/144837-PR-reviews/topic/.231521.20rename.20type.20variables

This change is not 100% syntactic. The order of arguments seems to be permuted in six declarations. As far as we can tell, this is all that's happened, there are no unified universe levels. So I'll merge now, and note the alpha-normalized diff here (thanks @rwbarton ) for future reference.

--- /dev/fd/63	2019-10-09 18:34:15.239630758 -0400
+++ /dev/fd/62	2019-10-09 18:34:15.239630758 -0400
@@ -116 +116 @@
-finsupp.dim_eq	Pi {a0 : Type.{u0}} {a1 : Type.{u0}} {a2 : Type.{u1}} [a3 : discrete_field.{u1} a2] [a4 : add_comm_group.{u0} a1] [a5 : vector_space.{u1 u0} a2 a1 a3 a4], (eq.{succ (succ u0)} cardinal.{u0} (vector_space.dim.{u1 u0} a2 (finsupp.{u0 u0} a0 a1 (add_monoid.to_has_zero.{u0} a1 (add_group.to_add_monoid.{u0} a1 (add_comm_group.to_add_group.{u0} a1 a4)))) a3 (finsupp.add_comm_group.{u0 u0} a0 a1 a4) (finsupp.vector_space.{u0 u0 u1} a0 a1 a2 a3 a4 a5)) (has_mul.mul.{succ u0} cardinal.{u0} cardinal.has_mul.{u0} (cardinal.mk.{u0} a0) (vector_space.dim.{u1 u0} a2 a1 a3 a4 a5)))	_
+finsupp.dim_eq	Pi {a0 : Type.{u0}} {a1 : Type.{u1}} {a2 : Type.{u1}} [a3 : discrete_field.{u0} a0] [a4 : add_comm_group.{u1} a1] [a5 : vector_space.{u0 u1} a0 a1 a3 a4], (eq.{succ (succ u1)} cardinal.{u1} (vector_space.dim.{u0 u1} a0 (finsupp.{u1 u1} a2 a1 (add_monoid.to_has_zero.{u1} a1 (add_group.to_add_monoid.{u1} a1 (add_comm_group.to_add_group.{u1} a1 a4)))) a3 (finsupp.add_comm_group.{u1 u1} a2 a1 a4) (finsupp.vector_space.{u1 u1 u0} a2 a1 a0 a3 a4 a5)) (has_mul.mul.{succ u1} cardinal.{u1} cardinal.has_mul.{u1} (cardinal.mk.{u1} a2) (vector_space.dim.{u0 u1} a0 a1 a3 a4 a5)))	_
@@ -120 +120 @@
-finsupp.is_basis_single	Pi {a0 : Type.{u0}} {a1 : Type.{u1}} {a2 : Type.{u2}} [a3 : discrete_field.{u2} a2] [a4 : add_comm_group.{u1} a1] [a5 : vector_space.{u2 u1} a2 a1 a3 a4] {a6 : a0 -> Type.{u3}} (a8 : Pi (a9 : a0) (a10 : a6 a9), a1) (a11 : Pi (a12 : a0), (is_basis.{u3 u2 u1} (a6 a12) a2 a1 (a8 a12) (domain.to_ring.{u2} a2 (division_ring.to_domain.{u2} a2 (field.to_division_ring.{u2} a2 (discrete_field.to_field.{u2} a2 a3)))) a4 (vector_space.to_module.{u2 u1} a2 a1 a3 a4 a5))), (is_basis.{(max u0 u3) u2 (max u0 u1)} (sigma.{u0 u3} a0 (fun (x13 : a0), (a6 x13))) a2 (finsupp.{u0 u1} a0 a1 (add_monoid.to_has_zero.{u1} a1 (add_group.to_add_monoid.{u1} a1 (add_comm_group.to_add_group.{u1} a1 a4)))) (fun (x14 : sigma.{u0 u3} a0 (fun (x15 : a0), (a6 x15))), (finsupp.single.{u0 u1} a0 a1 (add_monoid.to_has_zero.{u1} a1 (add_group.to_add_monoid.{u1} a1 (add_comm_group.to_add_group.{u1} a1 a4))) (sigma.fst.{u0 u3} a0 (fun (x16 : a0), (a6 x16)) x14) (a8 (sigma.fst.{u0 u3} a0 (fun (x17 : a0), (a6 x17)) x14) (sigma.snd.{u0 u3} a0 (fun (x18 : a0), (a6 x18)) x14)))) (domain.to_ring.{u2} a2 (division_ring.to_domain.{u2} a2 (field.to_division_ring.{u2} a2 (discrete_field.to_field.{u2} a2 a3)))) (finsupp.add_comm_group.{u0 u1} a0 a1 a4) (finsupp.module.{u0 u1 u2} a0 a1 a2 (domain.to_ring.{u2} a2 (division_ring.to_domain.{u2} a2 (field.to_division_ring.{u2} a2 (discrete_field.to_field.{u2} a2 a3)))) a4 (vector_space.to_module.{u2 u1} a2 a1 a3 a4 a5)))	_
