https://www.chenk.top/zh/tags/polynomials/Recent content in Polynomials on Chen Kai BlogHugozh-CNSat, 11 Sep 2021 09:00:00 +0000https://www.chenk.top/zh/abstract-algebra/06-%E5%A4%9A%E9%A1%B9%E5%BC%8F%E7%8E%AF/Sat, 11 Sep 2021 09:00:00 +0000https://www.chenk.top/zh/abstract-algebra/06-%E5%A4%9A%E9%A1%B9%E5%BC%8F%E7%8E%AF/<p>我记得刚上大学那会儿，盯着黑板上的 <span class="math-inline">$x^2 &#43; 1$</span> 发呆。高中老师信誓旦旦地说这玩意儿“不能再分了”，可眼前的教授随手写下 <span class="math-inline">$(x&#43;i)(x-i)$</span> ，转头又补了一句：“如果在模 <span class="math-inline">$5$</span> 的整数里，它等于 <span class="math-inline">$(x&#43;2)(x&#43;3)$</span> 。”我当时的脑子直接打结：同一个多项式，怎么换个地盘就换了一副面孔？它到底是个固定的对象，还是随环境变形的变色龙？</p>