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CAS Computer Algebra System Wspomaganie obliczeń matematycznych dr inż. Michał Michna Wspomaganie obliczeń matematycznych Potrzeby Projektowanie Modelowanie Symulacja Analiza wyników Narzędzia Obliczenia algebraiczne, optymalizacja Rozwiązywanie układów równań algebraicznych i różniczkowych Prezentacja wyników, interpolacja, aproksymacja Import / eksport danych 2 CAS Politechnika Gdańska 2011 Wspomaganie obliczeń matematycznych Numeryczne obliczenia Matlab Scilab Octave obliczenia w dużej skali algorytmy numeryczne wizualizacja wyników Toolbox’y – Matlab Simulink 3 CAS Politechnika Gdańska 2011 Wspomaganie obliczeń matematycznych CAS – computer algebra system Obliczenia symboliczne Maple Mathematica MathCad Maxima Algorytmy numeryczne, Wizualizacja wyników możliwości składu tekstów matematycznych 4 CAS Politechnika Gdańska 2011 Wspomaganie obliczeń matematycznych Metoda rachunku numeryczny symboliczny Możliwość rozwiązywania trudnych zazwyczaj tak zazwyczaj nie zadań praktycznych Wielość metod o różnej tak tak skuteczności Wymaga wiedzy wykraczającej poza najczęściej tak najczęściej nie rozwiązywane zadanie skończony zestaw liczb wzór lub informacja o Wynik lub rysunek charakterze rozwiązania 5 CAS Politechnika Gdańska 2011 Wspomaganie obliczeń matematycznych Metoda rachunku numeryczny symboliczny Potrafi działać na nie tak abstrakcyjnych obiektach Dobrze radzi sobie z zazwyczaj nie zazwyczaj tak nieskończonościami Dobrze radzi sobie z tak nie mnogością parametrów teoretycznie Precyzja wyniku ograniczona nieskończona Ostateczna jakość niepewna niepewna wyniku 6 CAS Politechnika Gdańska 2011 Zestawienie programów CAS Komercyjne: Algebrator · ClassPad Manager · LiveMath · Magma · Maple · Mathcad · Mathematica · MuPAD · TI InterActive! · WIRIS Open source Axiom · Cadabra · CoCoA · DoCon · Eigenmath · FriCAS · GAP · GiNaC · Macaulay2 · Mathomatic · Maxima · OpenAxiom · PARI/GP · Reduce · Sage · SINGULAR · SymPy · Xcas · Octave · Scilab Free/shareware Fermat Nierozwijane Derive · DCAS · Macsyma · muMATH · Yacas 7 CAS Politechnika Gdańska 2011 Wspomaganie obliczeń matematycznych Środowiska zintegrowane/hybrydowe Matlab Simulink Symbolic Math Toolbox™ (MuPAD) 8 CAS Politechnika Gdańska 2011 Obliczenie numeryczne - Scilab SCILAB I.N.R.I.A. (Institut National de Recherche en Informatique et Automatique) rozwiązywanie układów liniowych, wyznaczanie wartości własnych, wektorów własnych, szybka transformacja Fouriera, rozwiązywanie równań różniczkowych, algorytmy optymalizacji, rozwiązywanie równań nieliniowych, generowanie liczb losowych, 9 CAS Politechnika Gdańska 2011 Scilab Operacje na macierzach • dodawanie, odejmowanie, mnożenie • macierze jednostkowe 10 CAS Politechnika Gdańska 2011 Scilab Rysowanie przebiegów funkcji 2D 11 CAS Politechnika Gdańska 2011 Scilab Rysowanie przebiegów funkcji 3D 12 CAS Politechnika Gdańska 2011 Mathcad – środowisko pracy Mathcad 15.0, Mathcad Prime 1.0 Parametric Technology Corporation's 13 CAS Politechnika Gdańska 2011 Obliczenia symboliczne - Mathcad Rozwiązanie równania kwadratowego Język programowania LISP x = (-B+SQRT(B**2-4*A*C))/(2*A) Arkusz kalkulacyjny =(-B1+PIERWIASTEK(B1*B1-4*A1*C1))/(2*A1) Mathcad 14 CAS Politechnika Gdańska 2011 PTC Mathcad Prime 1.0 Środowisko obliczeń Document-centric Zaawansowane odkrywanie matematyki Biblioteki numeryczne Dynamiczna kontrola jednostek Reverse compatibility Edytor równań WYSIWYG Design of Experiments (DoE) 15 CAS Politechnika Gdańska 2011 Mathcad Prime 1.0 16 CAS Politechnika Gdańska 2011 Mathcad Prime 1.0 17 CAS Politechnika Gdańska 2011 Obliczenia symboliczne - WolframAlpha 18 CAS Politechnika Gdańska 2011 WolframAlpha Rozwiązywanie równań liniowych 19 CAS Politechnika Gdańska 2011 WolframAlpha Rozwiązywanie równań różniczkowych 20 CAS Politechnika Gdańska 2011 WolframAlpha Regresja liniowa 21 CAS Politechnika Gdańska 2011 WolframAlpha Regresja ekspotencjalna 22 CAS Politechnika Gdańska 2011 WolframAlpha Wykresy funkcji 2D 3D 23 CAS Politechnika Gdańska 2011 Wolfram Mathematica 24 dr inż. Michał Michna Wolfram Mathematica 25 dr inż. Michał Michna Maxima Różniczkowanie i całkowanie symboliczne Rozwiązywanie równań i układów równań algebraicznych Rozwiązywanie wybranych typów równań różniczkowych Upraszczanie wyrażeń algebraicznych Tworzenie wykresów 2D i 3D (za pośrednictwem Gnuplota) Szeregi Fouriera Operacje na macierzach Obliczenia dowolnej precyzji Eksport wyników do TeX’a Strukturalny język programowania (+Lisp) Wybrane operacje numeryczne Wybrane operacje statystyczne 26 CAS Politechnika Gdańska 2011 Maxima 1968 MIT Departamentu Energii USA programu Macsyma 1988 GPL 27 CAS Politechnika Gdańska 2011 Maxima Rozwiązywanie równań 28 CAS Politechnika Gdańska 2011 Maxima Wykresy 2D 29 CAS Politechnika Gdańska 2011 Maxima Wykresy 3D 30 CAS Politechnika Gdańska 2011 Maxima Rozwiązywanie równań liniowych 31 CAS Politechnika Gdańska 2011 Maxima Pochodne 32 CAS Politechnika Gdańska 2011 Maxima Funkcje 33 CAS Politechnika Gdańska 2011 Maxima Funkcje 34 CAS Politechnika Gdańska 2011 Maxima Web Maxima, a Computer Algebra System elearning.cerfacs.fr/miscellane ous/tools/maxima/index.p hp 35 CAS Politechnika Gdańska 2011 Analiza i wizualizacja danych AutoSignal DADISP Grapher IRISExplorer MapViewer Origin PeakFit SigmaScan SigmaPlot SigmaStat 36 CAS Politechnika Gdańska 2011 Modelowanie i symulacje Mechatronika SPICE – PSpice, LTSpice MAST/VHDL – SABER Grafy wiązań - 20-Sim Modelica - Dynasim 37 CAS Politechnika Gdańska 2011 .
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