feat(LinearAlgebra/SymplecticGroup): symplectic matrices have determinant 1

[Yu-Misaka]

This PR is still at early stage, wil mark it as ready for review when I finish refactoring.

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[mathlib-bors]

This pull request is now in draft mode. No active bors state needed cleanup.

While this PR remains draft, bors will ignore commands on this PR. Mark it ready for review before using commands like bors r+ or bors try.

[github-actions]

PR summary f0763376c3

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.SymplecticDetOne (new file)	2245

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Declarations diff (regex)

+ SymplecticGroup.fromBlocks_mem_iff
+ _root_.Matrix.J_map
+ _root_.Matrix.mulVec_apply
+ exists_symmetric_shear_making_P_invertible
+ field_exists_symmetric_X_invertible_sum
+ lift_symmetric_matrix
+ round1_core_entrywise
+ round1_main_step
+ round1_rank_normal_form
+ round1_transfer_rank
+ round1_transfer_symm
+ shear_mul_symplectic_blocks
+ symplecticGroup_map
+ symplectic_det_one_local_ring
+ symplectic_det_one_when_P_invertible
+ symplectic_matrix_det_main_statement

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 -- pending)

Computed after the build finishes.

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit f0763376c3
Reference commit 5a6fc726c8

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.sh 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).