mathematicianWu, Wen-tsun, 1919-
also spelled: Wu Wentsun
or Wu WenjunWu Algorithm
Wu Method (Wu fan-fa)
Wu's Formula
Wu's ClassesRitt-Wu's Decomposition Algorithm and Geometry Theorem Proving
Developed from J. F. Ritt's work on differential algebra, the Characteristic Set Method was discovered independently by the Chinese mathematician Wen-tsun Wu in 1978. Hence the name Wu's Method. Wu rediscovered the characteristic set method in the context of his work on mechanical geometry theorem proving. He transferred the algorithmic aspects of Ritt's method to ordinary polynomial rings with the intent of finding an effective method for automating theorem proving in elementary geometry. Since then the method has proven to have a variety of applications.Biography:born May 12, 1919 in Shanghai
http://www.mmrc.iss.ac.cn/~wtwu/main1.htmlBorn in Shanghai. Graduated from Shanghai Jiaotong University in 1940. Received Docteur es Sciences of France in 1949. Research professor and honorary director, Institute of Systems Science, Chinese Academy of Sciences.
Wu is the originator in the research on mathematics mechanization in China. In the 1950s, he made outstanding achievements in characteristic classes and imbedding classes (Wu’s Formulas, Wu’s classes, etc.). Recently, he has invented Wu’s Method to prove geometry theorems by computers, which will bring about the reformation of mathematical research methods.
He became Member of the Chinese Academy of Sciences in 1957.
02-20-2001
CAS Scientist Won the State Top S&T Award
As one of the two laureates for China’s Supreme Scientific and Technological Award in 2000, Prof. Wu Wenjun, a mathematician of the Chinese Academy of Sciences (CAS), received the country’s top award in science and technology on Feb. 19 in Beijing.
Prof. Wu Wenjun, a member of CAS and the Third World Academy of Sciences, is a research professor at the Academy of Mathematics and System Sciences and honorary director of CAS the Institute of Systems Science. He served as the president of the Chinese Society of Mathematicians from 1984 to 1987, director of the CAS Division of Mathematics & Physics from 1992 to 1994.
Born in Shanghai in 1919, Wu was graduated from Shanghai Jiaotong University in 1940 and in 1946 he was introduced by Mr. S. S. Chern to work in the Institute of Mathematics under Academia Sinica, specializing in topology. In 1947, he went to France for advanced study under the tutelage of C. Ehresmann and Henri Cartan. In 1949, he obtained his national doctorial degree of France. In 1951, he came back home and became a professor at Peking University. He joined the CAS Institute of Mathematics as a research professor in 1950 and CAS Institute of Systems Science in 1980.
As a disciplinary precursor, Wu makes monumental contributions to the field of topology by the introduction of Wu’s imbedding and characteristic classes and the establishment of Wu’s Formulae.
In the late 1970s, he enriched his prolific personal career by opening a new horizon in mathematics mechanization. In the field of mathematics mechanization, Wu suggested a computerized method for proving geometrical theorems, known as Wu’s method in the international community. In line with the conventional approach in traditional Chinese mathematics, a geometric problem is converted into an algebraic problem. Different from the logical approach, Wu’s approach realizes highly effective proving of geometric theorems on a portable calculator, displaying an unmatched superiority in computational effectiveness. His work in this aspect is widely known as a harbinger in automated reasoning and in 1997, he was conferred a Herbrand Prize for Distinguished Contributions to Automated Reasoning.
Because of his meritorious service and creative work, he won a first-grade prize from the 1956 National Awards for Natural Sciences, the first of its kind in the history of the People’s Republic. In 1993, he was conferred with a prize from Chen Jiageng (Tan Kah-kee) Awards for Mathematics & Physics and in the next year, he became a laureate of the prize for outstanding scientists granted by Hong Kong’s Qiushi S&T Foundation. In 1993, he received the Herbrand Award for Distinguished Contributions to Automated Reasoning.
