feat(Algebra/SkewPolynomial/Basic): add API

[mariainesdff]

We add API for SkewPolynomial, including monomial, coeff, C and X.

Co-authored by: @xgenereux.

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[github-actions]

PR summary 429fc043ad

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Algebra.SkewPolynomial.Basic	1006	1013	+7 (+0.70%)

Import changes for all files

Files	Import difference
Mathlib.Algebra.SkewPolynomial.Basic	7

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Declarations diff

+ C
+ CRingHom
+ CRingHom_eq_C
+ C_0
+ C_1
+ C_add
+ C_eq_natCast
+ C_eq_zero
+ C_inj
+ C_injective
+ C_mul
+ C_mul_X_eq_monomial
+ C_mul_X_pow_eq_monomial
+ C_mul_monomial
+ C_pow
+ Nontrivial.of_polynomial_ne
+ X
+ X_mul
+ X_mul_monomial
+ X_pow_mul
+ X_pow_mul_monomial
+ addHom_ext
+ addHom_ext'
+ coeff
+ coeff_C
+ coeff_C_ne_zero
+ coeff_C_succ
+ coeff_C_zero
+ coeff_X
+ coeff_X_of_ne_one
+ coeff_X_one
+ coeff_X_zero
+ coeff_monomial
+ coeff_monomial_succ
+ coeff_natCast_ite
+ coeff_ofNat_succ
+ coeff_ofNat_zero
+ coeff_one
+ coeff_one_zero
+ coeff_zero
+ eq_zero_of_eq_zero
+ ext
+ ext_iff
+ instSemiring
+ instance : AddCommMonoid (SkewPolynomial R) := SkewMonoidAlgebra.instAddCommMonoid
+ instance : Inhabited (SkewPolynomial R) := SkewMonoidAlgebra.instInhabited
+ linearMap_ext'
+ mem_support_iff
+ monomial_eq_monomial_iff
+ monomial_eq_zero_iff
+ monomial_injective
+ monomial_mul_C
+ monomial_mul_X
+ monomial_mul_X_pow
+ monomial_one_one_eq_X
+ monomial_one_right_eq_X_pow
+ monomial_zero_left
+ mul_def
+ notMem_support_iff
+ sum
+ sum_C_index
+ sum_def
+ sum_def'
+ sum_monomial
+ sum_monomial_index
+ sum_sum_index
+ sum_zero
+ support_eq_skewMonoidAlgebra_support
+ zero_def

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.

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

Current number	Change	Type
614	2	erw

Current commit 9a6d8a2f08
Reference commit 429fc043ad

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).