+finsupp.is_basis_single	Pi {a0 : Type.{u0}} {a1 : Type.{u1}} {a2 : Type.{u2}} [a3 : discrete_field.{u0} a0] [a4 : add_comm_group.{u1} a1] [a5 : vector_space.{u0 u1} a0 a1 a3 a4] {a6 : a2 -> Type.{u3}} (a8 : Pi (a9 : a2) (a10 : a6 a9), a1) (a11 : Pi (a12 : a2), (is_basis.{u3 u0 u1} (a6 a12) a0 a1 (a8 a12) (domain.to_ring.{u0} a0 (division_ring.to_domain.{u0} a0 (field.to_division_ring.{u0} a0 (discrete_field.to_field.{u0} a0 a3)))) a4 (vector_space.to_module.{u0 u1} a0 a1 a3 a4 a5))), (is_basis.{(max u2 u3) u0 (max u2 u1)} (sigma.{u2 u3} a2 (fun (x13 : a2), (a6 x13))) a0 (finsupp.{u2 u1} a2 a1 (add_monoid.to_has_zero.{u1} a1 (add_group.to_add_monoid.{u1} a1 (add_comm_group.to_add_group.{u1} a1 a4)))) (fun (x14 : sigma.{u2 u3} a2 (fun (x15 : a2), (a6 x15))), (finsupp.single.{u2 u1} a2 a1 (add_monoid.to_has_zero.{u1} a1 (add_group.to_add_monoid.{u1} a1 (add_comm_group.to_add_group.{u1} a1 a4))) (sigma.fst.{u2 u3} a2 (fun (x16 : a2), (a6 x16)) x14) (a8 (sigma.fst.{u2 u3} a2 (fun (x17 : a2), (a6 x17)) x14) (sigma.snd.{u2 u3} a2 (fun (x18 : a2), (a6 x18)) x14)))) (domain.to_ring.{u0} a0 (division_ring.to_domain.{u0} a0 (field.to_division_ring.{u0} a0 (discrete_field.to_field.{u0} a0 a3)))) (finsupp.add_comm_group.{u2 u1} a2 a1 a4) (finsupp.module.{u2 u1 u0} a2 a1 a0 (domain.to_ring.{u0} a0 (division_ring.to_domain.{u0} a0 (field.to_division_ring.{u0} a0 (discrete_field.to_field.{u0} a0 a3)))) a4 (vector_space.to_module.{u0 u1} a0 a1 a3 a4 a5)))	_
@@ -124 +124 @@
-finsupp.linear_independent_single	Pi {a0 : Type.{u0}} {a1 : Type.{u1}} {a2 : Type.{u2}} [a3 : ring.{u2} a2] [a4 : add_comm_group.{u1} a1] [a5 : module.{u2 u1} a2 a1 a3 a4] {a6 : a0 -> Type.{u3}} {a8 : Pi (a9 : a0) (a10 : a6 a9), a1} (a11 : Pi (a12 : a0), (linear_independent.{u3 u2 u1} (a6 a12) a2 a1 (a8 a12) a3 a4 a5)), (linear_independent.{(max u0 u3) u2 (max u0 u1)} (sigma.{u0 u3} a0 (fun (x13 : a0), (a6 x13))) a2 (finsupp.{u0 u1} a0 a1 (add_monoid.to_has_zero.{u1} a1 (add_group.to_add_monoid.{u1} a1 (add_comm_group.to_add_group.{u1} a1 a4)))) (fun (x14 : sigma.{u0 u3} a0 (fun (x15 : a0), (a6 x15))), (finsupp.single.{u0 u1} a0 a1 (add_monoid.to_has_zero.{u1} a1 (add_group.to_add_monoid.{u1} a1 (add_comm_group.to_add_group.{u1} a1 a4))) (sigma.fst.{u0 u3} a0 (fun (x16 : a0), (a6 x16)) x14) (a8 (sigma.fst.{u0 u3} a0 (fun (x17 : a0), (a6 x17)) x14) (sigma.snd.{u0 u3} a0 (fun (x18 : a0), (a6 x18)) x14)))) a3 (finsupp.add_comm_group.{u0 u1} a0 a1 a4) (finsupp.module.{u0 u1 u2} a0 a1 a2 a3 a4 a5))	_
