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You searched for subject:(perfect powers). Showing records 1 – 2 of 2 total matches.

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University of Waterloo

1. Roche, Daniel Steven. Efficient Computation with Sparse and Dense Polynomials.

Degree: 2011, University of Waterloo

Computations with polynomials are at the heart of any computer algebra system and also have many applications in engineering, coding theory, and cryptography. Generally speaking, the low-level polynomial computations of interest can be classified as arithmetic operations, algebraic computations, and inverse symbolic problems. New algorithms are presented in all these areas which improve on the state of the art in both theoretical and practical performance. Traditionally, polynomials may be represented in a computer in one of two ways: as a "dense" array of all possible coefficients up to the polynomial's degree, or as a "sparse" list of coefficient-exponent tuples. In the latter case, zero terms are not explicitly written, giving a potentially more compact representation. In the area of arithmetic operations, new algorithms are presented for the multiplication of dense polynomials. These have the same asymptotic time cost of the fastest existing approaches, but reduce the intermediate storage required from linear in the size of the input to a constant amount. Two different algorithms for so-called "adaptive" multiplication are also presented which effectively provide a gradient between existing sparse and dense algorithms, giving a large improvement in many cases while never performing significantly worse than the best existing approaches. Algebraic computations on sparse polynomials are considered as well. The first known polynomial-time algorithm to detect when a sparse polynomial is a perfect power is presented, along with two different approaches to computing the perfect power factorization. Inverse symbolic problems are those for which the challenge is to compute a symbolic mathematical representation of a program or "black box". First, new algorithms are presented which improve the complexity of interpolation for sparse polynomials with coefficients in finite fields or approximate complex numbers. Second, the first polynomial-time algorithm for the more general problem of sparsest-shift interpolation is presented. The practical performance of all these algorithms is demonstrated with implementations in a high-performance library and compared to existing software and previous techniques.

Subjects/Keywords: computer algebra; symbolic computation; polynomials; multiplication; interpolation; perfect powers

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Roche, D. S. (2011). Efficient Computation with Sparse and Dense Polynomials. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/5869

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Roche, Daniel Steven. “Efficient Computation with Sparse and Dense Polynomials.” 2011. Thesis, University of Waterloo. Accessed August 06, 2020. http://hdl.handle.net/10012/5869.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Roche, Daniel Steven. “Efficient Computation with Sparse and Dense Polynomials.” 2011. Web. 06 Aug 2020.

Vancouver:

Roche DS. Efficient Computation with Sparse and Dense Polynomials. [Internet] [Thesis]. University of Waterloo; 2011. [cited 2020 Aug 06]. Available from: http://hdl.handle.net/10012/5869.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Roche DS. Efficient Computation with Sparse and Dense Polynomials. [Thesis]. University of Waterloo; 2011. Available from: http://hdl.handle.net/10012/5869

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

2. Fedele, Dante. Naissance de la diplomatie moderne. L'ambassadeur au croisement du droit, de l'éthique et de la politique : The Birth of Modern Diplomacy. the Ambassador between Law, Ethics and Politics.

Degree: Docteur es, Histoire de la pensée politique - Cultures juridiques européennes, 2014, Lyon, École normale supérieure; Università degli studi di Napoli Federico II

S’appuyant sur un corpus de textes que l’on qualifie normalement de « traités sur l’ambassadeur », cette thèse s’attache à reconstruire la naissance de la diplomatie moderne tout au long d’une période qui va du XIIIe au XVIIe siècle, en essayant d’analyser la manière dont la figure de l’ambassadeur à été élaborée à l’intérieur d’un champ de problématisation qui se caractérise par une imbrication réciproque du droit, de l’éthique et de la politique et va constituer une véritable expérience de la diplomatie.Ce travail s’articule en deux parties. Dans la première il s’agit de comprendre comment la figure de l’ambassadeur a été façonnée sous le profil de son statut juridique, à savoir comme une persona publica chargée d’un officium et devant représenter son mandant, avec les conséquences qui en découlent quant à l’établissement de son pouvoir de négociation, à la définition de ses immunités ainsi qu’à la détermination des honneurs qu’il a le droit de recevoir. L’analyse de ces questions permettra d’apprécier la contribution apportée par notre corpus non seulement à la définition du statut juridique de l’ambassadeur, mais aussi à la formation du nouveau droit des gens destiné à régir l’Europe moderne. La seconde partie s’attache à comprendre comment la figure de l’ambassadeur a été façonnée sous le profil de son statut professionnel : on s’interroge alors sur les fonctions qui lui sont attribuées, sur les moyens qui lui sont fournis et les conditions qui lui sont demandées pour s’en acquitter de la manière la plus efficace, ainsi que sur la problématisation éthique à laquelle son action est soumise. Tout en essayant de faire ressortir la spécificité de l’ambassadeur, cette partie se propose aussi de contribuer à l’étude de la professionnalisation du fonctionnaire public.

