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1
Content available remote Symbolic tensor calculus - functional and dynamic approach
Woszczyna A., Plaszczyk P., Czaja W., Golda Z. A.
Czasopismo Techniczne. Nauki Podstawowe
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2015
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Y. 112, iss. 1-NP
61--70
EN
In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.
PL
Krótko omawiamy zastosowania programowania dynamicznego i funkcyjnego do symbolicznego rachunku tensorowego. Demonstrując ten rodzaj programowania, posługujemy się pakietem ccgrg.m napisanym dla języka Wolfram Language/Mathematica. Zamieszczamy kilka przykładów ilustrujących funkcjonalność pakietu.
2
Content available remote On the Computational Complexity of Bongartz’s Algorithm
Mróz A.
Fundamenta Informaticae
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2013
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Vol. 123, nr 3
317--329
EN
We study the complexity of Bongartz’s algorithm for determining a maximal common direct summand of a pair of modules M,N over k-algebra ; in particular, we estimate its pessimistic computational complexity O(rm6n2(n + mlog n)), where m = dimkM ≤ n = dimkN and r is a number of common indecomposable direct summands of M and N. We improve the algorithm to another one of complexity O(rm4n2(n+mlogm)) and we show that it applies to the isomorphism problem (having at least an exponential complexity in a direct approach). Moreover, we discuss a performance of both algorithms in practice and show that the “average” complexity is much lower, especially for the improved one (which becomes a part of QPA package for GAP computer algebra system).
3
Content available remote Computational Methods with Symbolic Computation Systems
Krowiak A., Palej R., Struk R.
Vibrations in Physical Systems
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2004
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Vol. 21
223--226
4
Content available remote Regexpcount, a symbolic package for counting problems on regular expressions and words
Nicodeme P.
Fundamenta Informaticae
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2003
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Vol. 56, nr 1,2
71-88
EN
In previous work [10], we considered algorithms related to the statistics of matches with words and regular expressions in texts generated by Bernoulli or Markov sources. In this work these algorithms are extended for two purposes: to determine the statistics of simultaneous counting of different motifs, and to compute the waiting time for the first match with a motif in a model which may be constrained. This extension also handles matches with errors. The package is fully implemented and gives access to high and low level commands. We also consider an example corresponding to a practical biological problem: getting the statistics for the number of matches of words of size 8 in a genome (a Markovian sequence), knowing that an (overrepresented DNA protecting) pattern named Chi occurs a given number of times.
5
An application of computer algebra systems in teaching of kinematics of mechanisms
Grabysz W.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
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1999
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z. 11
21-26
EN
Students of mechanical engineering are taught graphical methods for solving problems of kinematics of mechanisms only to learn later, that in the real world they should avoid them. It is proposed to make students acąuaint with computer algebra systems instead of exercising the graphical methods.
PL
Studenci wydziałów mechanicznych uczeni są metod wykreślnych rozwiązywania zadań kinematyki mechanizmów tylko po to, aby później dojść do wniosku, że w praktyce są one bezużyteczne. Proponuje się zapoznać studentów z programami algebry symbolicznej zamiast ćwiczenia metod wykreślnych.
6
Content available remote A pragmatic approach to extending provers by computer algebra-with applications to coding theory
Ballarin C., Paulson L.C.
Fundamenta Informaticae
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1999
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Vol. 39, Nr 1,2
1-20
EN
The use of computer algebra is usually considered beneficial for mechanised reasoning in mathematical domains. We present a case study, in the application domain of coding theory, that supports this claim: the mechanised proofs depend on non-trivial algorithms from computer algebra and increase the reasoning power of the theorem prover. The unsoundness of computer algebra systems is a major problem in interfacing them to theorem provers. Our approach to obtaining a sound overall system is not blanket distrust but based on the distinction between algorithms we call sound and ad hoc respectively. This distinction is blurred in most computer algebra systems. Our experimental interface therefore uses a computer algebra library. It is based on formal specifications for the algorithms, and links the computer algebra library Sumit to the prover Isabelle. We give details of the interface, the use of the computer algebra system on the tactic-level of Isabelle and its integration into proof procedures.
7
Content available remote Using Modern Technology to Teach Precalculus
Rys P., Zdráhal T.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2000/2001
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Vol. 8
169--172
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