+finsupp.linear_independent_single	Pi {a0 : Type.{u0}} {a1 : Type.{u1}} {a2 : Type.{u2}} [a3 : ring.{u0} a0] [a4 : add_comm_group.{u1} a1] [a5 : module.{u0 u1} a0 a1 a3 a4] {a6 : a2 -> Type.{u3}} {a8 : Pi (a9 : a2) (a10 : a6 a9), a1} (a11 : Pi (a12 : a2), (linear_independent.{u3 u0 u1} (a6 a12) a0 a1 (a8 a12) a3 a4 a5)), (linear_independent.{(max u2 u3) u0 (max u2 u1)} (sigma.{u2 u3} a2 (fun (x13 : a2), (a6 x13))) a0 (finsupp.{u2 u1} a2 a1 (add_monoid.to_has_zero.{u1} a1 (add_group.to_add_monoid.{u1} a1 (add_comm_group.to_add_group.{u1} a1 a4)))) (fun (x14 : sigma.{u2 u3} a2 (fun (x15 : a2), (a6 x15))), (finsupp.single.{u2 u1} a2 a1 (add_monoid.to_has_zero.{u1} a1 (add_group.to_add_monoid.{u1} a1 (add_comm_group.to_add_group.{u1} a1 a4))) (sigma.fst.{u2 u3} a2 (fun (x16 : a2), (a6 x16)) x14) (a8 (sigma.fst.{u2 u3} a2 (fun (x17 : a2), (a6 x17)) x14) (sigma.snd.{u2 u3} a2 (fun (x18 : a2), (a6 x18)) x14)))) a3 (finsupp.add_comm_group.{u2 u1} a2 a1 a4) (finsupp.module.{u2 u1 u0} a2 a1 a0 a3 a4 a5))	_
@@ -241 +241 @@
-linear_equiv.smul_of_ne_zero	Pi {a0 : Type.{u0}} (a1 : Type.{u1}) [a2 : field.{u0} a0] [a3 : add_comm_group.{u1} a1] [a4 : module.{u0 u1} a0 a1 (domain.to_ring.{u0} a0 (division_ring.to_domain.{u0} a0 (field.to_division_ring.{u0} a0 a2))) a3] (a5 : a0) (a6 : ne.{succ u0} a0 a5 (has_zero.zero.{u0} a0 (no_zero_divisors.to_has_zero.{u0} a0 (domain.to_no_zero_divisors.{u0} a0 (division_ring.to_domain.{u0} a0 (field.to_division_ring.{u0} a0 a2)))))), (linear_equiv.{u0 u1 u1} a0 a1 a1 (domain.to_ring.{u0} a0 (division_ring.to_domain.{u0} a0 (field.to_division_ring.{u0} a0 a2))) a3 a3 a4 a4)	fun {x0 : Type.{u0}} (x1 : Type.{u1}) [x2 : field.{u0} x0] [x3 : add_comm_group.{u1} x1] [x4 : module.{u0 u1} x0 x1 (domain.to_ring.{u0} x0 (division_ring.to_domain.{u0} x0 (field.to_division_ring.{u0} x0 x2))) x3] (x5 : x0) (x6 : ne.{succ u0} x0 x5 (has_zero.zero.{u0} x0 (no_zero_divisors.to_has_zero.{u0} x0 (domain.to_no_zero_divisors.{u0} x0 (division_ring.to_domain.{u0} x0 (field.to_division_ring.{u0} x0 x2)))))), (linear_equiv.smul_of_unit.{u0 u1} x0 x1 (nonzero_comm_ring.to_comm_ring.{u0} x0 (integral_domain.to_nonzero_comm_ring.{u0} x0 (field.to_integral_domain.{u0} x0 x2))) x3 x4 (units.mk0.{u0} x0 (field.to_division_ring.{u0} x0 x2) x5 x6))
