[PawelTroka]

Problem

Addresses #111.

Math.NET's general polynomial implementation is already shipped, but it has no short TSL type name, completion entries or authored function reference. The named orthogonal polynomials do not provide the requested coefficient-based arithmetic, evaluation and general root workflow. Fully qualified calls to the dependency were possible before this change; this PR makes that existing capability part of the discoverable application API.

Change

• Add Polynomial = MathNet.Numerics.Polynomial to the shared TSL preamble used by portable execution and both the legacy and precompiled desktop/web evaluators.
• Expose coefficient construction, Polynomial.Zero and all callable static methods in scripting completion; numeric evaluation overloads also appear in expression completion. Exclude CLR operator/accessor names that cannot be called as methods, and show a readable quotient/remainder tuple caption.
• Add 14 authored reference articles covering 18 completion entries, plus a practical guide to arithmetic, scalar division, quotient/remainder, derivatives, antiderivatives, real/complex evaluation, least-squares fitting and all numerical complex roots of a real-coefficient polynomial.
• Keep the existing Math.NET 5.0.0 algorithms and dependencies. There is no duplicate polynomial solver or new emitted ToCode implementation.

var p = new Polynomial(-6,11,-6,1); // x³ - 6x² + 11x - 6
var roots = p.Roots();             // approximately 1, 2, 3; order unspecified
write(Polynomial.Evaluate(2,1,-3,2)); // 3

var division = Polynomial.DivideRemainder(
    new Polynomial(1,0,1), new Polynomial(1,1));
// Item1: x - 1; Item2: 2

The help explains ascending coefficient order, mutable/shared coefficient arrays, the single-integer constructor convention, zero/constant root arrays, coefficientwise versus polynomial arithmetic, and numerical conditioning. General roots use the dependency's companion-matrix eigenvalue routine; a new GSL backend and symbolic algebra are not included. General member completion after an arbitrary variable remains the separate #54 workstream.

Validation

Check	Result
New execution fixture against unchanged master	46 failed, all missing the Polynomial type/name
Same fixture after the alias is added	46 passed, zero failed/skipped
Complete portable Engine Release suite	1,484 passed, zero failed/skipped
Windows Core.Tests Release cross-build	Passed, zero errors; two existing unused-field warnings in Charting
Python reference-authoring suite	63 passed
Deterministic reference regeneration	Passed; all 1,220 existing article blocks remain byte-identical, with 14 additions
git diff --check	Passed

Execution tests cover independent analytic real/complex values, arithmetic and input preservation, quotient/remainder reconstruction, real and nonreal roots, repeated roots, trailing zero coefficients, zero/constant conventions, fitting, calculus and custom definitions. Twelve native Core evaluator/completion cases are also committed for Windows CI.

Validated the exact uploaded tree 3c36aad333b0031b06f8510a05d566b5d2310f76 (identical to the reviewed local commit), using .NET SDK 10.0.403 on Linux x64:

dotnet test Computator.NET.Engine.Tests/Computator.NET.Engine.Tests.csproj -c Release
dotnet build Computator.NET.Core.Tests/Computator.NET.Core.Tests.csproj -c Release -p:EnableWindowsTargeting=true -m:1 -nodeReuse:false -p:UseSharedCompilation=false
python3 -m unittest discover -s build/reference -p 'test_*.py'

Reference generation uses the authenticated successful master Reference-Validate inventory and the actual new production reflection/source output. The local reflection harness replaces the WinForms item/settings shell; native full-catalog validation remains a CI gate. Native Windows tests and remaining platform CI were not executed here and are not claimed by the Linux cross-build.

Existing-work review

Reviewed all 78 open issues, all 14 existing open PRs, closed PR titles and targeted all-state searches before implementation. No existing PR owns #111's polynomial integration. The open Euclid integration (#309), parser (#304), secant (#305), Debye (#307), trapezoidal overflow (#308) and chart/platform work cover different capabilities.

Independently based on master fe1aba49b5f9538355ffaaa3d1683f69a23d2d9c. The shared alias/provider/reference files can also be edited by other catalog additions; preserve all additions when integrating. Draft for owner review and native CI; no merge performed.

Combined compatibility check — 2026-10-30

Also tested the final contributions in #311, #313, #314 and #315 together with the seven existing maintenance PRs (#304–#310), using the existing #312 candidate 189d28c0ec7acbf77d380f14f95ef450e7bfbd84 as the local integration base.

• Complete combined Engine Release suite: 1,819 passed, zero failed/skipped.
• Combined Python reference-authoring suite: 76 passed.
• Windows-targeted Core.Tests and Desktop.Tests cross-builds: passed, zero errors, with existing warnings.
• Deterministic reference check: passed, covering 1,251 articles and 1,351 completion items.

Eight shared paths required composition resolutions. These preserved all Euclid/ODE/polynomial aliases, completion and authoring registrations; Debye/unitary documentation; and Find/Replace/printing methods, test-source links and documentation entries. No feature behavior or numerical algorithm needed changing to combine the contributions. The independently published PRs remain based on master.

Combined local tree: 63225a973ea2883974a91ab26afcdc83d866e77b, SDK 10.0.403, Linux x64. The reference check used the authenticated master inventory plus current production reflection for changed entries through a portable UI shell. Native Windows tests, full native catalog execution and printer acceptance remain pending. The existing #312 PR was not changed by this local verification.