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Bibliography

1
S.S. Abhyankar.
Algebraic Geometry for Scientists and Engineers, volume 35 of Mathematical Surveys and Monographs.
American Mathematical Society, Providence, Rhode Island, 1990.

2
E.L. Allgower.
Bifurcation arising in the calculation of critical points via homotopy methods.
In T. Kupper, H.D. Mittleman, and N. Weber, editors, Numerical Methods for Bifurcation Problems, pages 15-28. Birkhäuser, Boston, 1984.

3
E.L. Allgower and K. Georg.
Numerical Continuation Methods, an Introduction, volume 13 of Springer Ser. in Comput. Math.
Springer-Verlag, Berlin Heidelberg New York, 1990.

4
E.L. Allgower and K. Georg.
Continuation and path following.
Acta Numerica, pages 1-64, 1993.

5
E.L. Allgower and K. Georg.
Numerical Path Following.
In P.G. Ciarlet and J.L. Lions, editors, Techniques of Scientific Computing (Part 2), volume 5 of Handbook of Numerical Analysis, pages 3-203. North-Holland, 1997.

6
D.C.S. Allison, A. Chakraborty, and L.T. Watson.
Granularity issues for solving polynomial systems via globally convergent algorithms on a hypercube.
J. of Supercomputing, 3:5-20, 1989.

7
D.N. Bernshtein.
The number of roots of a system of equations.
Functional Anal. Appl., 9(3):183-185, 1975.
Translated from Funktsional. Anal. i Prilozhen., 9(3):1-4,1975.

8
G. Björck.
Functions of modulus one on Zn whose Fourier transforms have constant modulus, and "cyclic n-roots".
In J.S. Byrnes and J.F. Byrnes, editors, Recent Advances in Fourier Analysis and its Applications, volume 315 of NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., pages 131-140. Kluwer, 1989.

9
G. Björck and R. Fröberg.
A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots.
J. Symbolic Computation, 12(3):329-336, 1991.

10
L. Blum, F. Cucker, M. Shub, and S. Smale.
Complexity and Real Computation.
Springer-Verlag, New York, 1997.

11
P. Brunovský and P. Meravý.
Solving systems of polynomial equations by bounded and real homotopy.
Numer. Math., 43(3):397-418, 1984.

12
C.I. Byrnes.
Pole assignment by output feedback.
In H. Nijmacher and J.M. Schumacher, editors, Three Decades of Mathematical Systems Theory, volume 135 of Lecture Notes in Control and Inform. Sci., pages 13-78. Springer-Verlag, Berlin, 1989.

13
J. Canny and J.M. Rojas.
An optimal condition for determining the exact number of roots of a polynomial system.
In Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation, pages 96-101. ACM, 1991.

14
S.N. Chow, J. Mallet-Paret, and J.A. Yorke.
Homotopy method for locating all zeros of a system of polynomials.
In H.O. Peitgen and H.O. Walther, editors, Functional differential equations and approximation of fixed points, volume 730 of Lecture Notes in Mathematics, pages 77-88, Berlin Heidelberg, 1979. Springer-Verlag.

15
D. Cox, J. Little, and D. O'Shea.
Ideals, Varieties and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra.
Undergraduate Texts in Mathematics. Springer-Verlag, New York, 2nd edition, 1997.

16
D. Cox, J. Little, and D. O'Shea.
Using Algebraic Geometry, volume 185 of Graduate Texts in Mathematics.
Springer-Verlag, New York, 1998.

17
J.P. Dedieu and M. Shub.
Multihomogeneous Newton methods.
To appear in Math. Comp.

18
P. Dietmaier.
The Stewart-Gough platform of general geometry can have 40 real postures.
In J. Lenarcic and M.L. Husty, editors, Advances in Robot Kinematics: Analysis and Control, pages 1-10. Kluwer Academic Publishers, Dordrecht, 1998.

19
F.J. Drexler.
Eine Methode zur Berechnung sämtlicher Lösungen von Polynomgleichungssystemen.
Numer. Math., 29(1):45-58, 1977.