+linear_equiv.smul_of_ne_zero	Pi {a0 : Type.{u1}} (a1 : Type.{u0}) [a2 : field.{u1} a0] [a3 : add_comm_group.{u0} a1] [a4 : module.{u1 u0} a0 a1 (domain.to_ring.{u1} a0 (division_ring.to_domain.{u1} a0 (field.to_division_ring.{u1} a0 a2))) a3] (a5 : a0) (a6 : ne.{succ u1} a0 a5 (has_zero.zero.{u1} a0 (no_zero_divisors.to_has_zero.{u1} a0 (domain.to_no_zero_divisors.{u1} a0 (division_ring.to_domain.{u1} a0 (field.to_division_ring.{u1} a0 a2)))))), (linear_equiv.{u1 u0 u0} a0 a1 a1 (domain.to_ring.{u1} a0 (division_ring.to_domain.{u1} a0 (field.to_division_ring.{u1} a0 a2))) a3 a3 a4 a4)	fun {x0 : Type.{u1}} (x1 : Type.{u0}) [x2 : field.{u1} x0] [x3 : add_comm_group.{u0} x1] [x4 : module.{u1 u0} x0 x1 (domain.to_ring.{u1} x0 (division_ring.to_domain.{u1} x0 (field.to_division_ring.{u1} x0 x2))) x3] (x5 : x0) (x6 : ne.{succ u1} x0 x5 (has_zero.zero.{u1} x0 (no_zero_divisors.to_has_zero.{u1} x0 (domain.to_no_zero_divisors.{u1} x0 (division_ring.to_domain.{u1} x0 (field.to_division_ring.{u1} x0 x2)))))), (linear_equiv.smul_of_unit.{u1 u0} x0 x1 (nonzero_comm_ring.to_comm_ring.{u1} x0 (integral_domain.to_nonzero_comm_ring.{u1} x0 (field.to_integral_domain.{u1} x0 x2))) x3 x4 (units.mk0.{u1} x0 (field.to_division_ring.{u1} x0 x2) x5 x6))
@@ -530,2 +530,2 @@
-sesq_form.ortho_smul_left	Pi {a0 : Type.{u0}} [a1 : add_comm_group.{u0} a0] {a2 : Type.{u1}} [a3 : domain.{u1} a2] [a4 : module.{u1 u0} a2 a0 (domain.to_ring.{u1} a2 a3) a1] {a5 : ring_anti_equiv.{u1 u1} a2 a2 (domain.to_ring.{u1} a2 a3) (domain.to_ring.{u1} a2 a3)} {a6 : sesq_form.{u1 u0} a2 a0 (domain.to_ring.{u1} a2 a3) a5 a1 a4} {a7 : a0} {a8 : a0} {a9 : a2} (a10 : ne.{succ u1} a2 a9 (has_zero.zero.{u1} a2 (no_zero_divisors.to_has_zero.{u1} a2 (domain.to_no_zero_divisors.{u1} a2 a3)))), (iff (sesq_form.is_ortho.{u1 u0} a2 a0 (domain.to_ring.{u1} a2 a3) a1 a4 a5 a6 a7 a8) (sesq_form.is_ortho.{u1 u0} a2 a0 (domain.to_ring.{u1} a2 a3) a1 a4 a5 a6 (has_scalar.smul.{u1 u0} a2 a0 (mul_action.to_has_scalar.{u1 u0} a2 a0 (ring.to_monoid.{u1} a2 (domain.to_ring.{u1} a2 a3)) (distrib_mul_action.to_mul_action.{u1 u0} a2 a0 (ring.to_monoid.{u1} a2 (domain.to_ring.{u1} a2 a3)) (add_group.to_add_monoid.{u0} a0 (add_comm_group.to_add_group.{u0} a0 a1)) (semimodule.to_distrib_mul_action.{u1 u0} a2 a0 (ring.to_semiring.{u1} a2 (domain.to_ring.{u1} a2 a3)) (add_comm_group.to_add_comm_monoid.{u0} a0 a1) (module.to_semimodule.{u1 u0} a2 a0 (domain.to_ring.{u1} a2 a3) a1 a4)))) a9 a7) a8))	_
-sesq_form.ortho_smul_right	Pi {a0 : Type.{u0}} [a1 : add_comm_group.{u0} a0] {a2 : Type.{u1}} [a3 : domain.{u1} a2] [a4 : module.{u1 u0} a2 a0 (domain.to_ring.{u1} a2 a3) a1] {a5 : ring_anti_equiv.{u1 u1} a2 a2 (domain.to_ring.{u1} a2 a3) (domain.to_ring.{u1} a2 a3)} {a6 : sesq_form.{u1 u0} a2 a0 (domain.to_ring.{u1} a2 a3) a5 a1 a4} {a7 : a0} {a8 : a0} {a9 : a2} (a10 : ne.{succ u1} a2 a9 (has_zero.zero.{u1} a2 (no_zero_divisors.to_has_zero.{u1} a2 (domain.to_no_zero_divisors.{u1} a2 a3)))), (iff (sesq_form.is_ortho.{u1 u0} a2 a0 (domain.to_ring.{u1} a2 a3) a1 a4 a5 a6 a7 a8) (sesq_form.is_ortho.{u1 u0} a2 a0 (domain.to_ring.