메뉴 건너뛰기




Volumn 4, Issue 4, 2006, Pages 470-504

Theorema: Towards computer-aided mathematical theory exploration

Author keywords

"Lazy Thinking"; Automated reasoning; Mathematical assistant; Theorema; Theory exploration

Indexed keywords

ALGORITHMS; COMPUTER AIDED ANALYSIS; COMPUTER SOFTWARE; FORMAL LOGIC; THEOREM PROVING;

EID: 33750069824     PISSN: 15708683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jal.2005.10.006     Document Type: Article
Times cited : (96)

References (94)
  • 3
    • 35048850991 scopus 로고    scopus 로고
    • Synthesis of programs in computational logic
    • Program Development in Computational Logic. Bruynooghe M., and Lau K.-K. (Eds), Springer, Berlin
    • Basin D., Deville Y., Flener P., Hamfelt A., and Nilsson J.F. Synthesis of programs in computational logic. In: Bruynooghe M., and Lau K.-K. (Eds). Program Development in Computational Logic. Lecture Notes in Comput. Sci. vol. 3049 (2004), Springer, Berlin 30-65
    • (2004) Lecture Notes in Comput. Sci. , vol.3049 , pp. 30-65
    • Basin, D.1    Deville, Y.2    Flener, P.3    Hamfelt, A.4    Nilsson, J.F.5
  • 4
    • 24344470890 scopus 로고    scopus 로고
    • Interactive Theorem Proving and Program Development: Coq'Art: The Calculus of Inductive Constructions
    • Springer, Berlin
    • Bertot Y., and Castèran P. Interactive Theorem Proving and Program Development: Coq'Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science, An EATCS Series (2004), Springer, Berlin
    • (2004) Texts in Theoretical Computer Science, An EATCS Series
    • Bertot, Y.1    Castèran, P.2
  • 5
    • 0342729091 scopus 로고
    • Challenge problems in elementary analysis
    • Bledsoe W. Challenge problems in elementary analysis. J. Automat. Reason. 6 (1990) 341-359
    • (1990) J. Automat. Reason. , vol.6 , pp. 341-359
    • Bledsoe, W.1
  • 6
    • 33750478723 scopus 로고    scopus 로고
    • A. Buch, T. Hillenbrand, Waldmeister: Development of a high preformance completion based theorem prover, SEKI-Report SR-96-01, University of Kaiserslautern, Germany, 1996
  • 7
    • 33750488789 scopus 로고    scopus 로고
    • B. Buchberger, An algorithm for finding the basis elements in the residue class ring modulo a zero dimensional polynomial ideal, PhD thesis, Mathematical Institute, University of Innsbruck, Austria, 1965, in German
  • 8
    • 0002803133 scopus 로고
    • Gröbner-bases: An algorithmic method in polynomial ideal theory
    • Bose N.K. (Ed), Reidel Publishing Company, Dordrecht
    • Buchberger B. Gröbner-bases: An algorithmic method in polynomial ideal theory. In: Bose N.K. (Ed). Multidimensional Systems Theory (1985), Reidel Publishing Company, Dordrecht 184-232
    • (1985) Multidimensional Systems Theory , pp. 184-232
    • Buchberger, B.1
  • 9
    • 0005398778 scopus 로고    scopus 로고
    • Symbolic computation: Computer algebra and logic
    • Frontiers of Combining Systems. Baader F., and Schulz K.U. (Eds), Kluwer Academic Publishers, Dordrecht
    • Buchberger B. Symbolic computation: Computer algebra and logic. In: Baader F., and Schulz K.U. (Eds). Frontiers of Combining Systems. Applied Logic Series vol. 3 (1996), Kluwer Academic Publishers, Dordrecht 193-219
    • (1996) Applied Logic Series , vol.3 , pp. 193-219
    • Buchberger, B.1
  • 10
    • 33750454149 scopus 로고    scopus 로고
    • B. Buchberger, Introduction to Gröbner bases, in: [21], pp. 3-31
  • 11
    • 19144373037 scopus 로고    scopus 로고
    • Theory exploration versus theorem proving