20
M.E. Dyer and A.M. Frieze.
On the complexity of computing the volume of a polyhedron.
SIAM J. Comput., 17(5):967-974, 1988.

21
M. Dyer, P. Gritzmann, and A. Hufnagel.
On the complexity of computing mixed volumes.
SIAM J. Comput., 27(2):356-400, 1998.

22
D. Eisenbud.
Commutative Algebra with a View Toward Algebraic Geometry, volume 150 of Graduate Texts in Mathematics.
Springer-Verlag, New York, 1995.

23
I.Z. Emiris.
Sparse Elimination and Applications in Kinematics.
PhD thesis, Computer Science Division, Dept. of Electrical Engineering and Computer Science, University of California, Berkeley, 1994.

24
I.Z. Emiris and J.F. Canny.
Efficient incremental algorithms for the sparse resultant and the mixed volume.
J. Symbolic Computation, 20(2):117-149, 1995.
Software available at http://www.inria.fr/saga/emiris.

25
I.Z. Emiris.
On the complexity of sparse elimination.
J. Complexity, 12(2):134-166, 1996.

26
I.Z. Emiris and J. Verschelde.
How to count efficiently all affine roots of a polynomial system.
Discrete Applied Mathematics, 93(1):21-32, 1999.

27
P. Falb.
Methods of Algebraic Geometry in Control Theory: Part I, Scalar Linear Systems and Affine Algebraic Geometry, volume 4 of Systems & Control: Foundations & Applications.
Birkhäuser, Boston, 1990.

28
O.D. Faugeras and S. Maybank.
Motion from point matches: multiplicity of solutions.
Intern. J. Comp. Vision, 4:225-246, 1990.

29
T. Gao, T.Y. Li, and X. Wang.
Finding isolated zeros of polynomial systems in Cn with stable mixed volumes.
To appear in J. of Symbolic Computation.

30
T. Gao, T.Y. Li, J. Verschelde, and M. Wu.
Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods.
To appear in Applied Math. Comput.

31
C.B. Garcia and W.I. Zangwill.
Finding all solutions to polynomial systems and other systems of equations.
Math. Programming, 16(2):159-176, 1979.

32
C.B. Garcia and T.Y. Li.
On the number of solutions to polynomial systems of equations.
SIAM J. Numer. Anal., 17(4):540-546, 1980.

33
I.M. Gel'fand, M.M. Kapranov, and A.V. Zelevinsky.
Discriminants, Resultants and Multidimensional Determinants.
Birkhäuser, Boston, 1994.

34
T. Giordano.
Implémention distribuée du calcul du volume mixte.
Master's thesis, University of Nice, Sophia-Antipolis, 1996.

35
J.E. Goodman and J. O'Rourke (editors).
Handbook of Discrete and Computational Geometry.
CRC Press, New York, 1997.

36
S. Harimoto and L.T. Watson.
The granularity of homotopy algorithms for polynomial systems of equations.
In G. Rodrigue, editor, Parallel processing for scientific computing, pages 115-120. SIAM, 1989.

37
J. Harris.
Algebraic Geometry, A first Course, volume 133 of Graduate Texts in Mathematics.
Springer-Verlag, New York, 1992.
Corrected third printing, 1995.

38
M.E. Henderson and H.B. Keller.
Complex bifurcation from real paths.
SIAM J. Appl. Math., 50:460-482, 1990.

39
B. Huber.
Pelican manual.
Available at http://www.msri.org/people/members/birk.

40
B. Huber and B. Sturmfels.
A polyhedral method for solving sparse polynomial systems.
Math. Comp., 64(212):1541-1555, 1995.

41
B.T. Huber.
Solving Sparse Polynomial Systems.
PhD thesis, Cornell University, 1996.
Available at http://www.msri.org/people/members/birk.