{u1} a2 a3) a1 a4 a5 a6 a7 (has_scalar.smul.{u1 u0} a2 a0 (mul_action.to_has_scalar.{u1 u0} a2 a0 (ring.to_monoid.{u1} a2 (domain.to_ring.{u1} a2 a3)) (distrib_mul_action.to_mul_action.{u1 u0} a2 a0 (ring.to_monoid.{u1} a2 (domain.to_ring.{u1} a2 a3)) (add_group.to_add_monoid.{u0} a0 (add_comm_group.to_add_group.{u0} a0 a1)) (semimodule.to_distrib_mul_action.{u1 u0} a2 a0 (ring.to_semiring.{u1} a2 (domain.to_ring.{u1} a2 a3)) (add_comm_group.to_add_comm_monoid.{u0} a0 a1) (module.to_semimodule.{u1 u0} a2 a0 (domain.to_ring.{u1} a2 a3) a1 a4)))) a9 a8)))	_
+sesq_form.ortho_smul_left	Pi {a0 : Type.{u1}} [a1 : domain.{u1} a0] {a2 : Type.{u0}} [a3 : add_comm_group.{u0} a2] [a4 : module.{u1 u0} a0 a2 (domain.to_ring.{u1} a0 a1) a3] {a5 : ring_anti_equiv.{u1 u1} a0 a0 (domain.to_ring.{u1} a0 a1) (domain.to_ring.{u1} a0 a1)} {a6 : sesq_form.{u1 u0} a0 a2 (domain.to_ring.{u1} a0 a1) a5 a3 a4} {a7 : a2} {a8 : a2} {a9 : a0} (a10 : ne.{succ u1} a0 a9 (has_zero.zero.{u1} a0 (no_zero_divisors.to_has_zero.{u1} a0 (domain.to_no_zero_divisors.{u1} a0 a1)))), (iff (sesq_form.is_ortho.{u1 u0} a0 a2 (domain.to_ring.{u1} a0 a1) a3 a4 a5 a6 a7 a8) (sesq_form.is_ortho.{u1 u0} a0 a2 (domain.to_ring.{u1} a0 a1) a3 a4 a5 a6 (has_scalar.smul.{u1 u0} a0 a2 (mul_action.to_has_scalar.{u1 u0} a0 a2 (ring.to_monoid.{u1} a0 (domain.to_ring.{u1} a0 a1)) (distrib_mul_action.to_mul_action.{u1 u0} a0 a2 (ring.to_monoid.{u1} a0 (domain.to_ring.{u1} a0 a1)) (add_group.to_add_monoid.{u0} a2 (add_comm_group.to_add_group.{u0} a2 a3)) (semimodule.to_distrib_mul_action.{u1 u0} a0 a2 (ring.to_semiring.{u1} a0 (domain.to_ring.{u1} a0 a1)) (add_comm_group.to_add_comm_monoid.{u0} a2 a3) (module.to_semimodule.{u1 u0} a0 a2 (domain.to_ring.{u1} a0 a1) a3 a4)))) a9 a7) a8))	_
+sesq_form.ortho_smul_right	Pi {a0 : Type.{u1}} [a1 : domain.{u1} a0] {a2 : Type.{u0}} [a3 : add_comm_group.{u0} a2] [a4 : module.{u1 u0} a0 a2 (domain.to_ring.{u1} a0 a1) a3] {a5 : ring_anti_equiv.{u1 u1} a0 a0 (domain.to_ring.{u1} a0 a1) (domain.to_ring.{u1} a0 a1)} {a6 : sesq_form.{u1 u0} a0 a2 (domain.to_ring.{u1} a0 a1) a5 a3 a4} {a7 : a2} {a8 : a2} {a9 : a0} (a10 : ne.{succ u1} a0 a9 (has_zero.zero.{u1} a0 (no_zero_divisors.to_has_zero.{u1} a0 (domain.to_no_zero_divisors.{u1} a0 a1)))), (iff (sesq_form.is_ortho.{u1 u0} a0 a2 (domain.to_ring.{u1} a0 a1) a3 a4 a5 a6 a7 a8) (sesq_form.is_ortho.{u1 u0} a0 a2 (domain.to_ring.{u1} a0 a1) a3 a4 a5 a6 a7 (has_scalar.smul.{u1 u0} a0 a2 (mul_action.to_has_scalar.{u1 u0} a0 a2 (ring.to_monoid.{u1} a0 (domain.to_ring.{u1} a0 a1)) (distrib_mul_action.to_mul_action.{u1 u0} a0 a2 (ring.to_monoid.{u1} a0 (domain.to_ring.{u1} a0 a1)) (add_group.to_add_monoid.{u0} a2 (add_comm_group.to_add_group.{u0} a2 a3)) (semimodule.to_distrib_mul_action.{u1 u0} a0 a2 (ring.to_semiring.{u1} a0 (domain.to_ring.{u1} a0 a1)) (add_comm_group.to_add_comm_monoid.{u0} a2 a3) (module.to_semimodule.{u1 u0} a0 a2 (domain.to_ring.{u1} a0 a1) a3 a4)))) a9 a8)))	_