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The prestigious Supreme S&T Award was created only two years ago, awards in 2000 went to Wu Wenjun, a CAS mathematician, and Yuan Longping, an agronomist with Hunan Academy of Agricultural Sciences. This is one of the five national S&T awards conferred by the central government. The other four include State Award for Natural Science, State Award for Technological Inventions, State Award for S&T Progress and International S&T Cooperation Award.
+++++++++++++Mathematical Genealogy:
PhD Advisor: S. S. Chern
http://hcoonce.math.mankato.msus.edu/html/id.phtml?id=25433http://www.mmrc.iss.ac.cn/~wtwu/main6.html
Publications:
http://www.mmrc.iss.ac.cn/~wtwu/main7.html
http://www.mmrc.iss.ac.cn/~wtwu/main8.html
Mechanical Theorem Proving in Geometries: Basic Principles
by Wen-Tsun Wu
Released: January, 1994
Mathematics Mechanization: Mechanical Geometry Theorem-Proving, Mechanical Geometry Problem-Solving, and Polynomial Equations-Solving (Mathematics and Its Applications (Kluwer), 489)
by Wen-Tsun Wu
Kluwer Academic Publishers
Released: January, 2001
Rational Homotopy Type: A Constructive Study Via the Theory of the I*-Measure (Lecture Notes in Mathematics, Vol 1264)
by Wu Wen-Tsun
Springer Verlag
Released: October, 1987
Computer Mathematics: Proceedings of the Special Program at Nankai Institute of Mathematics Tianjin, China January-June 1991 (Nankai Series in Pure,)
by Wen-Tsun Wu , Hu Guo-Ding , Wu Wen-Tsun , Guoding Hu , China) Shu Hsueh Yen Chiu So Nan Kai Ta Hsueh (Tianjin
World Scientific Pub Co
Released: September, 1993
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Computer mathematics : proceedings of the Special Program at Nankai Institute of Mathematics, Tianjin, China, January-June 1991 / edited by Wu Wen-Tsün, Hu Guo-Ding.
Singapore ; [River Edge], N.J. : World Scientific, c1993.
viii, 160 p. : ill. ; 23 cm.
"Jiu zhang suan shu" yu Liu Hui / Wu Wenjun zhu bian.
Di 1 ban.
[Peking] : Beijing shi fan da xue chu ban she : Xin hua shu dian Beijing fa xing suo fa xing, 1982.
345 p., [3] p. of plates : ill. ; 21 cm.
Shi jie zhu ming ke xue jia zhuan ji. Shu xue jia / Wu Wenjun zhu bian ; "Ke xue jia zhuan ji da ci dian" shu xue xue ke bian wei hui.
Di 1 ban.
Beijing : Ke xue chu ban she : Xin hua shu dian Beijing fa xing suo fa xing, 1990-<1992 >
v. <1, 4 > : ill. ; 21
Zhongguo shu xue shi lun wen ji / Wu Wenjun zhu bian.
Di 1 ban.
Jinan : Shandong jiao yu chu ban she : Shandong sheng xin hua shu dian fa xing, <1986-1987>
v. <2-3 > : ill. ; 27 cm.
Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations = [1980 nian "shuang wei" Beijing tao lun hui wen ji] / chief editors, S.S. Chern, Wu Wen-tsün.
Beijing, China : Science Press ; New York : Gordon and Breach, Science Publishers, 1982.
3 v. (ix, 1743) ; 24 cm
Mathematics mechanization : mechanical geometry theorem-proving, mechanical geometry problem-solving, and polynomial equations-solving / by Wu Wen-tsun.
Dordrecht ; Boston : Kluwer Academic Publishers, c2000.
xii, 420 p. : ill. ; 25 cm.
Mechanical theorem proving in geometries : basic principles / Wen-tsün Wu ; translated from the Chinese by Xiaofan Jin and Dongming Wang.
Wien ; New York : Springer-Verlag, c1994.
xiv, 288 p. : ill. ; 25 cm.
Rational homotopy type : a constructive study via the theory of the I*-measure / Wu Wen-tsün.
Berlin ; New York : Springer-Verlag, c1987.
viii, 219 p. : ill. ; 25 cm.