Using a collection of texts commonly known as the “treatises on the ambassador”, this research examines the birth and the development of the experience of diplomacy from the 13th to the 17th Century. It aims, in particular, to explore the development of the figure of the ambassador within a field of problematization involving ethics, politics and law.After some methodological and historical remarks, the thesis deals with the development of the status of the ambassador from two perspectives, the legal and the professional. Regarding his legal status, the medieval legal conceptualisation of the role of the ambassador as a genuine public “office”, and that of the diplomatic function as “representation”, are examined. The way in which these conceptualisations help to define the negotiating powers conferred on the ambassador, his immunities and the honours to which he is entitled is then considered. This analysis allows for an investigation of the complex links between the exercise of diplomacy and claims to sovereignty during Europe’s transition from the Middle Ages to Modernity. Regarding his professional status, the thesis reconstructs the functions of the ambassador (particularly in relation to information gathering and negotiation), the means provided…

Advisors/Committee Members: Senellart, Michel (thesis director).

Subjects/Keywords: Traités sur l’ambassadeur; Histoire de la diplomatie; Pensée politique; Ius commune; Équilibre des puissances; Cérémonial diplomatique; Traités et conventions; Immunités diplomatiques; Droit d’ambassade; Professionnalisation du fonctionnaire public; « parfait ambassadeur »; Collecte d’informations; Raison d’État et intérêts des États; Treatises on the ambassador; History of diplomacy; History of political thoughts; Ius commune; Balance of competing powers; Diplomatic protocol; Treaties and conventions; Diplomatic immunities; Droit d’ambassade; Professionalization of public officials; Perfect ambassador; Information gathering; Reason of State and interest of the State

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Fedele, D. (2014). Naissance de la diplomatie moderne. L'ambassadeur au croisement du droit, de l'éthique et de la politique : The Birth of Modern Diplomacy. the Ambassador between Law, Ethics and Politics. (Doctoral Dissertation). Lyon, École normale supérieure; Università degli studi di Napoli Federico II. Retrieved from http://www.theses.fr/2014ENSL0968

Chicago Manual of Style (16th Edition):

Fedele, Dante. “Naissance de la diplomatie moderne. L'ambassadeur au croisement du droit, de l'éthique et de la politique : The Birth of Modern Diplomacy. the Ambassador between Law, Ethics and Politics.” 2014. Doctoral Dissertation, Lyon, École normale supérieure; Università degli studi di Napoli Federico II. Accessed August 06, 2020. http://www.theses.fr/2014ENSL0968.

MLA Handbook (7th Edition):

Fedele, Dante. “Naissance de la diplomatie moderne. L'ambassadeur au croisement du droit, de l'éthique et de la politique : The Birth of Modern Diplomacy. the Ambassador between Law, Ethics and Politics.” 2014. Web. 06 Aug 2020.

Vancouver:

Fedele D. Naissance de la diplomatie moderne. L'ambassadeur au croisement du droit, de l'éthique et de la politique : The Birth of Modern Diplomacy. the Ambassador between Law, Ethics and Politics. [Internet] [Doctoral dissertation]. Lyon, École normale supérieure; Università degli studi di Napoli Federico II; 2014. [cited 2020 Aug 06]. Available from: http://www.theses.fr/2014ENSL0968.

Council of Science Editors:

Fedele D. Naissance de la diplomatie moderne. L'ambassadeur au croisement du droit, de l'éthique et de la politique : The Birth of Modern Diplomacy. the Ambassador between Law, Ethics and Politics. [Doctoral Dissertation]. Lyon, École normale supérieure; Università degli studi di Napoli Federico II; 2014. Available from: http://www.theses.fr/2014ENSL0968

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