42
B. Huber and B. Sturmfels.
Bernstein's theorem in affine space.
Discrete Comput. Geom., 17(2):137-141, 1997.

43
B. Huber and J. Verschelde.
Polyhedral end games for polynomial continuation.
Numerical Algorithms, 18(1):91-108, 1998.

44
B. Huber, F. Sottile, and B. Sturmfels.
Numerical Schubert calculus.
J. of Symbolic Computation, 26(6):767-788, 1998.

45
B Huber, J. Rambau, and F. Santos.
The Cayley trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings.
Submitted to the Journal of the European Mathematical Society., 1999.

46
B. Huber and J. Verschelde.
Pieri homotopies for problems in enumerative geometry applied to pole placement in linear systems control.
MSRI Preprint #1998-064, 1999.

47
S. Katsura.
Users posing problems to posso.
PoSSo Newsletter, no. 2, July 1994, edited by L. Gonzalez-Vega and T. Recio. Available at http://posso.dm.unipi.it/.

48
G.R. Kempf.
Algebraic Varieties, volume 172 of London Mathematical Society Lecture Note Series.
Cambridge University Press, 1993.

49
A.G. Khovanskii.
Newton polyhedra and the genus of complete intersections.
Functional Anal. Appl., 12(1):38-46, 1978.
Translated from Funktsional. Anal. i Prilozhen., 12(1),51-61,1978.

50
H. Kobayashi, H. Suzuki, and Y. Sakai.
Numerical calculation of the multiplicity of a solution to algebraic equations.
Math. Comp., 67(221):257-270, 1998.

51
A.G. Kushnirenko.
Newton Polytopes and the Bézout Theorem.
Functional Anal. Appl., 10(3):233-235, 1976.
Translated from Funktsional. Anal. i Prilozhen., 10(3),82-83,1976.

52
T.Y. Li.
On Chow, Mallet-Paret and Yorke homotopy for solving systems of polynomials.
Bulletin of the Institute of Mathematics. Acad. Sin., 11:433-437, 1983.

53
T.Y. Li.
Solving polynomial systems.
The Mathematical Intelligencer, 9(3):33-39, 1987.

54
T.Y. Li and T. Sauer.
Regularity results for solving systems of polynomials by homotopy method.
Numer. Math., 50(3):283-289, 1987.

55
T.Y. Li, T. Sauer, and J.A. Yorke.
Numerical solution of a class of deficient polynomial systems.
SIAM J. Numer. Anal., 24(2):435-451, 1987.

56
T.Y. Li, T. Sauer, and J.A. Yorke.
The random product homotopy and deficient polynomial systems.
Numer. Math., 51(5):481-500, 1987.

57
T.Y. Li, T. Sauer, and J.A. Yorke.
The cheater's homotopy: an efficient procedure for solving systems of polynomial equations.
SIAM J. Numer. Anal., 26(5):1241-1251, 1989.

58
T.Y. Li and X. Wang.
Solving deficient polynomial systems with homotopies which keep the subschemes at infinity invariant.
Math. Comp., 56(194):693-710, 1991.

59
T.Y. Li and X. Wang.
Nonlinear homotopies for solving deficient polynomial systems with parameters.
SIAM J. Numer. Anal., 29(4):1104-1118, 1992.

60
T.Y. Li and X. Wang.
Solving real polynomial systems with real homotopies.
Math. Comp., 60:669-680, 1993.

61
T.Y. Li and X. Wang.
Higher order turning points.
Appl. Math. Comput., 64:155-166, 1994.

62
T.Y. Li and X. Wang.
The BKK root count in Cn.
Math. Comp., 65(216):1477-1484, 1996.

63
T.Y. Li, T. Wang, and X. Wang.
Random product homotopy with minimal BKK bound.
In J. Renegar, M. Shub, and S. Smale, editors, The Mathematics of Numerical Analysis, volume 32 of Lectures in Applied Mathematics, pages 503-512, 1996.
Proceedings of the AMS-SIAM Summer Seminar in Applied Mathematics, Park City, Utah, July 17-August 11, 1995, Park City, Utah.