Sur les espaces fibres et les variétés feuilletées, par Wu Wen-tsun et Georges Reeb.
Paris, Hermann, 1952.
158 p. 25 cm.
A theory of imbedding, immersion, and isotopy of polytopes in a Euclidean space / Wu Wen-tsün.
Peking : Science Press, distributed by Guozi Shudian, 1974.
xv, 291 p. ; 24 cm.
Wu Wen-tsun:
A zero structure theorem for polynomial-equations-solving and its applications. EUROCAL 1987: 44
Wu Wen-Tsun
Mechanical theorem proving of differential geometries and some of its applications in mechanics
Journal of Automated Reasoning July 1991
Volume 7 Issue 2
Wen-Tsun Wu
Basic principles of mechanical theorem proving in elementary geometrics
Journal of Automated Reasoning August 1986
Volume 2 Issue 3
Sur les espaces fibr¨¦s et les vari¨¦t¨¦s feuillet¨¦es, Actualit¨¦s Sci. Ind., No. 1183=Publ. Inst. Math. Univ. Strasbourg 11, Hermann & Cie, Paris (1952)
Some applications of mechanics in geometry, (in Chinese), Chinese Youth Press, 1962.
Wu, W. T.
On the Decision Problem and the Mechanization of Theorem-Proving in Elementary Geometry
Sci. Sinica 21, pp. 159-172, 1978. (Also in: Automated Theorem Proving: after 25 years. Contemporary Mathematics, 29, pp. 213-234, 1984.)
Wu, W. T.
Basic Principles of Mechanical Theorem Proving in Elementary Geometries
Journal of Sys. Sci. & Math. Scis. 4, pp. 207-235, 1984. (Also in: Journal of Automated Reasoning 2, pp. 221-252, 1986.)
A theory of imbedding, immersion, and isotopy of polytopes in a euclidean spacd. Science Press, Beijing (1965). Chinese version with an Appendix: The layout problem of printed circuits and integrated circuits, Science Press, Beijing, (1978).
``Nine Chapters in Arithmetic'' and Liu Hui, (in Chinese, ed.), Beijing Normal University Press, Beijing, 1981.
Proceedings of the 1980 Beijing symposium on differential geometry and differential equations(co-editor with S. S. Chern), Science Press, Beijing, 1982.
Basic principles of mechanical theorem proving in geometries (Part on elementary geometries), (in Chinese, ed.), Science Press, Beijing (1984). English translation by D. M. Wang et al, Springer (1994).
On triangles with two equal bisectors, (in Chinese, ed. with X.L. L¨¹), People's Education Press, Beijing (1985).
Sellected works of Wu Wen-ts¨¹n, (in Chinese, ed.), Shandong science and Technology Press, Jinan, 1987.
Rational homotopy type --- A constructive study via the theory of the I*-measure, Lect. Notes in Math., No. 1264, Springer Verlag, Berlin (1987).
Historical studies on ``Mathematical Treatise in Nine-Chapters (Shu-Shu-Jiu-Zhang)'' (in Chinese, ed.), Beijing Normal University Press, Beijing, 1987.
New developments of today mathematics --- a collection of articles on Liu Hui seminar of mathematics (in Chinese, ed.), Anhui Science and Technology Press, Hefei, 1988.
Chinese Mathematics onto the 21st Century, (Ed. with Cheng Min-de), Peking University Press, Beijing, 1991.
Computer Mathematics, (Proc. Special Program at Nankai Inst. of Math. in Tianjin 1991, Ed. with Hu Guoding), World Scientific, Singapore, 1993.
Proc. 1992 International Workshop on Mathematics Mechanization in Beijing, (Ed. with Cheng Min-de), Intern. Acad. Publishers, Beijing, 1992.
Studies on Liu Hui, (in Chinese, ed. with Bai Shangshu, Li Di and Shen Kangshen), Shanxi People's Education Press and Nine-Chapters Press, 1993.
Wu Wents¨¹n on Mathematics Mechanization, (in Chinese), Shangdong Education Press, Shangdong, 1996.
