متعددة الحدود
في الرياضيات، متعدد الحدود هوهجريب جبري يتكون من واحد أوكثر من الثوابت والمتغيرات، يتم بناؤه باستخدام العمليات الأربعة الأساسية فقط: الجمع والطرح والضرب والقسمة.
في الرياضيات ، كثير الحدود Polynomial (أوالحدودية) هوتعبير عن دالة رياضية أوهجريب جبري سهل وأملس Smooth.
بسيط بمعنى إنه لا يحوي من عمليات سوى الضرب والجمع وأملس بمعنى أنه قابل للمفاضلة بلا حدود infinitely differentiable أي أنه يملك مشتقات من جميع الرتب في جميع النقاط .
والقانون: ان كثير الحدود Polynomial (أوالحدودية) في الدرجة [ن] لها على الأكثر [ن] اصفار حقيقية [ن] = هي الاس لاول متغير في كثير الحدود Polynomial (أوالحدودية)
التاريخ
Determining the roots of polynomials, or "solving algebraic equations", is among the oldest problems in mathematics. However, the elegant and practical notation we use today only developed beginning in the 15th century. Before that, equations were written out in words. For example, an algebra problem from the Chinese Arithmetic in Nine Sections, circa 200 BCE, begins "Three sheafs of good crop, two sheafs of mediocre crop, and one sheaf of bad crop are sold for 29 dou." We would write 3x + 2y + z = 29.
History of the notation
The earliest known use of the equal sign is in Robert Recorde's The Whetstone of Witte, 1557. The signs + for addition, − for subtraction, and the use of a letter for an unknown appear in Michael Stifel's Arithemetica integra, 1544. René Descartes, in La géometrie, 1637, introduced the concept of the graph of a polynomial equation. He popularized the use of letters from the beginning of the alphabet to denote constants and letters from the end of the alphabet to denote variables, as can be seen above, in the general formula for a polynomial in one variable, where the a's denote constants and x denotes a variable. Descartes introduced the use of superscripts to denote exponents as well.
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الهامش
- ^ Howard Eves, An Introduction to the History of Mathematics, Sixth Edition, Saunders, نطقب:Isbn
المراجع
- Barbeau, E.J. (2003). . Springer. ISBN .
- Bronstein, Manuel; et al., eds. (2006). . Springer. ISBN .
- Cahen, Paul-Jean; Chabert, Jean-Luc (1997). . American Mathematical Society. ISBN .
- نطقب:Lang Algebra. This classical book covers most of the content of this article.
- Leung, Kam-tim; et al. (1992). . Hong Kong University Press. ISBN .
- Mayr, K. Über die Auflösung algebraischer Gleichungssysteme durch hypergeometrische Funktionen. Monatshefte für Mathematik und Physik vol. 45, (1937) pp. 280–313.
- Prasolov, Victor V. (2005). . Springer. ISBN .
- Sethuraman, B.A. (1997). "Polynomials". . Springer. ISBN .
- Umemura, H. Solution of algebraic equations in terms of theta constants. In D. Mumford, Tata Lectures on Theta II, Progress in Mathematics 43, Birkhäuser, Boston, 1984.
- von Lindemann, F. Über die Auflösung der algebraischen Gleichungen durch transcendente Functionen. Nachrichten von der Königl. Gesellschaft der Wissenschaften, vol. 7, 1884. Polynomial solutions in terms of theta functions.
- von Lindemann, F. Über die Auflösung der algebraischen Gleichungen durch transcendente Functionen II. Nachrichten von der Königl. Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen, 1892 edition.
وصلات خارجية
- Hazewinkel, Michiel, ed. (2001), "Polynomial", Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104
- "Euler's Investigations on the Roots of Equations". Archived from the original on September 24, 2012.
- Eric W. Weisstein, Polynomial at MathWorld.
نطقب:Polynomials