64
T.Y. Li.
Numerical solution of multivariate polynomial systems by homotopy continuation methods.
Acta Numerica, 6:399-436, 1997.

65
T.Y. Li and X. Wang.
Counterexamples to the connectivity conjecture of the mixed cells.
Discrete Comput. Geom., 20(4):515-521, 1998.

66
G. Malajovich.
pss 2 - Polynomial System Solver.
Available at http://www.labma.ufrj.br:80/~gregorio.

67
R.D. McKelvey and A. McLennan.
The maximal number of regular totally mixed Nash equilibria.
Journal of Economic Theory, 72:411-425, 1997.

68
A. McLennan.
The maximal generic number of pure Nash equilibria.
Journal of Economic Theory, 72:408-410, 1997.

69
K. Meintjes and A.P. Morgan.
A methodology for solving chemical equilibrium systems.
Appl. Math. Comput., 22(4):333-361, 1987.

70
A.P. Morgan.
A method for computing all solutions to systems of polynomial equations.
ACM Trans. Math. Softw., 9(1):1-17, 1983.

71
A. Morgan.
Solving polynomial systems using continuation for engineering and scientific problems.
Prentice-Hall, Englewood Cliffs, N.J., 1987.

72
A. Morgan and A. Sommese.
A homotopy for solving general polynomial systems that respects m-homogeneous structures.
Appl. Math. Comput., 24(2):101-113, 1987.

73
A. Morgan and A. Sommese.
Computing all solutions to polynomial systems using homotopy continuation.
Appl. Math. Comput., 24(2):115-138, 1987.
Errata: Appl. Math. Comput. 51 (1992), p. 209.

74
A.P. Morgan, A.J. Sommese, and L.T. Watson.
Finding all isolated solutions to polynomial systems using HOMPACK.
ACM Trans. Math. Softw., 15(2):93-122, 1989.

75
A.P. Morgan and A.J. Sommese.
Coefficient-parameter polynomial continuation.
Appl. Math. Comput., 29(2):123-160, 1989.
Errata: Appl. Math. Comput. 51:207(1992).

76
A.P. Morgan and A.J. Sommese.
Generically nonsingular polynomial continuation.
In E.L. Allgower and K. Georg, editors, Computational Solution of Nonlinear Systems of Equations, pages 467-493, Providence, R.I., 1990. AMS.

77
A.P. Morgan, A.J. Sommese, and C.W. Wampler.
Computing singular solutions to nonlinear analytic systems.
Numer. Math., 58(7):669-684, 1991.

78
A.P. Morgan, A.J. Sommese, and C.W. Wampler.
Computing singular solutions to polynomial systems.
Adv. Appl. Math., 13(3):305-327, 1992.

79
A.P. Morgan, A.J. Sommese, and C.W. Wampler.
A power series method for computing singular solutions to nonlinear analytic systems.
Numer. Math., 63:391-409, 1992.

80
A.P. Morgan, A.J. Sommese, and C.W. Wampler.
A product-decomposition theorem for bounding Bézout numbers.
SIAM J. Numer. Anal., 32(4):1308-1325, 1995.

81
D. Mumford.
Algebraic Geometry I; Complex Projective Varieties, volume 221 of Grundlehren der mathematischen Wissenschaften.
Springer-Verlag, Berlin Heidelberg New York, 1976.

82
M. Pieri.
Formule di coincidenza per le serie algebriche $\infty^n$ di coppie di punti dello spazio a n dimensioni.
Rend. Circ. Mat. Palermo, 5:252-268, 1891.

83
M.S. Ravi, J. Rosenthal, and X. Wang.
Dynamic pole placement assignment and Schubert calculus.
SIAM J. Control and Optimization, 34(3):813-832, 1996.

84
M.S. Ravi, J. Rosenthal, and X. Wang.
Degree of the generalized Plücker embedding of a quot scheme and quatum cohomology.
Math. Ann., 311:11-26, 1998.