Note sur les produits essentiels sym??triques des espaces topologiques. C. R. Acad. Sci. Paris 224, 1139-1141(1947).
On the product of sphere bundles and the duality theorem modulo two. Ann. of Math. (2) 49, 641-653 (1948).
Sur L'existence d'un champ d'??l??ments de contact ou d'une structure complexe sur une sph??re. C. R. Acad. Sci. Paris 226, 2117-2119(1948).
Sur les classes caract??ristiques d'un espace fibr?? en sph??res. C. R. Acad. Sci. Paris 227, 582-584(1948).
Sur le second obstacle d'un champ d'??l??ments de contact dans une structure fibr??e sph??rique. C. R. Acad. Sci. Paris 227, 815-817(1948).
Sur la structure presque complexe d'une vari??t?? diff??rentiable r??elle de dimension 4. C. R. Acad. Sci Paris 227, 1076-1078 (1948).
Sur la structure presque complexe d'une vari??t?? diff??rentiable r??elle. C. R. Acad. Sci. Paris 228, 972-973(1949).
Classes caract??ristiques et i-carr??s d'une vari??t??. C. R. Acad. Sci. Paris 230, 508-511(1950).
Les i-carr??s dans une vari??t?? grassmanni??nne. C. R. Acad. Sci. Paris 230, 918-920(1950).
Sur les puissances de Steenrod. Colloque de Topologie de Strasbourg. 1951, no. IX, 9pp. La Biblioth??que Nationale et Universitaire de Strasbourg, 1952.
Topological invariants of new type of finite polyhedrons. Acta Math. Sinica 3, 261-290(1953).(in Chinese, English summary).
On Pontrjagin classes I. Acta Math. Sinica 3, 291-315(1953) (in Chinese, English summary) 17-521. Sci. Sinica 3, 353-367(1954). Amer. Math. Soc. Translations, Ser. 2, 92(1970), 49-62.
On squares in Grassmannian manifolds. Acta Sci. Sinica 2, 91-115(1953). Amer. Math. Soc. Translations, Ser. 2, 38(1964), 235-258.
On squares in Grassmann manifolds. J. Chinese Math. Soc. 2(1953) 205-230. (in Chinese, English summary) 17-396.
Proof of a certain conjecture of H. Hopf, Acta Math. Sinica 4(1954), 491-500.
``On Pontrjagin classes II'', Acta Math. Sinica 4(1954). 171-199(in Chinese, English summary). Amer. Math. Soc. Translations, Ser. 2, 92(1970), 63-92.
On Pontrjagin classes. III. Acta Math. Sinica 4(1954), 323-346. (in Chinese, English summary) 18-225. American Mathematical Society Translations, Ser. 2, Vol. II, pp. 155-172, American Mathematical Society, Providence R I. 1959.
On Pontrjagin classes. IV. Acta Math. Sinica 5(1955), 37-63. (in Chinese, English summary). Amer. Math. Soc. Translations, Ser. 2, 92, 93-121.
On Pontrjagin classes. V. Acta Math. Sinica 5(1955), 401-410. (in Chinese, English summary). Amer. Math. Soc. Translations, Ser. 2, 38(1964), 259-268.
On the realization of complexe in euclidean spaces I. Acta Math. Sinica 5(1955), 505-552. (in Chinese, English summary). Amer. Math. Soc. Translations, Ser. 2, 78(1968), 137-184.
On the imbedding of polyhedrons in Euclidean spaces. Bull. Acad. Polon. Sci. C1. III. 4(1956)573-577.
On the realization of complexes in euclidean spaces. II. Acta Math. Sinica 7(1957), 79-101 (in Chinese, English summary). Amer. Math. Soc. Translations, Ser. 2, 78(1968), 185-208.
On the $\Phi_p$-classes of a topological space. Sci. Record (N. S.), 1(1957), 377-380.
On the relations between smith operations and Steenrod powers. (in Chinese, English summary) Acta Math. Sinica 7(1957), 235-241. Fund. Math. 44(1957), 262-269. Amer. Math. Soc. Translations, Ser. 2, 38(1964), 269-276.