@@ -537 +537 @@
-sesq_form.to_module	Pi {a0 : Type.{u0}} [a1 : add_comm_group.{u0} a0] {a2 : Type.{u1}} [a3 : comm_ring.{u1} a2] [a4 : module.{u1 u0} a2 a0 (comm_ring.to_ring.{u1} a2 a3) a1] {a5 : ring_anti_equiv.{u1 u1} a2 a2 (comm_ring.to_ring.{u1} a2 a3) (comm_ring.to_ring.{u1} a2 a3)}, (module.{u1 (max u1 u0)} a2 (sesq_form.{u1 u0} a2 a0 (comm_ring.to_ring.{u1} a2 a3) a5 a1 a4) (comm_ring.to_ring.{u1} a2 a3) (sesq_form.add_comm_group.{u1 u0} a2 a0 (comm_ring.to_ring.{u1} a2 a3) a1 a4 a5))	fun {x0 : Type.{u0}} [x1 : add_comm_group.{u0} x0] {x2 : Type.{u1}} [x3 : comm_ring.{u1} x2] [x4 : module.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x1] {x5 : ring_anti_equiv.{u1 u1} x2 x2 (comm_ring.to_ring.{u1} x2 x3) (comm_ring.to_ring.{u1} x2 x3)}, (module.mk.{u1 (max u1 u0)} x2 (sesq_form.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x5 x1 x4) (comm_ring.to_ring.{u1} x2 x3) (sesq_form.add_comm_group.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x1 x4 x5) (semimodule.mk.{u1 (max u1 u0)} x2 (sesq_form.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x5 x1 x4) (ring.to_semiring.{u1} x2 (comm_ring.to_ring.{u1} x2 x3)) (add_comm_group.to_add_comm_monoid.{(max u1 u0)} (sesq_form.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x5 x1 x4) (sesq_form.add_comm_group.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x1 x4 x5)) (distrib_mul_action.mk.{u1 (max u1 u0)} x2 (sesq_form.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x5 x1 x4) (semiring.to_monoid.{u1} x2 (ring.to_semiring.{u1} x2 (comm_ring.to_ring.{u1} x2 x3))) (add_comm_monoid.to_add_monoid.{(max u1 u0)} (sesq_form.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x5 x1 x4) (add_comm_group.to_add_comm_monoid.{(max u1 u0)} (sesq_form.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x5 x1 x4) (sesq_form.add_comm_group.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x1 x4 x5))) (mul_action.mk.{u1 (max u1 u0)} x2 (sesq_form.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x5 x1 x4) (semiring.to_monoid.{u1} x2 (ring.to_semiring.{u1} x2 (comm_ring.to_ring.{u1} x2 x3))) (has_scalar.mk.{u1 (max u1 u0)} x2 (sesq_form.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x5 x1 x4) (fun (x6 : x2) (x7 : sesq_form.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x5 x1 x4), (sesq_form.mk.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x5 x1 x4 (fun (x8 : x0) (x9 : x0), (has_mul.mul.{u1} x2 (mul_zero_class.to_has_mul.{u1} x2 (semiring.to_mul_zero_class.{u1} x2 (ring.to_semiring.{u1} x2 (comm_ring.to_ring.