25
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Characteristic sets verses generalized characteristic sets

, , , , &

References

  • D. Wang. Elimination practice: software tools and applications, Imperial College Press, London, (2004).
  • D. Wang. An elimination method for differential polynomial systems, System Science and Mathematical Sciences, 9, (1996), 216–228.
  • D. Wang. A generalized algorithm for computing characteristic sets, World Scientific Publishing Company, Singapore, (2001), 165–174.
  • D. Wang. Elimination methods, texts and monograms in symbolic computations, Springer-Verlag, Wien New York, (2001).
  • F. Afzal. Generalized char sets for ordinary differential polynomial sets, Science International, 28 (3), (2016).
  • M. Cancan, F. Afzal, A. Maqbool and Deeba Afzal. Algorithm for computing differential char sets efficiently, Journal of Discrete Mathematical Sciences and Cryptography, 23(6), (2020), 1203-1206. doi: 10.1080/09720529.2020.1809114
  • F. Afzal. Some Applications of Generalized Characteristic Sets of Ordinary Differential Polynomial Sets, MATEC Web of Conferences, 7 0 (2016), ICMMR 2016, 1–5.
  • J. Meng, L. Xiaoliang, D. Wang. A new algorithmic scheme for computing characteristic sets, Journal of Symbolic Computation, 50, (2013), 431–449. doi: 10.1016/j.jsc.2012.04.004
  • Kalkbrener, M. A, generalized Euclidean algorithm for computing triangular representations of algebraic varieties, Journal of Symbolic Computation, 15, (1993) 14–167. doi: 10.1006/jsco.1993.1011
  • Li, Y, Some properties of triangular sets and improvement upon algorithm CharSer, In: Calmet, J., Ida, T., Wang, D. (Eds.), Artificial Intelligence and Symbolic Computation, Lecture Notes in Computer Science. Springer-Verlag, Beijing, 4120, (2006) 82–93.
  • W. T. Wu. Mathematics-mechanization research preprints, No 1-6, MM Research Center, Academia Sinica, 986, (1987-1991).
  • X.S. Gao, J. Van der Hoeven, Y. Luo, and C. Yuan. Characteristic set method for differential-difference polynomial systems. Journal of Symbolic Computation, 44, (2009), 1137–1163. doi: 10.1016/j.jsc.2008.02.010
  • X.S. Gao and Z. Huang, Characteristic set algorithms for equation solving in finite fields and applications in cryptanalysis, Journal of Symbolic Computation, 47, (2012), 655–679. doi: 10.1016/j.jsc.2011.12.025
  • A.J. M. Khalaf, H. Dilawer, F. Afzal, A. Maqbool, D. Afzal, F. Chaudhry. Right zero divisor graph of 2×2 matrices over Z3. Journal of Information and Optimization Sciences, Published online: 11 Nov 2020. DOI:10.1080/02522667.2020.1826168
  • A.J. M. Khalaf, D. Afzal, F.K. Sherwani, A. Maqbool, M. Mahsud, F. Afzal. A study of right zero divisor graph of 3×3 matrices over Z2. Journal of Information and Optimization Sciences, Published online: 11 Nov 2020. DOI:10.1080/02522667.2020.1835035
  • S. Ahmad, H. M. A. Siddiqui, A. Ali, M.R. Farahani, M. Imran, I. N. Cangul. On Wiener index and Wiener polarity index of some polyomino chains. Journal of Discrete Mathematical Sciences and Cryptography. 22(7), 2019, 1151-1164. DOI:10.1080/09720529.2019.1688965
  • A.J.M. Khalaf, A.Q. Baig, M.R. Azhar, M. Imran, M.R. Farahani. The Eccentric Based Zagreb Indices of Carbon Graphite. Journal of Discrete Mathematical Sciences, Cryptography. 23(6), (2020), 1121–1137. DOI:10.1080/09720529.2020.1818448
  • W. Gao, M.R. Farahani. Generalization Bounds and Uniform Bounds for Multi-Dividing Ontology Algorithms with Convex Ontology Loss Function. The Computer Journal, 60(9), 2017, 1289–1299, DOI:10.1093/comjnl/bxw107
  • L. Zhu, Y. Pan, M.R. Farahani, W. Gao. Theoretical Characteristics on Scoring Function in Multi-dividing Setting. IAENG International Journal of Applied Mathematics, 47(1), 28-36, 2017.
  • L. Zhu, Y. Pan, M.R. Farahani, W. Gao. Graph Laplacian Based Ontology Regularization Distance Framework for Ontology Similarity Measuring and Ontology Mapping. Journal of Computational Mathematics 1(1):2017. DOI:10.26524/cm6
  • Y. Gao, W. Gao, M.R. Farahani. Ontology optimization tactics via distance calculating. Applied Mathematics and Nonlinear Sciences. 1(1), (2016) 154–169. DOI:10.21042/AMNS.2016.1.00012
  • Y. Gao, M.R. Farahani, W. Gao. A Neighborhood Union Condition for Fractional (k,n’,m)-Critical Deleted Graphs. Transactions on Combinatorics 6(1), 2017, 13-19. DOI:10.22108/TOC.2017.20355
  • J. Wu, M.R. Farahani, X. Yu, W. Gao. Ontology computation for graph spaces focus on partial vertex. Journal of Difference Equations and Applications. 2016. 23(1-2). DOI:10.1080/10236198.2016.1200567

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.