On the realization of complexes in euclidean spaces. III. Acta Math. Sinica 8(1958), 79-94. (in Chinese, English summary). Sci. Sinica 8(1959), 133-150.
On the reduced products and the reduced cyclic powers of a space. Jber Deutsch. Math. Verein. 61(1958), Abt. 1, 65-75.
On the dimension of a normal space with countable base. Sci. Record (N. S.) 2(1958), 65-69.
On the isotopy of Cr-manifolds of dimension (n) in Euclidean (2n+1)-space. Sci. Record (N. S.) 2(1958), 271-275.
On the realization of complexes in Euclidean spaces. Sci. Sinica 7(1958), 365-387.
On the isotopy of a complex in a Euclidean space. I. (in Chinese .English summary). Acta Math. Sinica 9(1959), 475-493. Sci. Sinica 9(1960), 21-46.
Topologie combinatoire et invariants combinatoires. Colloq. Math. 7(1959), 1-8.
On certain invariants of cell-bundles. Sci. Record (N. S.) 3(1959), 137-142.
A remark on the fundamental theorem in the theory of games. Sci. Record (N.S.) 3(1959), 229-233.
On the isotopy of a finite complex in a Euclidean space. I, II. Sci. Record (N.S.) 3(1959), 342-351.
On non-cooperative games with restricted domains of activities. Acta Math. Sinica 11(1961), 47-62 (in Chinese); translated as Chinese Math. 2(1962), 54-76. Russian version in Beskonec. Anagonist. Igry, 1963, 459-488.
On a theorem of Leray. Acta Math. Sinica 11(1961), 348-356(in Chinese); Chinese Math. 2(1962), 398-410. Sci. Sinica 10(1961), 793-805.
Essential equilibrium points of $n$-person non-cooperative games(with Jiang Jia-he), Sci.Sinica, 12 (1962) 1307-1322.
The characteristic classes of certain real quadrics(with Li Pei-hsin), Acta Math. Sinica, 12 (1962) 203-215 (in Chinese). Translated in Chinese Math., 3 (1963) 218-231.
On the imbedding of orientable manifolds in a Euclidean space. Sci. Sinica
12(1963), 25-33.Rotations in Euclidean space. (in Chinese) Shuxue Jinzhan 6(1963), 96-97.
A theorem on immersion. Sci. Sinica 13(1964), 160.
On the immersion of $C^{\infty}$-3-manifolds in a Euclidean space. Sci. Sinica 13(1964), 335-336.
On the notion of imbedding classes. Sci. Sinica 13(1964), 681-682.
On the imbedding of manifolds in a Euclidean space I. Sci. Sinica 13(1964), 682-683.
On complex analytic cycles and their real traces. Sci. Sinica 14(1965), 831-839.
On critical sections of convex bodies. Sci. Sinica 14(1965), 1721-1728.
Algebraic varieties with dual rational dissections. (in Chinese) Shuxue Jinzhan 8(1965), 402-409.
The Chern characteristic classes on an algebraic variety. (in Chinese) Shuxue Jinzhan 8(1965), 395-401.
A mathematical problem in the design of integrated circuits, Math. in Practice and Theory, (1973) 20-40. (in Chinese).
Planar imbedding of linear graphs, Kexue Tongbao, (1973) 226-228. (in Chinese).
Homology classes that contain singularities of type Sk (in Chinese), Acta Math. Sinica, 17(1974), 28-37.
On singularities of Sk-type, Acta Math. Sinica (1975) (in Chinese).
On universal invariant forms, Acta Math. Sinica, 18(1975), 263-273 (in Chinese).
A new functor in algebraic topology, Kexue Tongbao, 20(1975), 311-312 (in Chinese).
Theory of I*-functor in algebraic topology - Real topology of homogeneous spaces, Acta Math. Sinica 18(1975), 162-172 (in Chinese).
Theory of I*-functor in algebraic topology - Real topology of fibre squares, Sci. Sci. Sinica, 18(1975), 464-482.