    • Proc. of Calculemus'99. Armando A., and Jebelean T. (Eds), Elsevier, Amsterdam
    • Buchberger B. Theory exploration versus theorem proving. In: Armando A., and Jebelean T. (Eds). Proc. of Calculemus'99. ENTCS vol. 23 (1999), Elsevier, Amsterdam
    • (1999) ENTCS , vol.23
    • Buchberger, B.1
  • 13
    • 33750475262 scopus 로고    scopus 로고
    • B. Buchberger, Algorithm invention and verification by Lazy Thinking, in: [65], pp. 2-26
  • 14
    • 33750476360 scopus 로고    scopus 로고
    • B. Buchberger, Algorithm-supported mathematical theory exploration: A personal view and strategy, in: [16], pp. 236-250
  • 16
    • 33750432537 scopus 로고    scopus 로고
    • Buchberger B., and Campbell J.A. (Eds), Springer, Berlin
    • In: Buchberger B., and Campbell J.A. (Eds). Proc. of the 7th Int. Conf. on Artificial Intelligence and Symbolic Computation, AISC'04, Hagenberg, Austria. Lecture Notes in Artif. Intell. vol. 3249 (2004), Springer, Berlin
    • (2004) Lecture Notes in Artif. Intell. , vol.3249
  • 17
    • 18944377207 scopus 로고    scopus 로고
    • Algorithm synthesis by Lazy Thinking: Examples and implementation in Theorema
    • Proc. of the Mathematical Knowledge Management Workshop, Edinburgh. Kamareddine F. (Ed), Elsevier, Amsterdam
    • Buchberger B., and Crǎciun A. Algorithm synthesis by Lazy Thinking: Examples and implementation in Theorema. In: Kamareddine F. (Ed). Proc. of the Mathematical Knowledge Management Workshop, Edinburgh. ENTCS vol. 93 (2003), Elsevier, Amsterdam 24-59
    • (2003) ENTCS , vol.93 , pp. 24-59
    • Buchberger, B.1    Crǎciun, A.2
  • 18
    • 33750447340 scopus 로고    scopus 로고
    • B. Buchberger, A. Crǎciun, Algorithm synthesis by Lazy Thinking: Using problem schemes, in: [66], pp. 90-106
  • 19
    • 33750452006 scopus 로고    scopus 로고
    • B. Buchberger, C. Dupré, T. Jebelean, F. Kriftner, K. Nakagawa, D. Vǎsaru, W. Windsteiger, The Theorema project: A progress report, in: [44], pp. 98-113
  • 21
    • 0042243811 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, UK Proc. of the Int. Conf. "33 Years of Gröbner Bases", RISC, Austria, London Mathematical Society Lecture Note Series, vol. 251, 1998
    • Buchberger B., and Winkler F. Gröbner Bases and Applications (1998), Cambridge University Press, Cambridge, UK Proc. of the Int. Conf. "33 Years of Gröbner Bases", RISC, Austria, London Mathematical Society Lecture Note Series, vol. 251, 1998
    • (1998) Gröbner Bases and Applications
    • Buchberger, B.1    Winkler, F.2
  • 22
    • 33749479175 scopus 로고    scopus 로고
    • OpenMath and MathML: Semantic mark up for mathematics
    • special issue on Markup Languages
    • Caprotti O., and Carlisle D. OpenMath and MathML: Semantic mark up for mathematics. ACM Crossroads 6 2 (1999) special issue on Markup Languages
    • (1999) ACM Crossroads , vol.6 , Issue.2
    • Caprotti, O.1    Carlisle, D.2
  • 26
    • 85029837057 scopus 로고
    • Quantifier elimination for real closed fields by cylindrical algebraic decomposition
    • Second GI Conf. on Authomata Theory and Formal Languages, Springer, Berlin
    • Collins G.E. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Second GI Conf. on Authomata Theory and Formal Languages. Lecture Notes in Comput. Sci. vol. 33 (1975), Springer, Berlin 134-183
    • (1975) Lecture Notes in Comput. Sci. , vol.33 , pp. 134-183
    • Collins, G.E.1
  • 28
    • 33750471999 scopus 로고    scopus 로고
    • A. Crǎciun, B. Buchberger, Preprocessed Lazy Thinking: Synthesis of sorting algorithms, Technical Report 04-17, RISC, Linz, Austria, 2004
