Excel VBA alkalmazás fejlesztése komplex szám gyökeinek kiszámítására

Komplex számokkal műveletek végzését már számológépeink is támogatják. Viszont a gyökvonás csak egyetlen eredményt ad, még számítógépes programokkal is, annak ellenére, hogy annyi különböző komplex számot kellene kapnunk, ahányadik gyököt vonunk. Ezért szükséges kifejleszteni az Excel táblázatkezelő program Visual Basic for Applications szolgáltatásával egy gyökvonást elvégző alkalmazást, mely az összes eredményt megjeleníti. A felhasználóbarát kezeléshez egyetlen űrlap biztosítja az adatok megadását és az eredmények megjelenítését különböző vezérlők segítségével. Az alkalmazás lehetőséget ad a komplex számok kanonikus, trigonometrikus és exponenciális alakja esetén is a használatra, támogatja a megjelenített számok könnyebb értelmezéséhez a gyökös formát, valamint a szögek esetén a fok és radián mértékegységet a Pi karakter (π) felhasználásával. Abstract: Calculating operations with complex numbers is already supported by calculators. However, root extraction gives only one result, even with computer programs, despite giving as many different complex numbers as many radicals. Therefore, it is necessary to develop a root extraction application with Visual Basic for Applications in Excel that displays all the results. For user-friendly operation, a single form allows you to enter data and display results using different controls. The application allows the use of complex numbers in canonical, trigonometric and exponential forms, supports the radical form for easier interpretation of the displayed numbers, and the degree and radian units for angles using the Pi character (π)

On the denesting of nested square roots

We present the basic theory of denesting nested square roots, from an elementary point of view, suitable for lower level coursework. Necessary and sufficient conditions are given for direct denesting, where the nested expression is rewritten as a sum of square roots of rational numbers, and for indirect denesting, where the nested expression is rewritten as a sum of fourth-order roots of rational numbers. The theory is illustrated with several solved examples

Excel VBA alkalmazás fejlesztése komplex szám gyökeinek kiszámítására

Calculating operations with complex numbers is already supported by calculators. However, root extraction gives only one result, even with computer programs, despite giving as many different complex numbers as many radicals. Therefore, it is necessary to develop a root extraction application with Visual Basic for Applications in Excel that displays all the results. For user-friendly operation, a single form allows you to enter data and display results using different controls. The application allows the use of complex numbers in canonical, trigonometric and exponential forms, supports the radical form for easier interpretation of the displayed numbers, and the degree and radian units for angles using the Pi character (π).Komplex számokkal műveletek végzését már számológépeink is támogatják. Viszont a gyökvonás csak egyetlen eredményt ad, még számítógépes programokkal is, annak ellenére, hogy annyi különböző komplex számot kellene kapnunk, ahányadik gyököt vonunk. Ezért szükséges kifejleszteni az Excel táblázatkezelő program Visual Basic for Applications szolgáltatásával egy gyökvonást elvégző alkalmazást, mely az összes eredményt megjeleníti. A felhasználóbarát kezeléshez egyetlen űrlap biztosítja az adatok megadását és az eredmények megjelenítését különböző vezérlők segítségével. Az alkalmazás lehetőséget ad a komplex számok kanonikus, trigonometrikus és exponenciális alakja esetén is a használatra, támogatja a megjelenített számok könnyebb értelmezéséhez a gyökös formát, valamint a szögek esetén a fok és radián mértékegységet a Pi karakter (π) felhasználásával

Towards a Certified Version of the Encyclopedia of Triangle Centers

Triangle centers such as the center of gravity, the circumcenter, the orthocenter are well studied by geometers. Recently, under the guidance of Clark Kimberling, an electronic encyclopedia of triangle centers (ETC) has been developed, it contains more than 7000 centers and many properties of these points. In this paper, we describe how we created a certified version of ETC such that some of the properties described come along with a computer checked proof of its validity

On methods of computing galois groups and their implementations in MAPLE.

