Generator (mathematics)

（重定向自Generating set）

The 5th roots of unity in the complex plane form a group of order 5. Each non-identity element by itself is a generator for the whole group.

In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that of a smaller set of objects, together with a set of operations that can be applied to it, that result in the creation of a larger collection of objects, called the generated set. The larger set is then said to be generated by the smaller set. It is commonly the case that the generating set has a simpler set of properties than the generated set, thus making it easier to discuss and examine. It is usually the case that properties of the generating set are in some way preserved by the act of generation; likewise, the properties of the generated set are often reflected in the generating set.

单词	Generating set
释义	Generating set 原声例句双语版 TED-Ed 演讲精选 Pairs of massive bodies in our solar system generate sets of five Lagrange points. 太阳系中每对大型天体会产生五个拉格朗日点。 TED演讲（音频版） 2022年3月合集 Using a randomly generated set of these blueprints, we can create an initial population of 10 or more robots to kick-start this evolutionary process. 使用一组随机生成的这些蓝图，我们可以创建 10 个或更多机器人的初始种群来启动这个进化过程。英语百科 Generator (mathematics) （重定向自Generating set） In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that of a smaller set of objects, together with a set of operations that can be applied to it, that result in the creation of a larger collection of objects, called the generated set. The larger set is then said to be generated by the smaller set. It is commonly the case that the generating set has a simpler set of properties than the generated set, thus making it easier to discuss and examine. It is usually the case that properties of the generating set are in some way preserved by the act of generation; likewise, the properties of the generated set are often reflected in the generating set.
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