三种方法都可以利用直角三角形的性质及代数计算来加以证明。
Three methods can be proved using the feature of a right triangle and algebraic computation.
虽然这些计算无非是最基本的三角形和代数计算，但是所使用的公式非常复杂。
Although these calculations are nothing more than basic trigonometry and algebra, the formulas are very complicated.
得到了通过回热器的焓流、质量流量及脉管冷端压力和流量相位差的代数计算公式。
The algebraic expressions of enthalpy flux and mass flow rate in regenerator as well as the phase difference between pressure and mass flow rate at pulse tube cold end are presented.
不幸的是，这一方法仍然包含了一系列复杂的代数计算，还涉及了复杂得三角函数。
Unfortunately, the solution still included a complicated set of sums of algebraic series involving tricky powers of trigonometric functions.
哈克认为，这样的课程可以弥补成年人在数字方面的盲点，这些人已经完成了像代数这样的高级数学，但却无法按面积计算出一块地毯的价格。
Such courses, Hacker argues, are a remedy for the numerical illiteracy of adults who have completed high-level math like algebra but are unable to calculate the price of a carpet by area.
哈克认为，这样的课程可以弥补成年人在数字方面的盲点，这些人虽然已经学习了像代数这样的高等数学，但却无法按面积计算出一块地毯的价格。
Such courses, Hacker argues, are a remedy for the numerical illiteracy of adults who have completed high-level math like algebra but are unable to calculate the price of, say, a carpet by area.
而另外一些深入探究了数学计算过程，但只面向熟悉代数的读者。
Yet others go into mathematical procedures, but assume that the reader is adept in using algebra.
要想用一个经济模型来计算，那这个模型就必须要有具体的以代数形式给出的表达式。
But to compute an economic model, this theory has to be given concrete form, spelt out in definite algebraic terms.
这是一个代数游戏，可是在计算中，却十分关键。
It's just an algebraic game but very important when you make your calculations.
苏先生向BBC新闻记者解释道：“非常有趣，通过一些代数处理，我们的公式就能够跳跃式的计算PI值了；换句话，它允许计算pi的具体数位”。
"Interestingly, by some algebraic manipulations, (our) formula can compute PI with some bits skipped; in other words, it allows computing specific bits of PI," Mr Sze explained to BBC News.
计算机代数领域几乎为数学研究的每个方面提供了丰富多彩的方法。
The field of computer algebra offers a rich diversity of methodologies for almost every aspect of mathematical research.
可用于计算机代数的大多数系统还突出体现了某种绘图机制，允许您可视化所标绘的数据。
Most systems available for computer algebra also feature a graphing mechanism that lets you visualize the data that is being plotted.
SAGE的独特之处在于，它能够用作其他各种计算机代数系统的集成器，从而允许用户利用不同软件包的各自强项。
SAGE is unique in that it can function as an integrator of other diverse computer algebra systems, allowing the user to leverage the individual strengths of the various packages.
它在各种各样的计算机系统上运行，尤其擅长于涉及任意长度整数和小数、图、矩阵和多项式代数的算术。
It runs on a variety of computer systems and is especially good at arithmetic involving arbitrary-length integers and fractions, graphics, and matrix and polynomial algebra.
现今大部分云计算基础设施都能提供可靠的服务，这些服务通过由基于计算和存储虚拟化技术的下一代数据中心交付。
The majority of cloud computing infrastructure currently consists of reliable services delivered through next-generation data centers that are built on compute and storage virtualization technologies.
为这些任务而设计的程序领域的最常用名称是“计算机代数系统”(Computer Algebraic Systems,CAS)。
The most common designation for the field of programs designed for these tasks is computer algebraic systems (CAS).
Macaulay计算机代数系统对于多项式计算非常有用，并重点强调grobner基计算。
The Macaulay computer algebra system is useful for polynomial computations with emphasis on Grobner basis calculations.
这个专有共享软件计算机代数系统是为纪念已故最著名数学家之一pierredeFermat而命名的。
This proprietary, shareware computer algebra system is named for one of the most famous mathematicians who ever lived: Pierre DE Fermat.
Computationsin CommutativeAlgebra (CoCoA)是另一个免费计算机代数系统，用于处理超大型整数、有理数和多项式。
Computations in Commutative algebra (CoCoA) is another free computer algebra system for working with very large integers, rational Numbers, and polynomials.
Maxima基于商业软件包Macsyma，并包括一种完整的ALGOL风格的编程语言，对于教授计算机代数方面的编程概念最有用。
Based on the commercial package Macsyma, Maxima includes a complete ALGOL-like programming language and is most useful for teaching programming concepts in computer algebra.
最初的版本(一个计算机代数系统)名为DOE Macsyma，它开辟了后来开发的更知名的应用程序(例如Mathematica)的道路。
The original version (a computer algebra system) was called DOE Macsyma and led the way for later development of more commonly known applications such as Mathematica.
OpenMath(参见参考资料)是一种较老的格式，起源于计算机代数系统。
OpenMath (see Resources) is an older format with origins in computer algebra systems.
与大多数计算机代数系统一样，Maxima是使用Lisp语言编写的。
Like most computer algebra systems, Maxima is written in Lisp.
计算数学的其他领域包括计算机代数和符号计算。
Other areas of computational mathematics include computer algebra and symbolic computation.
这是由比杰甘尼坦——这个名字而来，给予和计算的代数形式。
This is borne out by the name - Bijaganitam, which was given to the algebraic form of computation.
它是现代数学的一个重要分支，是计算机专业基础理论的核心课程之一。
It is important subject of modern mathematics, one of core courses in computer science and technology.
递归算法是计算稠密线性代数的一种新的有效方法。
Recursion is a new effective method for computing dense linear algebra.
提出一种可以在联合代数重建方法中快速计算投影系数矩阵并优化内存的方法。
An efficient way to compute projection coefficient matrix together with memory optimization is presented in this paper.
在频域灵敏度分析中，利用计算线性代数系统的偏导数的纯代数方法是简单和有效的。
Purely algebraic methods for computing the sensitivity of linear algebraic system have been proven to be simple and effective in the frequency domain.
在频域灵敏度分析中，利用计算线性代数系统的偏导数的纯代数方法是简单和有效的。
Purely algebraic methods for computing the sensitivity of linear algebraic system have been proven to be simple and effective in the frequency domain.
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