{u1} x2 x3)))) x6 (coe_fn.{(max (succ u1) (succ u0)) (max (succ u0) (succ u1))} (sesq_form.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x5 x1 x4) (sesq_form.has_coe_to_fun.{u1 u0} x2 x0 (comm_ring.to_ring.{u1} x2 x3) x1 x4 x5) x7 x8 x9))) (sesq_form.to_module._proof_1.{u1 u0} x0 x1 x2 x3 x4 x5 x6 x7) (sesq_form.to_module._proof_2.{u1 u0} x0 x1 x2 x3 x4 x5 x6 x7) (sesq_form.to_module._proof_3.{u1 u0} x0 x1 x2 x3 x4 x5 x6 x7) (sesq_form.to_module._proof_4.{u1 u0} x0 x1 x2 x3 x4 x5 x6 x7)))) (sesq_form.to_module._proof_5.{u1 u0} x0 x1 x2 x3 x4 x5) (sesq_form.to_module._proof_6.{u1 u0} x0 x1 x2 x3 x4 x5)) (sesq_form.to_module._proof_7.{u1 u0} x0 x1 x2 x3 x4 x5) (sesq_form.to_module._proof_8.{u1 u0} x0 x1 x2 x3 x4 x5)) (sesq_form.to_module._proof_9.{u1 u0} x0 x1 x2 x3 x4 x5) (sesq_form.to_module._proof_10.{u1 u0} x0 x1 x2 x3 x4 x5)))
+sesq_form.to_module	Pi {a0 : Type.{u1}} [a1 : comm_ring.{u1} a0] {a2 : Type.{u0}} [a3 : add_comm_group.{u0} a2] [a4 : module.{u1 u0} a0 a2 (comm_ring.to_ring.{u1} a0 a1) a3] {a5 : ring_anti_equiv.{u1 u1} a0 a0 (comm_ring.to_ring.{u1} a0 a1) (comm_ring.to_ring.{u1} a0 a1)}, (module.{u1 (max u1 u0)} a0 (sesq_form.{u1 u0} a0 a2 (comm_ring.to_ring.{u1} a0 a1) a5 a3 a4) (comm_ring.to_ring.{u1} a0 a1) (sesq_form.add_comm_group.{u1 u0} a0 a2 (comm_ring.to_ring.{u1} a0 a1) a3 a4 a5))	fun {x0 : Type.{u1}} [x1 : comm_ring.{u1} x0] {x2 : Type.{u0}} [x3 : add_comm_group.{u0} x2] [x4 : module.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x3] {x5 : ring_anti_equiv.{u1 u1} x0 x0 (comm_ring.to_ring.{u1} x0 x1) (comm_ring.to_ring.{u1} x0 x1)}, (module.mk.{u1 (max u1 u0)} x0 (sesq_form.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x5 x3 x4) (comm_ring.to_ring.{u1} x0 x1) (sesq_form.add_comm_group.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x3 x4 x5) (semimodule.mk.{u1 (max u1 u0)} x0 (sesq_form.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x5 x3 x4) (ring.to_semiring.{u1} x0 (comm_ring.to_ring.{u1} x0 x1)) (add_comm_group.to_add_comm_monoid.{(max u1 u0)} (sesq_form.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x5 x3 x4) (sesq_form.add_comm_group.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x3 x4 x5)) (distrib_mul_action.mk.{u1 (max u1 u0)} x0 (sesq_form.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x5 x3 x4) (semiring.to_monoid.{u1} x0 (ring.to_semiring.{u1} x0 (comm_ring.to_ring.{u1} x0 x1))) (add_comm_monoid.to_add_monoid.{(max u1 u0)} (sesq_form.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x5 x3 x4) (add_comm_group.to_add_comm_monoid.{(max u1 u0)} (sesq_form.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x5 x3 x4) (sesq_form.add_comm_group.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x3 x4 x5))) (mul_action.mk.