feat(RingTheory): base change of Koszul complex and cocomplex

[Thmoas-Guan]

In this PR we added base change of Koszul complex and cocomplex.

---

• depends on: feat(RingTheory): definition of Koszul complex #40929
• depends on: feat(RingTheory): definition of Koszul cocomplex #40930
• depends on: feat(LinearAlgebra): exterior power commute with base change #40948

[github-actions]

PR summary 7ca1d136f8

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.LinearAlgebra.ExteriorPower.BaseChange (new file)	1781
Mathlib.RingTheory.KoszulComplex.Complex (new file)	2005
Mathlib.RingTheory.KoszulComplex.Cocomplex (new file)	2014

---

Declarations diff (regex)

+ GradedAlgebra.linearGMul
+ GradedAlgebra.linearGMul_eq_mul
+ baseChangeExteriorAlgebraToTensor
+ baseChangeGenerator
+ baseChangeGenerator_map_update_add
+ baseChangeGenerator_map_update_smul
+ baseChangeInverseAlternating
+ baseChangeInverseAlternating_apply_tmul
+ baseChangeIsoForward
+ baseChangeIsoForwardAux
+ baseChangeIsoForward_apply_one_tmul_ιMulti
+ baseChangeIsoForward_surjective
+ baseChangeIsoInverse
+ baseChangeIsoInverse_apply_tmul
+ baseChangeIso_apply_tmul
+ baseChangeIso_symm_apply_tmul
+ baseChange_left_inverse
+ baseChange_right_inverse
+ baseChangeι
+ baseChangeι_mul_add_swap
+ baseChangeι_sq_zero
+ d_def
+ degreeProjection
+ degreeProjection_apply_ιMulti
+ free
+ instance : IsScalarTower R S (ExteriorAlgebra S (S ⊗[R] M))
+ isZero_X_ofList_of_length_le
+ isZero_X_ofList_of_length_lt
+ koszulCocomplex
+ koszulCocomplex.d
+ koszulCocomplex.d_apply_ιMulti
+ koszulComplex
+ koszulComplex.d
+ koszulComplex.dAlternating
+ koszulComplex.dAlternating_apply
+ koszulComplex.d_comp_d
+ koszulComplex.d_def
+ map_dAlternating_apply
+ map_d_comm
+ map_id_refl
+ obj_d'
+ of_d'
+ removeNth_comp
++ exteriorPower.baseChangeIso_comm_aux
++ instance (T : Type v) [CommRing T] (g : R →+* T) :
++ isZero_X_of_span_eq_top
++ isoOfEquiv
++ map
++ map_comp
++ map_f
++ map_id
++ ofList
++ ofListBaseChangeIso
+++ baseChangeIso
- of.d

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 7ca1d13).

• +75 new declarations
• −4 removed declarations

+AlgebraicTopology.NormalizedMooreComplex.obj_d'
-ChainComplex.of.d
-ChainComplex.of.d.congr_simp
+ChainComplex.of_d'
+ExteriorAlgebra.baseChangeExteriorAlgebraToTensor
+ExteriorAlgebra.baseChangeι
+ExteriorAlgebra.baseChangeι_mul_add_swap
+ExteriorAlgebra.baseChangeι_sq_zero
+Fin.removeNth_comp
+GradedAlgebra.linearGMul
+GradedAlgebra.linearGMul.congr_simp
+GradedAlgebra.linearGMul_eq_mul
+exteriorPower.baseChangeGenerator
+exteriorPower.baseChangeGenerator_map_update_add
+exteriorPower.baseChangeGenerator_map_update_smul
+exteriorPower.baseChangeInverseAlternating
+exteriorPower.baseChangeInverseAlternating_apply_tmul
+exteriorPower.baseChangeIso
+exteriorPower.baseChangeIsoForward
+exteriorPower.baseChangeIsoForwardAux
+exteriorPower.baseChangeIsoForward_apply_one_tmul_ιMulti
+exteriorPower.baseChangeIsoForward_surjective
+exteriorPower.baseChangeIsoInverse
+exteriorPower.baseChangeIsoInverse_apply_tmul
+exteriorPower.baseChangeIso_apply_tmul
+exteriorPower.baseChangeIso_symm_apply_tmul
+exteriorPower.baseChange_left_inverse
+exteriorPower.baseChange_right_inverse
+exteriorPower.degreeProjection
+exteriorPower.degreeProjection_apply_ιMulti
+exteriorPower.instIsScalarTowerExteriorAlgebraTensorProduct
+groupHomology.chainsFunctor_obj
-groupHomology.chainsFunctor_obj_X_carrier
-groupHomology.chainsFunctor_obj_d
+koszulCocomplex
+koszulCocomplex.baseChangeIso
+koszulCocomplex.d
+koszulCocomplex.d_apply_ιMulti
+koszulCocomplex.d_def
+koszulCocomplex.exteriorPower.baseChangeIso_comm_aux
+koszulCocomplex.free
+koszulCocomplex.instAdditiveModuleCatExtendScalars
+koszulCocomplex.isZero_X_ofList_of_length_le
+koszulCocomplex.isZero_X_of_span_eq_top
+koszulCocomplex.isoOfEquiv
+koszulCocomplex.map
+koszulCocomplex.map.congr_simp
+koszulCocomplex.map_comp
+koszulCocomplex.map_comp_assoc
+koszulCocomplex.map_f
+koszulCocomplex.map_id
+koszulCocomplex.map_id_assoc
+koszulCocomplex.map_id_refl
+koszulCocomplex.map_id_refl_assoc
+koszulCocomplex.ofList
+koszulCocomplex.ofListBaseChangeIso
+koszulComplex
+koszulComplex.baseChangeIso
+koszulComplex.d
+koszulComplex.dAlternating
+koszulComplex.dAlternating_apply
+koszulComplex.d_comp_d
+koszulComplex.d_def
+koszulComplex.exteriorPower.baseChangeIso_comm_aux
+koszulComplex.instAdditiveModuleCatExtendScalars
+koszulComplex.isZero_X_ofList_of_length_lt
+koszulComplex.isZero_X_of_span_eq_top
+koszulComplex.isoOfEquiv
+koszulComplex.map
+koszulComplex.map.congr_simp
+koszulComplex.map_comp
+koszulComplex.map_comp_assoc
+koszulComplex.map_dAlternating_apply
+koszulComplex.map_d_comm
+koszulComplex.map_f
+koszulComplex.map_id
+koszulComplex.map_id_assoc
+koszulComplex.ofList
+koszulComplex.ofListBaseChangeIso

---

Decrease in strong tech debt: (relative, absolute) = (2.58, 0.00)

Current number	Change	Type (strong)
backward.defeqAttrib.useBackward	4224	-4
backward.isDefEq.respectTransparency	4678	-1

Increase in weak tech debt: (relative, absolute) = (2.00, 0.00)

Current number	Change	Type (weak)
exposed public sections	5063	2

Current commit 7ca1d136f8
Reference commit 98b840bb29

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.py pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib-dependent-issues]

This PR/issue depends on:

• feat(RingTheory): definition of Koszul complex #40929
• feat(RingTheory): definition of Koszul cocomplex #40930
• feat(LinearAlgebra): exterior power commute with base change #40948
  By Dependent Issues (🤖). Happy coding!