feat(FieldTheory): definition of transcendental separable field extension

[Thmoas-Guan]

In this PR, we intriduced the concept of separably generated field extension and transcendental separable field extension.

Further properties would be in #37838

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[github-actions]

PR summary 1a3500f1bf

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.FieldTheory.TranscendentalSeparable (new file)	1642

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Declarations diff

+ Algebra.IsSeparablyGenerated
+ Algebra.IsTranscendentalSeparable
+ Algebra.isSeparablyGenerated_of_equiv

You can run this locally as follows

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

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

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./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).