Анна Джонсон и ее гениальная теорема 1917 года
Ключевые слова:
евклидова последовательность полиномиальных остатков (ППО), модифицированная евклидова ППО, субрезультантная ППО, модифицированная субрезультантная ППО, метод Ван Флека, ППО Штурма
Аннотация
В этой статье мы представляем жизнь Анны Джонсон, женщины исключительно одаренной в области математики, наряду с тем, что мы считаем ее наибольшим вкладом: а именно, теоремой 1917 на модифицированных евклидовых последовательностях полиномиальных остатков (ППО), которая заложила основы теории субрезультантных ППО. Для того чтобы продемонстрировать различные математические понятия, представленные в этой статье, мы используем систему компьютерной алгебры SumPy (версия 1.0), которая основана на Python и находится в свободном доступе.
Литература
1. Akritas, A.G. 1987, “A simple proof of the validity of the reduced prs algorithm”, Computing, no. 38,
pp. 369–372.
2. Akritas, A.G., Malaschonok, G.I. & Vigklas, P.S. 2013, “On a Theorem by Van Vleck Regarding Sturm
Sequences”, Serdica Journal of Computing, no. 7(4), pp. 101–134.
3. Akritas, A.G., Malaschonok,G.I. & Vigklas, P.S. 2014, “Sturm Sequences and Modified Subresultant
Polynomial Remainder Sequences”, Serdica Journal of Computing, no. 8(1), pp. 29–46.
4. Akritas, A.G., Malaschonok, G.I., Vigklas, P.S. 2015, “On the Remainders Obtained in Finding the Greatest Common Divisor of Two Polynomials”, Serdica Journal of Computing, no. 9(2), pp. 123–138.
5. Akritas, A.G., Malaschonok, G.I. & Vigklas, P.S. “A Basic Result on the Theory of Subresultants”, Serdica
Journal of Computing. To appear.
6. Cohen, J.E., 2003. Computer Algebra and Symbolic Computation – Mathematical Methods. A.K. Peters,
Massachusetts.
7. Diaz–Toca, G.M. & Gonzalez–Vega, L. 2004, “Various New Expressions for Subresultants and Their
Applications”, Applicable Algebra in Engineering, Communication and Computing, no. 15, pp. 233–266.
8. Greenstein, L.S. & Campbell, P.J. 1982, “Anna Johnson Pell Wheeler: Her Life and Work”, Historia
Mathematica, no. 9, pp. 37–53.
9. Pell, A.J. & Gordon, R.L. 1917, “The Modified Remainders Obtained in Finding the Highest Common
Factor of Two Polynomials”, Annals of Mathematics, Second Series, no. 18(4), pp. 188–193.
10. Sylvester, J.J. 1840, “A method of determining by mere inspection the derivatives from two equations
of any degree”, Philosophical Magazine, no. 16, pp. 132–135.
11. Sylvester, J.J. 1853, “On the Theory of Syzygetic Relations of Two Rational Integral Functions, Comprising an Application to the Theory of Sturm’s Functions, and that of the Greatest Algebraical Common Measure”, Philosophical Transactions, no. 143, pp. 407–548.
12. Sylvester, J. J. 1853, “On a remarkable modification of Sturm’s theorem”, Philosophical Magazine and
Journal of Science, vol. V, Fourth Series, pp. 446–456, available at: https://books.google.gr/books?hl=
el&id=3Ov22-gFMnEC&q=sylvester#v=onepage&q&f=false [Accessed 15 Jan. 2016].
13. Van Vleck, E.B. 1899–1900, “On the Determination of a Series of Sturm’s Functions by the Calculation
of a Single Determinant”, Annals of Mathematics, Second Series, no. 1(1/4), pp. 1–13.
pp. 369–372.
2. Akritas, A.G., Malaschonok, G.I. & Vigklas, P.S. 2013, “On a Theorem by Van Vleck Regarding Sturm
Sequences”, Serdica Journal of Computing, no. 7(4), pp. 101–134.
3. Akritas, A.G., Malaschonok,G.I. & Vigklas, P.S. 2014, “Sturm Sequences and Modified Subresultant
Polynomial Remainder Sequences”, Serdica Journal of Computing, no. 8(1), pp. 29–46.
4. Akritas, A.G., Malaschonok, G.I., Vigklas, P.S. 2015, “On the Remainders Obtained in Finding the Greatest Common Divisor of Two Polynomials”, Serdica Journal of Computing, no. 9(2), pp. 123–138.
5. Akritas, A.G., Malaschonok, G.I. & Vigklas, P.S. “A Basic Result on the Theory of Subresultants”, Serdica
Journal of Computing. To appear.
6. Cohen, J.E., 2003. Computer Algebra and Symbolic Computation – Mathematical Methods. A.K. Peters,
Massachusetts.
7. Diaz–Toca, G.M. & Gonzalez–Vega, L. 2004, “Various New Expressions for Subresultants and Their
Applications”, Applicable Algebra in Engineering, Communication and Computing, no. 15, pp. 233–266.
8. Greenstein, L.S. & Campbell, P.J. 1982, “Anna Johnson Pell Wheeler: Her Life and Work”, Historia
Mathematica, no. 9, pp. 37–53.
9. Pell, A.J. & Gordon, R.L. 1917, “The Modified Remainders Obtained in Finding the Highest Common
Factor of Two Polynomials”, Annals of Mathematics, Second Series, no. 18(4), pp. 188–193.
10. Sylvester, J.J. 1840, “A method of determining by mere inspection the derivatives from two equations
of any degree”, Philosophical Magazine, no. 16, pp. 132–135.
11. Sylvester, J.J. 1853, “On the Theory of Syzygetic Relations of Two Rational Integral Functions, Comprising an Application to the Theory of Sturm’s Functions, and that of the Greatest Algebraical Common Measure”, Philosophical Transactions, no. 143, pp. 407–548.
12. Sylvester, J. J. 1853, “On a remarkable modification of Sturm’s theorem”, Philosophical Magazine and
Journal of Science, vol. V, Fourth Series, pp. 446–456, available at: https://books.google.gr/books?hl=
el&id=3Ov22-gFMnEC&q=sylvester#v=onepage&q&f=false [Accessed 15 Jan. 2016].
13. Van Vleck, E.B. 1899–1900, “On the Determination of a Series of Sturm’s Functions by the Calculation
of a Single Determinant”, Annals of Mathematics, Second Series, no. 1(1/4), pp. 1–13.
Опубликован
2016-04-29
Как цитировать
Akritas, A. (2016). Анна Джонсон и ее гениальная теорема 1917 года. Компьютерные инструменты в образовании, (2), 13-35. извлечено от http://cte.eltech.ru/ojs/index.php/kio/article/view/1391
Выпуск
Раздел
Информатика и Алгоритмическая математика
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