  • 29
    • 33750483649 scopus 로고    scopus 로고
    • J. W. de Bakker, D. Scott, A theory of programs, in: IBM Seminar, Vienna, Austria, 1969
  • 30
    • 33744933368 scopus 로고    scopus 로고
    • Available to download from
    • de Nivelle H. Bliksem resolution prover. Available to download from (1999). http://www.mpi-sb.mpg.de/~nivelle/software/bliksem/
    • (1999) Bliksem resolution prover
    • de Nivelle, H.1
  • 31
    • 33750486554 scopus 로고    scopus 로고
    • J. Denzinger, S. Schulz, Analysis and representation of equational proofs generated by a distributed completion based proof system, SEKI-Report SR-94-05, University of Kaiserslautern, Germany, 1994
  • 33
    • 33750443311 scopus 로고    scopus 로고
    • B. Elspas, M.W. Green, K.N. Lewitt, R.J. Waldinger, Research in interactive program-proving techniques, Technical Report, Stanford Research Institute, Menlo Park, CA, USA, May 1972
  • 34
    • 0347112373 scopus 로고    scopus 로고
    • An abstract formalization of correct schemas for program synthesis
    • Flener P., Lau K.-K., Ornaghi M., and Richardson J.D.C. An abstract formalization of correct schemas for program synthesis. J. Symbolic Comput. 30 1 (2000) 93-127
    • (2000) J. Symbolic Comput. , vol.30 , Issue.1 , pp. 93-127
    • Flener, P.1    Lau, K.-K.2    Ornaghi, M.3    Richardson, J.D.C.4
  • 35
    • 33750433259 scopus 로고    scopus 로고
    • Ganzinger H. (Ed), Springer, Berlin
    • In: Ganzinger H. (Ed). Proc. of the 16th Int. Conf. on Automated Deduction, CADE'99, Trento, Italy. Lecture Notes in Artif. Intell. vol. 1632 (1999), Springer, Berlin
    • (1999) Lecture Notes in Artif. Intell. , vol.1632
  • 36
    • 0038840100 scopus 로고
    • Decision procedures for indefinite hypergeometric summation
    • Gosper R.W. Decision procedures for indefinite hypergeometric summation. Proc. Nat. Acad. Sci. USA 75 5-6 (1978) 40-42
    • (1978) Proc. Nat. Acad. Sci. USA , vol.75 , Issue.5-6 , pp. 40-42
    • Gosper, R.W.1
  • 37
    • 33750460291 scopus 로고    scopus 로고
    • J. Harrison, Metatheory and reflection in theorem proving: A survey and critique, Technical Report CRC-053, SRI Cambridge, UK, 1995
  • 38
    • 33750493336 scopus 로고    scopus 로고
    • K. Hodgson, J. Slaney, Semantic guidance for saturation-based theorem proving, TR-ARP 04-2000, Automated Reasoning Project, Australian National University, Canberra, Australia, 2000
  • 39
    • 0030100852 scopus 로고    scopus 로고
    • Productive use of failure in inductive proof
    • Ireland A., and Bundy A. Productive use of failure in inductive proof. J. Automat. Reason. 16 1-2 (1996) 79-111
    • (1996) J. Automat. Reason. , vol.16 , Issue.1-2 , pp. 79-111
    • Ireland, A.1    Bundy, A.2
  • 40
    • 33750473073 scopus 로고    scopus 로고
    • T. Jebelean, Natural proofs in elementary analysis by S-decomposition, Technical Report 01-33, RISC, Linz, Austria, 2001
  • 41
    • 33750489790 scopus 로고    scopus 로고
    • T. Jebelean, L. Kovács, N. Popov, Experimental program verification in Theorema, in: Proc. of the 1st Int. Symposium on Leveraging Applications of Formal Methods, ISOLA'04, 2004
  • 43
    • 84959166733 scopus 로고
    • Using Gröbner bases to reason about geometry problems
    • Kapur D. Using Gröbner bases to reason about geometry problems. J. Symbolic Computation 2 (1986) 399-408
    • (1986) J. Symbolic Computation , vol.2 , pp. 399-408
    • Kapur, D.1
  • 44
    • 33750490130 scopus 로고    scopus 로고
    • M. Kerber, M. Kohlhase (Eds.), Proc. of Calculemus'2000, St. Andrews, UK, 2000
  • 45
