什么是符号计算? [英] What is symbolic computation?

问题描述

根据 Wiki :

在数学和计算机科学中，计算机代数也称为 符号计算或代数计算是一个科学领域 指的是算法和软件的研究与开发 用于处理数学表达式和其他数学运算 对象

In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects

符号计算是否专注于符号操作和计算? Lisp程序以原子作为树叶的AST形式编写.据说Lisp是用于符号计算的语言.这是否意味着在符号计算中是:

Does symbolic computation focus on symbol manipulation and computation? Lisp program is written in the form of an AST with atoms as leaves. Lisp is said to be language for symbolic computing. Does it mean that in symbolic computation, it is:

• 所有有关符号(符号是Lisp中的原子或非原子表达式)
• 每个符号都被赋予了语义
符号运算是一种使程序员专注于处理符号和语义(语义可以是执行某项操作的原子或表达式)以及符号之间关系的范式，而不是认为数据结构和代码是两个分开的实体.
• 程序设计是基于符号组成/操作和语义分配的语言设计.

• all about symbols (symbols are atoms or non-atom expressions in Lisp)
• every symbol is assigned a semantic
• symbolic computation is a paradigm that orients programmers to focus on working with symbols and semantics (a semantic can be an atom or expression that does something) and the relationships between symbols, as opposed to think that data structure and code are two separated entities.
• program design is language design, based on symbol composition/manipulation and semantic assignment.

根据此问题，符号计算的反义词是数值计算.两者之间的主要区别是什么?当我使用Octave(正在研究)时，我必须大量处理数字，并且必须多次猜测这些魔术数字的含义.这是数值计算的重点吗?

According to this question, the opposite of symbolic computation is numeric computation. What's the primary difference between these two? When I work with Octave (I'm studying it), I have to work with numbers a lot and have to guess the meaning of those magic numbers many times. Is this a numerical computation focus?

推荐答案

符号计算"是具有符号表达式的计算.

"Symbolic Computation" is the computation with symbolic expressions.

符号表达式的示例:

数学公式.例如整数表达式
• 逻辑定理
• 计划情况

• a mathematic formula. for example an integral expression
• a logic theorem
• a plan situation

对于后者:

• 从 a 到 b ， b 到 d ， c 的道路 e ， e 到 f ， b 到 f ，...
• 在 a 处包裹 p1 ，在 d 处包裹 p2 ，在 p3 处包裹em> f
• 一辆卡车 t1 在 d

• roads from a to b, b to d, c to e, e to f, b to f, ...
• parcels p1 at a, p2 at d and p3 at f
• a truck t1 at d

现在的任务是生成一个能够提取所有包裹的好计划

Now the task would be to generate a good plan which picks up all parcels

1. 在 d
领取包裹 p2
2. 将卡车 t1 从 d 移至 b
3. 将卡车 t1 从 b 移到 a
4. 在 a
处提取包裹 p1
5. ...

1. pick up parcel p2 at d
2. move truck t1 from d to b
3. move truck t1 from b to a
4. pick up parcel p1 at a
5. ...

在以上示例中，符号代表地点和事物(卡车，包裹).符号表达式描述了一种情况，计划生成器将返回一系列动作-再次描述为符号表达式.

In above examples symbols stand for places and for things (truck, parcel). Symbol expressions describe a situation, a plan generator will return a sequence of actions - again described as symbolic expressions.

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