by Tang Ko Cheung, Simon.Thesis date on t.p. originally printed as 1997, of which 7 has been overwritten as 8 to become 1998.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.Includes bibliographical references (leaves 95-97).Chapter 1 --- Introduction --- p.5Chapter 1.1 --- Motivation --- p.5Chapter 1.1.1 --- Calculation of the Galois group --- p.5Chapter 1.1.2 --- Factorization of polynomials in a finite number of steps IS feasible --- p.6Chapter 1.2 --- Table & Diagram of Transitive Groups up to Degree 7 --- p.8Chapter 1.3 --- Background and Notation --- p.13Chapter 1.4 --- Content and Contribution of THIS thesis --- p.17Chapter 2 --- Stauduhar's Method --- p.20Chapter 2.1 --- Overview & Restrictions --- p.20Chapter 2.2 --- Representation of the Galois Group --- p.21Chapter 2.3 --- Groups and Functions --- p.22Chapter 2.4 --- Relative Resolvents --- p.24Chapter 2.4.1 --- Computing Resolvents Numerically --- p.24Chapter 2.4.2 --- Integer Roots of Resolvent Polynomials --- p.25Chapter 2.5 --- The Determination of Galois Groups --- p.26Chapter 2.5.1 --- Searching Procedures --- p.26Chapter 2.5.2 --- "Data: T(x1,x2 ,... ,xn), Coset Rcpresentatives & Searching Diagram" --- p.27Chapter 2.5.3 --- Examples --- p.32Chapter 2.6 --- Quadratic Factors of Resolvents --- p.35Chapter 2.7 --- Comment --- p.35Chapter 3 --- Factoring Polynomials Quickly --- p.37Chapter 3.1 --- History --- p.37Chapter 3.1.1 --- From Feasibility to Fast Algorithms --- p.37Chapter 3.1.2 --- Implementations on Computer Algebra Systems --- p.42Chapter 3.2 --- Squarefree factorization --- p.44Chapter 3.3 --- Factorization over finite fields --- p.47Chapter 3.4 --- Factorization over the integers --- p.50Chapter 3.5 --- Factorization over algebraic extension fields --- p.55Chapter 3.5.1 --- Reduction of the problem to the ground field --- p.55Chapter 3.5.2 --- Computation of primitive elements for multiple field extensions --- p.58Chapter 4 --- Soicher-McKay's Method --- p.60Chapter 4.1 --- "Overview, Restrictions and Background" --- p.60Chapter 4.2 --- Determining cycle types in GalQ(f) --- p.62Chapter 4.3 --- Absolute Resolvents --- p.64Chapter 4.3.1 --- Construction of resolvent --- p.64Chapter 4.3.2 --- Complete Factorization of Resolvent --- p.65Chapter 4.4 --- Linear Resolvent Polynomials --- p.67Chapter 4.4.1 --- r-sets and r-sequences --- p.67Chapter 4.4.2 --- Data: Orbit-length Partitions --- p.68Chapter 4.4.3 --- Constructing Linear Resolvents Symbolically --- p.70Chapter 4.4.4 --- Examples --- p.72Chapter 4.5 --- Further techniques --- p.72Chapter 4.5.1 --- Quadratic Resolvents --- p.73Chapter 4.5.2 --- Factorization over Q(diac(f)) --- p.73Chapter 4.6 --- Application to the Inverse Galois Problem --- p.74Chapter 4.7 --- Comment --- p.77Chapter A --- Demonstration of the MAPLE program --- p.78Chapter B --- Avenues for Further Exploration --- p.84Chapter B.1 --- Computational Galois Theory --- p.84Chapter B.2 --- Notes on SAC´ؤSymbolic and Algebraic Computation --- p.88Bibliography --- p.9

Errata and Addenda to Mathematical Constants

We humbly and briefly offer corrections and supplements to Mathematical Constants (2003) and Mathematical Constants II (2019), both published by Cambridge University Press. Comments are always welcome.Comment: 162 page