feat(Algebra/NonAssoc): dendriform algebras

[ntapiam]

Define dendriform semirings and algebras

This PR introduces dendriform structures such as dendriform semirings
and algebras, and proves basic facts linking them to their pre-Lie
counterparts.

[github-actions]

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[github-actions]

PR summary b80f227194

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Algebra.NonAssoc.Dendriform.Defs (new file)	462

---

Declarations diff

+ DendriformAlgebra
+ DendriformRing
+ DendriformSemiring
+ NonUnitalDendriformSemiring
+ add_left
+ add_right
+ instance : Algebra R M := Algebra.ofModule (by simp) (by simp)
+ instance : Mul M
+ instance : NonUnitalSemiring M
+ instance : Ring M
+ instance : Semiring M
+ left_add
+ left_mul_eq_left_left
+ left_neg
+ left_one
+ left_smul
+ left_sub
+ left_zero
+ mul_def
+ neg_left
+ neg_right
+ one_left
+ one_mul_one_eq_one
+ one_right
+ prelie_lr
+ prelie_rl
+ right_add
+ right_left_assoc
+ right_neg
+ right_one
+ right_right_eq_mul_right
+ right_smul
+ right_sub
+ right_zero
+ smul_left
+ smul_right
+ sub_left
+ sub_right
+ toLeftPreLieRing
+ toNonAssocNonUnitalRingLR
+ toNonAssocNonUnitalRingRL
+ toRightPreLieRing
+ zero_left
+ zero_right

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.

---

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).

[github-actions]

✅ PR Title Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!