{u1 (max u1 u0)} x0 (sesq_form.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x5 x3 x4) (semiring.to_monoid.{u1} x0 (ring.to_semiring.{u1} x0 (comm_ring.to_ring.{u1} x0 x1))) (has_scalar.mk.{u1 (max u1 u0)} x0 (sesq_form.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x5 x3 x4) (fun (x6 : x0) (x7 : sesq_form.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x5 x3 x4), (sesq_form.mk.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x5 x3 x4 (fun (x8 : x2) (x9 : x2), (has_mul.mul.{u1} x0 (mul_zero_class.to_has_mul.{u1} x0 (semiring.to_mul_zero_class.{u1} x0 (ring.to_semiring.{u1} x0 (comm_ring.to_ring.{u1} x0 x1)))) x6 (coe_fn.{(max (succ u1) (succ u0)) (max (succ u0) (succ u1))} (sesq_form.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x5 x3 x4) (sesq_form.has_coe_to_fun.{u1 u0} x0 x2 (comm_ring.to_ring.{u1} x0 x1) x3 x4 x5) x7 x8 x9))) (sesq_form.to_module._proof_1.{u1 u0} x0 x1 x2 x3 x4 x5 x6 x7) (sesq_form.to_module._proof_2.{u1 u0} x0 x1 x2 x3 x4 x5 x6 x7) (sesq_form.to_module._proof_3.{u1 u0} x0 x1 x2 x3 x4 x5 x6 x7) (sesq_form.to_module._proof_4.{u1 u0} x0 x1 x2 x3 x4 x5 x6 x7)))) (sesq_form.to_module._proof_5.{u1 u0} x0 x1 x2 x3 x4 x5) (sesq_form.to_module._proof_6.{u1 u0} x0 x1 x2 x3 x4 x5)) (sesq_form.to_module._proof_7.{u1 u0} x0 x1 x2 x3 x4 x5) (sesq_form.to_module._proof_8.{u1 u0} x0 x1 x2 x3 x4 x5)) (sesq_form.to_module._proof_9.{u1 u0} x0 x1 x2 x3 x4 x5) (sesq_form.to_module._proof_10.{u1 u0} x0 x1 x2 x3 x4 x5)))

@robertylewis robertylewis removed the awaiting-review The author would like community review of the PR label Oct 10, 2019
@robertylewis robertylewis added the ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) label Oct 10, 2019
@mergify mergify bot merged commit 43d3dee into master Oct 10, 2019
@mergify mergify bot deleted the lin_alg_rename branch October 10, 2019 11:15
anrddh pushed a commit to anrddh/mathlib that referenced this pull request May 15, 2020
* doc(linear_algebra/basis): add doc

* doc(linear_algebra/basis): shorten docstrings

* refactor(linear_algebra/basis): rename type vars

* style(linear_algebra/basic): change variable names

* chore(linear_algebra/dimension): rename type variables

* remove commented code

* style(linear_algebra/bilinear_form): change variable names

* style(linear_algebra/direct_sum_module): change variable names

* style(linear_algebra/matrix): change variable names

* Rename variables in finsupp_vector_space.lean

* style(linear_algebra/sesquilinear_form): change variable names

* style(linear_algebra/tensor_product): change variable names

* change kappas to bb k's

* style(linear_algebra/finsupp): change variable names

* change universe levels

* change bb k to K
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