一元多项式运算实现研究与设计详解

The research and implementation of the representation and operation of univariate polynomials is a crucial aspect in the field of mathematics and computer science. Through the comprehensive study outlined in the document "Representation and Operation of Univariate Polynomials," we have delved into the intricacies of efficiently representing and performing operations on univariate polynomials. The primary aim of the course design is to equip students with the necessary skills to analyze and manipulate univariate polynomials effectively. By focusing on the addition and subtraction operations between created polynomials, students are able to grasp the fundamental principles underlying polynomial manipulation. In summarizing the detailed design process, it is evident that the mathematical model of univariate polynomials serves as the foundation for the program. Each univariate polynomial, such as Pn(x), can be expressed in terms of its coefficients and powers of x. By representing these polynomials as linear arrays, denoted as Pn=(a0, a1, a2, ..., an), the necessary information for performing operations is readily available. Furthermore, the multiplication rule for polynomials is a crucial component in effectively manipulating univariate polynomials. This rule allows for the efficient computation of products between polynomials, enabling students to navigate complex mathematical expressions with ease. Overall, the research and implementation of the representation and operation of univariate polynomials sheds light on the intricate processes involved in working with polynomials. By honing their skills in polynomial manipulation, students are better equipped to tackle challenging mathematical problems and contribute to the advancement of the field. Through a thorough understanding of the principles outlined in the document, individuals are able to unlock the potential of univariate polynomials and harness their power in various applications.