feat(Algebra/QuadraticAlgebra): base change of quadratic algebras

[xroblot]

A base change R → S induces an R-algebra homomorphism QuadraticAlgebra R a b →ₐ[R] QuadraticAlgebra S (algebraMap R S a) (algebraMap R S b) sending ω to ω, injective when S is faithful over R, and compatible with the norm, the trace and the discriminant.

Prepared with Claude Code 🤖

[github-actions]

PR summary d6f3bff347

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ baseChange
+ baseChange_injective
+ baseChange_omega
+ discr_algebraMap
+ norm_baseChange
+ trace_baseChange

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 d6f3bff).

• +8 new declarations
• −0 removed declarations

+QuadraticAlgebra.baseChange
+QuadraticAlgebra.baseChange_injective
+QuadraticAlgebra.baseChange_omega
+QuadraticAlgebra.discr_algebraMap
+QuadraticAlgebra.im_baseChange_apply
+QuadraticAlgebra.norm_baseChange
+QuadraticAlgebra.re_baseChange_apply
+QuadraticAlgebra.trace_baseChange

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit d6f3bff347
Reference commit ffbfefaec6

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).