    • 33750444648 scopus 로고    scopus 로고
    • M. Kirchner, Program verification with the mathematical software system Theorem, Technical Report 99-16, RISC, Linz, Austria, 1999
  • 46
    • 0346843261 scopus 로고    scopus 로고
    • OMDoc: An infrastructure for OpenMath content dictionary information
    • Kohlhase M. OMDoc: An infrastructure for OpenMath content dictionary information. ACM SIGSAM Bull. 34 2 (2000) 43-48
    • (2000) ACM SIGSAM Bull. , vol.34 , Issue.2 , pp. 43-48
    • Kohlhase, M.1
  • 47
    • 33750446714 scopus 로고    scopus 로고
    • B. Konev, T. Jebelean, Using meta-variables for natural deduction in Theorema, in: [44], pp. 160-175
  • 48
    • 33750477346 scopus 로고    scopus 로고
    • L. Kovács, T. Jebelean, Automated generation of loop invariants by recurrence solving in Theorema, in: [66]
  • 49
    • 0030100979 scopus 로고    scopus 로고
    • Middle-out reasoning for synthesis and induction
    • Kraan I., Basin D., and Bundy A. Middle-out reasoning for synthesis and induction. J. Automat. Reason. 16 1-2 (1996) 113-145
    • (1996) J. Automat. Reason. , vol.16 , Issue.1-2 , pp. 113-145
    • Kraan, I.1    Basin, D.2    Bundy, A.3
  • 50
    • 0008717743 scopus 로고
    • D. Reidel Publishing Company, Dordrecht
    • Krall A.M. Applied Analysis (1986), D. Reidel Publishing Company, Dordrecht
    • (1986) Applied Analysis
    • Krall, A.M.1
  • 51
    • 84947804294 scopus 로고    scopus 로고
    • Equational prover of Theorema
    • Proc. of the 14th Int. Conf. on Rewriting Techniques and Applications, RTA'03, Valencia, Spain. Nieuwenhuis R. (Ed), Springer, Berlin
    • Kutsia T. Equational prover of Theorema. In: Nieuwenhuis R. (Ed). Proc. of the 14th Int. Conf. on Rewriting Techniques and Applications, RTA'03, Valencia, Spain. Lecture Notes in Comput. Sci. vol. 2706 (2003), Springer, Berlin 367-379
    • (2003) Lecture Notes in Comput. Sci. , vol.2706 , pp. 367-379
    • Kutsia, T.1
  • 52
    • 33750474909 scopus 로고    scopus 로고
    • T. Kutsia, Solving equations involving sequence variables and sequence functions, in: [16], pp. 157-170
  • 53
    • 33750484339 scopus 로고    scopus 로고
    • Predicate logic with sequence variables and sequence function symbols
    • Proc. of the 3rd Int. Conf. on Mathematical Knowledge Management. Asperti A., Bancerek G., and Trybulec A. (Eds), Springer, Berlin
    • Kutsia T., and Buchberger B. Predicate logic with sequence variables and sequence function symbols. In: Asperti A., Bancerek G., and Trybulec A. (Eds). Proc. of the 3rd Int. Conf. on Mathematical Knowledge Management. Lecture Notes in Comput. Sci. vol. 3119 (2004), Springer, Berlin 205-219
    • (2004) Lecture Notes in Comput. Sci. , vol.3119 , pp. 205-219
    • Kutsia, T.1    Buchberger, B.2
  • 54
    • 33750446006 scopus 로고    scopus 로고
    • T. Kutsia, K. Nakagawa, An interface between Theorema and external automated deduction systems, Technical Report 00-29, RISC, Linz, 2000
  • 55
    • 84915834809 scopus 로고
    • On the application of Buchberger's Algorithm to automated geometry theorem proving
    • Kutzler B., and Stifter S. On the application of Buchberger's Algorithm to automated geometry theorem proving. J. Symbolic Comput. 2 (1986) 389-397
    • (1986) J. Symbolic Comput. , vol.2 , pp. 389-397
    • Kutzler, B.1    Stifter, S.2
  • 58
    • 33750438139 scopus 로고    scopus 로고
    • W. McCune, Otter 3.0 reference manual and guide, ANL-TR 94/6, Argonne National Laboratory, Argonne, USA, 1994
  • 59
    • 33750450577 scopus 로고    scopus 로고
    • Available from
