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Płoski, Arkadiusz (8)
García Barroso, Evelia Rosa (2)Barroso, Evelia Rosa Garcia (1)Brzostowski, Szymon (1)Krasinski, Tadeusz (1)Lenarcik, Andrzej (1)Skalski, Grzegorz (1)Spodzieja, Stanisław (1)Szurek, Michał (1)Sękalski, Maciej (1)SubjectBézout’s Theorem (1)geometria algebraiczna (1)geometria analityczna (1)Jacobi Formula (1)Katedra Funkcji Analitycznych i Równań Różniczkowych (1)Katedra Geometrii Algebraicznej i Informatyki Teoretycznej (1)materiały konferencyjne (1)Uniwersytet Łódzki (1)warsztaty (1)Wydział Matematyki i Informatyki (1)... View MoreDate Issued2013 (2)2017 (2)2022 (2)2016 (1)2019 (1)Has File(s)Yes (8)

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Euclidean algorithm and polynomial equations after Labatie 

García Barroso, Evelia Rosa; Płoski, Arkadiusz (Wydawnictwo Uniwersytetu Łódzkiego, 2013)
We recall Labatie's effective method of solving polynomial equations with two unknowns by using the Euclidean algorithm.
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Bézout’s inequality for real polynomials 

Płoski, Arkadiusz; Sękalski, Maciej (Łódź University Press, 2017)
Let F(X, Y ), G(X, Y ) be polynomials of degrees m, n > 0 respectively. We prove, that the set {(x, y) Є R² : F(x, y) = G(x, y) = 0} has at most mn connected components.
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Formal and convergent solutions of analytic equations 

Płoski, Arkadiusz (Łódź University Press, 2017)
We provide the detailed proof of a sharpened version of the M. Artin Approximation Theorem.
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Contact exponent and the Milnor number of plane curve singularities 

Barroso, Evelia Rosa Garcia; Płoski, Arkadiusz (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
We investigate properties of the contact exponent (in the sense of Hironaka [Hi]) of plane algebroid curve singularities over algebraically closed fields of arbitrary characteristic. We prove that the contact exponent is ...
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Introduction to the local theory of plane algebraic curves 

Płoski, Arkadiusz (Wydawnictwo Uniwersytetu Łódzkiego, 2013)
We consider the algebroid plane curves de ned by formal power series of two variables with coe cients in an algebraically closed eld. Using quadratic transformations we prove the local normalization theorem. Then we study ...
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On Lê’s formula in arbitrary characteristic 

García Barroso, Evelia Rosa; Płoski, Arkadiusz (Wydawnictwo Uniwersytetu Łódzkiego, 2022)
In this note we extend, to arbitrary characteristic, Lˆe’s formula (Calculation of Milnor number of isolated singularity of complete intersection. Funct. Anal. Appl. 8 (1974), 127–131).
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Lectures on polynomial equations: Max Noether’s Fundamental Theorem, The Jacobi Formula and Bézout’s Theorem 

Płoski, Arkadiusz (Wydawnictwo Uniwersytetu Łódzkiego, 2022)
Using some commutative algebra we prove Max Noether’s Theorem, the Jacobi Formula and B´ezout’s Theorem for systems of polynomial equations defining transversal hypersurfaces without common points at infinity.
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Materiały na XXXVII Konferencję i warsztaty z geometrii analitycznej i algebraicznej 

Spodzieja, Stanisław; Skalski, Grzegorz; Krasinski, Tadeusz; Brzostowski, Szymon; Lenarcik, Andrzej; Płoski, Arkadiusz; Szurek, Michał (Wydawnictwo Uniwersytetu Łódzkiego, 2016)

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