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Qualitative computing [[electronic resource] ] : a computational journey into nonlinearity / / Françoise Chatelin
| Qualitative computing [[electronic resource] ] : a computational journey into nonlinearity / / Françoise Chatelin |
| Autore | Chaitin-Chatelin Françoise |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (599 p.) |
| Disciplina | 511.8 |
| Soggetto topico |
Social sciences - Data processing
Qualitative research - Data processing |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-59365-3
9786613906106 981-4322-93-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Pour mes enfants, petits et grands; Preface; Contents; 7. Homotopic Deviation in Linear Algebra; 1. Introduction to Qualitative Computing; 1.1 The art of computing before the 20th century; 1.1.1 Numeracy is not ubiquitous; 1.1.2 An irrational consequence of nonlinearity; 1.1.3 Zero: Thinking the unthinkable; 1.1.4 v1-: A complex consequence of nonlinearity; 1.1.5 Infinity: Decoding divergent series; 1.2 The unending evolution of logic due to complexification; 1.2.1 Classical analysis; 1.2.2 The creative role of zero; 1.2.3 The evolutive pressure of paradoxes on logic
1.2.4 Hypercomplex numbers of dimension 2k, k (1843 1912)1.3 The 20th century; 1.3.1 A paradigm shift; 1.3.2 Fixing the laws of logic a priori; 1.3.3 The eclipse of the art of computing; 1.3.4 The rise of numerical linear algebra; 1.3.5 Contemporary experimental sciences; 1.4 Back to the art of computing; 1.4.1 Hypercomputation in Dickson algebras; 1.4.2 Homotopic Deviation in associative linear algebra over C; 1.4.3 Understanding why and explaining how; 1.4.4 Qualitative Computing; 2. Hypercomputation in Dickson Algebras; 2.1 Associativity in algebra; 2.1.1 Groups, rings and fields 2.1.2 Real algebras 2.2 Dickson algebras over the real field; 2.2.1 The doubling process of Dickson (1912); 2.2.2 "Complexification" of Ak-1: Ak = Ak-11 Ak-1D7; , k 1; 2.2.3 The k basic generators for Ak, k 2265; 1; 2.2.4 Productive coupling of linear subspaces in Ak, k 2265; 4; 2.2.5 Other inductive multiplicative processes; 2.3 Properties of the multiplication; 2.3.1 The partition Ak = R1 2295; Ak, k 2265; 1; 2.3.2 The commutator for k 2265; 2; 2.3.3 The associator for k 2265; 3; 2.3.4 The four real division algebras; 2.3.5 The alternator for k 2265; 4; 2.3.6 The normalisatrix function for k 2265; 4 2.3.7 The subalgebra σx generated by x 2208; A, x 02.4 Left and right multiplication maps; 2.4.1 Definition; 2.4.2 The real scalar product La, Lb F; 2.5 The partition Ak = C1 2295; Dk, k 2265; 2; 2.5.1 A characterization of C in Ak, k 2265; 4; 2.5.2 Algebraic computation in Dk, k 2265; 2; 2.5.3 The map La for a 2208; Dk; 2.5.4 The complex scalar product La,Lb F* for a 2208; Dk; 2.6 Alternative vectors in Ak for k 2265; 4; 2.6.1 Definition; 2.6.2 Colinearity of X and Y in Ak, k 2265; 4; 2.6.3 Characterization of alternativity for vectors inAk, k 2265; 4; 2.6.4 Alternative subspaces in Ak, k 2265; 4 2.9.4.3 The exponential of a product x D7; u in Ak, k 2265; 2 |
| Record Nr. | UNINA-9910465488103321 |
Chaitin-Chatelin Françoise
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Qualitative computing [[electronic resource] ] : a computational journey into nonlinearity / / Françoise Chatelin
| Qualitative computing [[electronic resource] ] : a computational journey into nonlinearity / / Françoise Chatelin |
| Autore | Chaitin-Chatelin Françoise |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (599 p.) |
| Disciplina | 511.8 |
| Soggetto topico |
Social sciences - Data processing
Qualitative research - Data processing |
| ISBN |
1-283-59365-3
9786613906106 981-4322-93-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Pour mes enfants, petits et grands; Preface; Contents; 7. Homotopic Deviation in Linear Algebra; 1. Introduction to Qualitative Computing; 1.1 The art of computing before the 20th century; 1.1.1 Numeracy is not ubiquitous; 1.1.2 An irrational consequence of nonlinearity; 1.1.3 Zero: Thinking the unthinkable; 1.1.4 v1-: A complex consequence of nonlinearity; 1.1.5 Infinity: Decoding divergent series; 1.2 The unending evolution of logic due to complexification; 1.2.1 Classical analysis; 1.2.2 The creative role of zero; 1.2.3 The evolutive pressure of paradoxes on logic
1.2.4 Hypercomplex numbers of dimension 2k, k (1843 1912)1.3 The 20th century; 1.3.1 A paradigm shift; 1.3.2 Fixing the laws of logic a priori; 1.3.3 The eclipse of the art of computing; 1.3.4 The rise of numerical linear algebra; 1.3.5 Contemporary experimental sciences; 1.4 Back to the art of computing; 1.4.1 Hypercomputation in Dickson algebras; 1.4.2 Homotopic Deviation in associative linear algebra over C; 1.4.3 Understanding why and explaining how; 1.4.4 Qualitative Computing; 2. Hypercomputation in Dickson Algebras; 2.1 Associativity in algebra; 2.1.1 Groups, rings and fields 2.1.2 Real algebras 2.2 Dickson algebras over the real field; 2.2.1 The doubling process of Dickson (1912); 2.2.2 "Complexification" of Ak-1: Ak = Ak-11 Ak-1D7; , k 1; 2.2.3 The k basic generators for Ak, k 2265; 1; 2.2.4 Productive coupling of linear subspaces in Ak, k 2265; 4; 2.2.5 Other inductive multiplicative processes; 2.3 Properties of the multiplication; 2.3.1 The partition Ak = R1 2295; Ak, k 2265; 1; 2.3.2 The commutator for k 2265; 2; 2.3.3 The associator for k 2265; 3; 2.3.4 The four real division algebras; 2.3.5 The alternator for k 2265; 4; 2.3.6 The normalisatrix function for k 2265; 4 2.3.7 The subalgebra σx generated by x 2208; A, x 02.4 Left and right multiplication maps; 2.4.1 Definition; 2.4.2 The real scalar product La, Lb F; 2.5 The partition Ak = C1 2295; Dk, k 2265; 2; 2.5.1 A characterization of C in Ak, k 2265; 4; 2.5.2 Algebraic computation in Dk, k 2265; 2; 2.5.3 The map La for a 2208; Dk; 2.5.4 The complex scalar product La,Lb F* for a 2208; Dk; 2.6 Alternative vectors in Ak for k 2265; 4; 2.6.1 Definition; 2.6.2 Colinearity of X and Y in Ak, k 2265; 4; 2.6.3 Characterization of alternativity for vectors inAk, k 2265; 4; 2.6.4 Alternative subspaces in Ak, k 2265; 4 2.9.4.3 The exponential of a product x D7; u in Ak, k 2265; 2 |
| Record Nr. | UNINA-9910792082703321 |
|
Chaitin-Chatelin Françoise
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||