    • McCune W. EQP. Available from (1999). http://www.mcs.anl.gov/AR/eqp/
    • (1999) EQP
    • McCune, W.1
  • 60
    • 33750440236 scopus 로고    scopus 로고
    • W. McCune, Mace 2.0 user manual and guide, Technical memorandum ANL/MCS-TM 249, Argonne National Laboratory, Argonne, USA, 2001
  • 61
    • 0033322284 scopus 로고    scopus 로고
    • Knowledge-based proof planning
    • Mellis E., and Siekmann J. Knowledge-based proof planning. Artificial Intelligence 115 1 (1999) 65-105
    • (1999) Artificial Intelligence , vol.115 , Issue.1 , pp. 65-105
    • Mellis, E.1    Siekmann, J.2
  • 62
    • 33750478046 scopus 로고    scopus 로고
    • K. Nakagawa, Supporting user-friendliness in the mathematical software system Theorema, PhD thesis, RISC, Johannes Kepler University, Linz, Austria, 2002
  • 64
    • 0000210471 scopus 로고
    • A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities
    • Paule P., and Schorn M. A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities. J. Symbolic Comput. 20 5-6 (1995) 673-698
    • (1995) J. Symbolic Comput. , vol.20 , Issue.5-6 , pp. 673-698
    • Paule, P.1    Schorn, M.2
  • 67
    • 33750442947 scopus 로고    scopus 로고
    • F. Piroi, Tools for using automated provers in mathematical theory exploration, PhD thesis, RISC, Johannes Kepler University, Linz, Austria, August 2004
  • 68
    • 33750463458 scopus 로고    scopus 로고
    • F. Piroi, B. Buchberger, An environment for building mathematical knowledge libraries, in: C. Benzmüller, W. Windsteiger (Eds.), Proc. of the first Workshop on Computer-Supported Mathematical Theory Development, IJCAR'04, Cork, Ireland, 2004, pp. 19-29
  • 69
    • 33750459761 scopus 로고    scopus 로고
    • F. Piroi, B. Buchberger, Label management in mathematical theories, Technical Report 2004-16, RICAM, Linz, Austria, 2004
  • 70
    • 33750470852 scopus 로고    scopus 로고
    • N. Popov, Verification of simple recursive programs: Sufficient conditions, Technical Report 04-06, RISC, Linz, Austria, 2004
  • 71
    • 33750463117 scopus 로고    scopus 로고
    • A. Riazanov, A. Voronkov, Vampire, in: [35], pp. 292-296
  • 72
    • 33750489459 scopus 로고    scopus 로고
    • J. Robu, Systematic exploration of geometric configurations using Theorema based on Mathematica, in: Proc. of 3rd Int. Workshop on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC'01, Timişoara, Romania, 2001, pp. 209-216
  • 73
    • 33750466927 scopus 로고    scopus 로고
    • J. Robu, Automated geometric theorem proving, PhD thesis, RISC, Johannes Kepler University, Linz, Austria, 2002
  • 75
    • 33750479077 scopus 로고    scopus 로고
    • M. Rosenkranz, A polynomial approach to linear boundary value problems, PhD thesis, RISC, Johannes Kepler University, Linz, Austria, September 2003
  • 76
    • 33750474134 scopus 로고    scopus 로고
    • M. Rosenkranz, The algorithmization of physics: Math between science and engineering, in: [16], pp. 1-8, invited talk
  • 77
    • 13244272152 scopus 로고    scopus 로고
    • A new symbolic method for solving linear two-point boundary value problems on the level of operators
    • Rosenkranz M. A new symbolic method for solving linear two-point boundary value problems on the level of operators. J. Symbolic Comput. 39 2 (2005) 171-199
    • (2005) J. Symbolic Comput. , vol.39 , Issue.2 , pp. 171-199
    • Rosenkranz, M.1
  • 78
    • 33750429658 scopus 로고    scopus 로고
    • M. Rosenkranz, B. Buchberger, H.W. Engl, A symbolic algorithm for solving two-point BVPs on the operator, SFB Report 2003-41, Johannes Kepler University, Linz, Austria, 2003