Theory of I*-functor in algebraic topology - Effective calculation and axiomatization of I*-functor on complexes, Sci. Sinica, 19(1976), 647-664.
The layout problem of printed circuits and integrated circuits, Appendix to A theory of imbedding, immersion and isotopy of polytopes in a Euclidean space, (1977) 213-261 (in Chinese).
The out-in complementary principle, (in Chinese), in Achievements in Science and Technology of Ancient China (1977), 80-100.
On the decision problem and the mechanization of theorem-proving in elementary geometry, Scientia Sinica 21 (1978) 159-172. Re-published in Automated Theorem Proving: After 25 Years (Eds. W.W. Bledsoe & D. W. Loveland), (1984) 213-234. Chinese version in Sci. Sinica, 20(1977), 507-516.
Theory of I*-functor in algebraic topology- I*-functor of a fiber space(with Wang Qi-ming), Sci.Sinica, 21 (1978) 1-18.
Mechanical theorem proving in elementary differential geometry ( in Chinese), Kexue Tongbao, 23(1978), 523-524.
Layout problems in printed circuits and intergrated circuits (in Chinese), Appendix in Chinese version of [3], 213-261. 1979
On the mechanization of theorem-proving in elementary differential geometry, Scientia Sinica, Math. Supplement (I), 94-102 (1979).(in Chinese).
On the mechanization of theorem proving in elementary differential geometry (in Chinese),Sci. Sinica, Special Issue(I) on Math., 94-102. 1980.
On calculability of I*-measure with respect to complex-union and other related constructions, Kexue Tongbao, 25(1980) 196-198 (in Chinese); Kexue Tongbao 25(1980), 185-188.
de Rham-Sulliven measure of spaces and its calculability, in Proc. Chern Symposium, (1980), 229-245.
A constructive theory of algebraic topology - Part I. Notions of measure and calculability, J. Systems Science and Math. Science. 1(1981), 53-68.
Investigations on the Original Proofs about "Sea-Island Arithmetic", (in Chinese), in ``Nine Chapters in Arithmetic" and Liu Hui, Ed. Wu Wen-ts??n, Beijing Normal University Press, Beijing, (1981) 58-75.
Mechanical theorem proving in elementary geometry and differential geometry, in Proc.1980 Beijing DD-Symposium, Beijing, v.2, 1073-1092 (1982).
On the double-difference theory in measurement-studies of ancient China with criticisms about methodology in study of history of mathematics, (in Chinese), in Monographs on History of Science and Technology, No. 8, Shanghai Science Press, Shanghai, (1982) 10-30.
Toward mechanization of geometry --- Some comments on Hilbert's "Grundlagen der Geometrie", Acta Math.Scientia, 2 (1982) 125-138. Chinese version 126-136.
Some remarks on mechanical theorem-proving in elementary geometry, Acta Math. Scientia 3 (1983) 357-360.
The out-in complementary principle, in Ancient China's Technology and Science, Foreign Languages Press, Beijing(1983), 66-89.
de Rham theorem from constructive point of view, in Proc. 1981 Shanghai Symposium on Differential Geometry and Differential Equations, Science Press, Beijing, (1984) 497-528.
Chern classes on algebraic varieties with arbitrary singularities, in Several Complex Variables, Birkhausser Boston, Mass., (1984) 247-249.
Some recent advance in mechanical theorem-proving of geometries, in Automated Theorem Proving:After 25 Years (Eds.W.W.Bledsoe & D.W. Loveland), Contemp. Math., AMS, 29(1984) 235-242.
Basic principles of mechanical theorem-proving in elementary geometries, J.Sys.Sci. & Math.Scis.,4 (1984) 207-235. Re-published in J. Automated Reasoning, 2 (1986) 221-252.
A constructive theory of differential algebraic geometry based on works of J. F. Ritt with particular applications to mechanical theorem-proving in differential geometries. Differential Geometry and Differential Equations, Lect. Notes in Math. No. 1255, Springer (1984) 173-189.
