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Elementary symmetric polynomials, and writing a symmetric polynomial in them

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还没有人认领这个 Issue。

评估

难度
5/5
预计耗时
一周以上
新手友好度
35/100
Issue 类型
功能
描述清晰度
基本清楚
活跃度
活跃
技术栈
csharp
领域
backend

调研方向

The issue names no implementation files or tests. Start by tracing how the library represents and manipulates polynomials, and inspect the existing sum and product operations. Done means providing an elementary symmetric polynomial operation and a way to rewrite symmetric polynomials in those functions; the issue leaves the API and implementation scope open.

由索引模型根据 Issue 内容生成。

描述

Modenov's Chapter III (#2131) writes the orthocentre, the circumcentre and most of its formulas in the elementary symmetric functions of the vertices: σ₁ = a + b + c, σ₂ = ab + bc + ca, σ₃ = abc. Problem 21 argues "this line equation is symmetric in z₁ … z₄, so it serves both points". Readers counted the σ's in 10–12 rows of each part of Chapter III.

Wanted, on the polynomial layer:

  • elemsym(k, a, b, c, …), or another name, since #809's research plans divisorsigma and σ would clash;
  • rewriting a symmetric polynomial in the σ's, which is the fundamental theorem of symmetric polynomials.

Where these come from today: sum and product exist, and the σ's can be written out by hand.

主要语言
C#
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1 小时 17 分钟
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环境准备

  • 没有 Dockerfile 或 Docker Compose 文件
  • 没有 Pull Request 模板
  • 阅读贡献指南

从这里开始

  1. 先读完整个 Issue，再读项目的贡献指南。
  2. 在 Issue 下留言说明你要接手 —— 这能避免两个人做同样的事。
  3. Fork 仓库，在一个分支上完成修改。
  4. 提交 Pull Request，并在描述里引用这个 Issue 编号。

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