  • 80
    • 0036323940 scopus 로고    scopus 로고
    • E-a brainiac theorem prover
    • Schulz S. E-a brainiac theorem prover. J. AI Comm. 15 2/3 (2002) 111-126
    • (2002) J. AI Comm. , vol.15 , Issue.2-3 , pp. 111-126
    • Schulz, S.1
  • 81
    • 33750449034 scopus 로고    scopus 로고
    • Omega: Computer supported mathematics
    • Proc. of the 27th German Conf. on Artificial Intelligence, KI'04, Ulm, Germany. Biundo S., Frühwirth T., and Palm G. (Eds), Springer, Berlin
    • Siekmann J., and Benzmüller C. Omega: Computer supported mathematics. In: Biundo S., Frühwirth T., and Palm G. (Eds). Proc. of the 27th German Conf. on Artificial Intelligence, KI'04, Ulm, Germany. Lecture Notes in Comput. Sci. vol. 3238 (2004), Springer, Berlin 3-28
    • (2004) Lecture Notes in Comput. Sci. , vol.3238 , pp. 3-28
    • Siekmann, J.1    Benzmüller, C.2
  • 83
    • 18944384585 scopus 로고    scopus 로고
    • Mechanizing the development of software
    • Broy M., and Steinbrueggen R. (Eds), IOS Press, Amsterdam
    • Smith D.R. Mechanizing the development of software. In: Broy M., and Steinbrueggen R. (Eds). Calculational System Design, Proc. of the NATO Advanced Study Institute (1999), IOS Press, Amsterdam 251-292
    • (1999) Calculational System Design, Proc. of the NATO Advanced Study Institute , pp. 251-292
    • Smith, D.R.1
  • 85
    • 0000410641 scopus 로고
    • Differentiably finite power series
    • Stanley R.P. Differentiably finite power series. European J. Combin. 1 2 (1980) 175-188
    • (1980) European J. Combin. , vol.1 , Issue.2 , pp. 175-188
    • Stanley, R.P.1
  • 86
    • 0032186666 scopus 로고    scopus 로고
    • The TPTP problem library: CNF Release v1.2.1
    • Sutcliffe G., and Suttner C. The TPTP problem library: CNF Release v1.2.1. J. Automat. Reason. 21 2 (1998) 177-203
    • (1998) J. Automat. Reason. , vol.21 , Issue.2 , pp. 177-203
    • Sutcliffe, G.1    Suttner, C.2
  • 87
  • 88
    • 0343646385 scopus 로고
    • Computer aider reasoning
    • Proc. of the Conf. Logic of Programs. Parikh R. (Ed), Springer, Berlin
    • Trybulec A., and Blair H.A. Computer aider reasoning. In: Parikh R. (Ed). Proc. of the Conf. Logic of Programs. Lecture Notes in Comput. Sci. vol. 193 (1985), Springer, Berlin 406-412
    • (1985) Lecture Notes in Comput. Sci. , vol.193 , pp. 406-412
    • Trybulec, A.1    Blair, H.A.2
  • 89
    • 0021774950 scopus 로고
    • Higher-order extensions of Prolog: are they needed?
    • Edinburgh University Press, Edinburgh, UK
    • Warren D.H.D. Higher-order extensions of Prolog: are they needed?. Machine Intelligence vol. 10 (1982), Edinburgh University Press, Edinburgh, UK 441-454
    • (1982) Machine Intelligence , vol.10 , pp. 441-454
    • Warren, D.H.D.1
  • 90
    • 33750430005 scopus 로고    scopus 로고
    • C. Weidenbach, B. Afshordel, U. Brahm, C. Cohrs, T. Engel, E. Keen, C. Theobalt, D. Topic, System abstract: Spass version 1.0.0. in: [35], pp. 378-382
  • 92
    • 33750476707 scopus 로고    scopus 로고
    • W. Windsteiger, A set theory prover in Theorema: Implementation and practical applications, PhD thesis, RISC, Johannes Kepler University, Linz, Austria, May 2001
  • 94
    • 0022786053 scopus 로고
    • Basic principles of mechanical theorem proving in elementary geometries
    • Wu W.T. Basic principles of mechanical theorem proving in elementary geometries. J. Automat. Reason. 2 (1986) 221-252
    • (1986) J. Automat. Reason. , vol.2 , pp. 221-252
    • Wu, W.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.