On zeros of algebraic equations --- an application of Ritt principle, Kexue Tongbao 31 (1986) 1-5. Chinese version, 30(1985), 881-883.
On the planar imbedding of linear graphs I, J. Sys. Sci. & Math. Scis., 5(1985), 290-302.
The renaissance of constructive mathematics, (in Chinese), Adv. in Math.,14(1985) 334-339.
On the planar imbedding of linear graphs II, J. Sys. Sci. & Math. Scis., 6(1986), 23-35.
A mechanization method of geometry and its applications I. Distances, areas, and volumes in euclidean and non-euclidean geometries, Kuxue Tongbao 32 (1986) 436-440.
A mechanization method of geometry I. Elementary geometry, Chinese Quart. J. Math., 1 (1986) 1-14, Errata and Addenda, ibid, 2 (1987) 20.
A mechanization method of geometry and its applications I. Distances, areas, and volumes, J.Sys.Sci. & Math.Scis.,6 (1986) 204-216
A general description of the SOLVER package system, (in Chinese), Math. in Practice and Theory, (1986 No.2), 32-39.
Examples of applications of the SOLVER package system, (in Chinese), Math. in Practice and Theory, (1986 No.3), 1-11.
Some remarks on jet-transformations, Bull. Soc. Math. Belgique,38 (1986) 409-414.
Recenct studies of the history of Chinese mathematics, in Proc. ICM 1986, Amer. Math. Soc.,(1987) 1657-1667.
On the Constructive and Mechanical characterictics of Chinese traditional
mathematics in view of "Mathematical Treatise in Nine Chapters" of Qin Jiu-shao, (in Chinese), in Qin Jiu-shao and "Mathematical Treatise in Nine Chapters", Ed. Wu Wen-ts??n, Beijing Normal University Press, Beijing, (1987) 73-88.On Chern numbers of algebraic varieties with arbitrary sigularities, Acta Math. Sinica, New Ser., 3, (1987) 227-238.
A mechanization method of geometry and its applications II. Curve pairs of Bertrand type, Kuxue Tongbao 32 (1987) 585-588. Chinese version 1281-1284.
On reducibility problem in mechanical theorem proving of elementary geometries, Chinese Quarterly J. of Math., 2 (1987) 1-19, also in MM-Res.Preprints, No.2, (1987) 18-36.
A zero structure theorem for polynomial-equations-solving and its applications, MM-Res.Preprints, No.1 (1987) 2-12.
Mechanical derivation of Newton's Gravitational Laws from Kepler's Laws, MM-Res. Preprints, No.1, (1987) 53-61.
On the special features of constructiveness and mechanical characterof chinese traditional mathematics as viewed from ``Mathematics in Nine Chapters'', (in Chinese), In [10](1987),78-88.
A mechanization method of geometry and its applications III. Mechanical proving of polynomial inequalities and equations-solving, MM-Res. Preprints, No.2, (1987) 1-17, also in Sys.Sci.& Math.Scis., 1 (1988) 1-17.
A mechanization method of geometry and its applications IV. Some theorems in planar kinematics, Sys.Sci. & Math.Scis., 2 (1989) 97-109.
On the foundation of algebraic differential geometry, MM-Res. Preprints, No.3 (1989) 1-26, also in Sys.Sci.& Math.Scis., 2 (1989) 289-312.
Some remarks on characteristic-set formation, MM-Res.Preprints, No.3 (1989) 27-29.
A review and prospect of mechanical theorem proving, (in Chinese), in New Developments of Today Mathematics -- A Collection of Articles on Liu-hui Seminar of Mathematics, (Ed. Wu Wen-ts??n), Anhui Science and Technology Press, Hefei, (1989) 181-188.
On the generic zero and Chow basis of an irreducible ascending set, MM-Res. Preprints, No.4 (1989) 1-21.
A mechanization method of geometries and its applications V(with Wu Tianjiao). Solving transcendental equations by algebraic methods, MM-Res.Preprints, No.3 (1989) 30-32.
A mechanization method of geometry and its applications VI. Solving inverse kinematic equations of PUMA-type robots, MM-Res. Preprints, N0.4 (1989) 49-54.
On a projection theorem of quasi-varieties in elimination theory, MM-Res. Preprints, No.4 (1989) 40-48. Also in Chinese Annals of Math., 11B (1990) 220-226.
On the chemical equilibrium problem and equations-solving, MM-Res.Preprints, No.4 (1989) 1-21. Also in Acta Math.Scientia, 10 (1990) 361-374.
Decompostion theorems for the zero-set of an ordinary or differential polynomial set and their applications, IV int. conf. on Computer Algebra in Physical Research 1990, (Eds. D.V. Shirkov et al), (1991) 198-205.
Automation of Theorem-Proving, MM-Res. Preprints, N0.5 (1990) 1-4. Also in Workshop on Advanced Computers for Artificial Intelligence, Beijing (1990) 11-15.
On the construction of Groebner basis of a polynomial ideal based on Riquier-Janet theory, MM-Res. Preprints, No.5 (1990) 5-22. Also in Sys.Sci. & Math.Scis., 4 (1991) 193-207.
A survey of developements of mathematics mechanization in China, in Chinese Mathematics into the 21st Century, (Ed. Wu Wen-ts??n & Cheng Min-de), Peking University Press, Beijing (1991) 15-40.
Mechanical theorem proving of differential geometries and some of its applications in mechanics, MM-Res. Preprints, No.6 (1991) 1-22. Also in J. Automated Reasoning, 7 (1991) 171-191.
On a finiteness theorem about optimization problems, MM-Res. Preprints, No. 8(1992) 1-18.
A report on mechnical geometry theorem proving, Progress in Natural Science, 2 (1992) 1-17.
On the char-set method and the linear equations method of non-linear polynomial equations-solving, in Proc. Intern. Workshop on Math. Mechanization(1992),101-109.
Equations-solving and theorem-proving: Zero-set formulation and ideal formulation, Proc. Asian Math. Conf. 1992, 1-10.
A mechanization method of equations-solving and theorem-proving, Adv. in Comp. Res., 6(1992), 103-138.
On problems involving inequalities, MM-Res. Preprints, No. 7(1992), 1-13.
On a linear equation method of non-linear polynomial equations-solving, MM-Res. Preprints, No.6 (1991) 23-36. Errata, loc.cit. No.7 (1992). Sys. Sci. & Math. Sci., 6(1993) 1-12.
On the development of polynomial equations solving in China, Proc. 1991 Nankai seminar on Mathematics Mechanization, Singapore (1993)
On a hybrid method of polynomial equations solving, MM-Res. Preprints, No. 9 (1993) 1-10.
On Surface-fitting problem in CAGD, MM-Res. Preprints, No. 10
(1993) 1-10.On a finiteness theorem about problems involving inequalities, Sys. Sci. & Math. Scis., 7 (1994)
On the algebraic surface-fitting problem in CAGD, (in Chinese, with Wang Ding-kang), Mathematics in practice and theory, No. 3(1994), 26-31.
Some remarks on factorization and GCD of multivariate polynomials, MM-Res. Preprints, No. 11(1994), 1-14.
Char-set method of polynomial equation-solving and its applications, Proc. Asian Symposium on Computer Mathematics(1995), 11-21.
Geometry problem-solving and its contemporary significance, in Proc. First Asian Tech. Conf., Assoc. of Math. Educators, Singapore, (1995), 67-62.
Central configurations in planet motions and votex mothions, MM-Res. Preprints, No. 13(1995) 1-14
On constructive algebraic geometry, MM-Res. Preprints, No. 16 (1998) 1-3.
The Research Work of Wu Wen-tsun
http://www.cas.ac.cn/html/Books/O61bg/b1/2002/3.1%20.htm
Wu Algorithm
Bradford, Russell. An Implementation of the Wu Algorithm
http://www.zib.de/Optimization/Software/Reduce/more/moredocs/wu.pdf
http://www.uni-koeln.de/REDUCE/wu/wu.html