85
J.M. Rojas.
A convex geometric approach to counting the roots of a polynomial system.
Theoret. Comput. Sci., 133(1):105-140, 1994.
Extensions and corrections available at http://www.cityu.edu.hk/ma/staff/rojas/.

86
J.M. Rojas and X. Wang.
Counting affine roots of polynomial systems via pointed Newton polytopes.
J. Complexity, 12:116-133, 1996.

87
J.M. Rojas.
Toric intersection theory for affine root counting.
Journal of Pure and Applied Algebra, 136(1):67-100, 1999.

88
J. Rosenthal.
On dynamic feedback compensation and compactifications of systems.
SIAM J. Control and Optimization, 32(1):279-296, 1994.

89
J. Rosenthal and F. Sottile.
Some remarks on real and complex output feedback.
Systems and Control Lett., 33(2):73-80, 1998.
See http://www.nd.edu/~rosen/pole for a description of computational aspects of the paper.

90
J. Rosenthal and J.C. Willems.
Open problems in the area of pole placement.
In V.D. Blondel, E.D. Sontag, M. Vidyasagar, and J.C. Willems, editors, Open Problems in Mathematical Systems and Control Theory, Communication and Control Engineering Series. Springer-Verlag, London, 1999.

91
H. Schubert.
Beziehungen zwischen den linearen Räumen auferlegbaren charakteristischen Bedingungen.
Math. Ann., 38:588-602, 1891.

92
B. Segre.
The Non-Singular Cubic Surfaces. A New Method of Investigation with Special Reference to Questions of Reality.
Oxford University Press, 1942.

93
A.J. Sommese and C.W. Wampler.
Numerical algebraic geometry.
In J. Renegar, M. Shub, and S. Smale, editors, The Mathematics of Numerical Analysis, volume 32 of Lectures in Applied Mathematics, pages 749-763, 1996.
Proceedings of the AMS-SIAM Summer Seminar in Applied Mathematics, Park City, Utah, July 17-August 11, 1995, Park City, Utah.

94
A.J. Sommese and J. Verschelde.
Numerical homotopies to compute generic points on positive dimensional algebraic sets.
MSRI Preprint #1999-038, 1999.

95
M. Sosonkina, L.T. Watson, and D.E. Stewart.
Note on the end game in homotopy zero curve tracking.
ACM Trans. Math. Softw., 22(3):281-287, 1996.

96
F. Sottile.
Enumerative geometry for real varieties.
In J. Kollár, R. Lazarsfeld, and D. R. Morrison, editors, Algebraic Geometry - Santa Cruz 1995 (University of California, Santa Cruz, July 1995), volume 62, Part I of Proceedings of Symposia in Pure Mathematics, pages 435-447. AMS, 1997.

97
F. Sottile.
Pieri's formula via explicit rational equivalence.
Can. J. Math., 49(6):1281-1298, 1997.

98
F. Sottile.
Real Schubert calculus: polynomial systems and a conjecture of Shapiro and Shapiro.
MSRI Preprint #1998-066, 1998.
Accepted for publication in Experimental Mathematics.

99
F. Sottile.
The special Schubert calculus is real.
Electronic Research Announcements of the AMS, 5:35-39, 1999.
Available at http://www.ams.org/era.

100
F. Sottile.
Real rational curves in Grassmannians.
MSRI Preprint #1999-025, 1999.

101
B. Sturmfels.
Algorithms in Invariant Theory.
Texts and Monographs in Symbolic Computation. Springer-Verlag, New York, 1993.

102
B. Sturmfels.
On the Newton polytope of the resultant.
Journal of Algebraic Combinatorics, 3:207-236, 1994.

103
B. Sturmfels.
Gröbner Bases and Convex Polytopes, volume 8 of University Lecture Series.
AMS, Providence, R.I., 1996.

104
B. Sturmfels.
Polynomial equations and convex polytopes.
Amer. Math. Monthly, 105(10):907-922, 1998.

105
J. Verschelde, M. Beckers, and A. Haegemans.
A new start system for solving deficient polynomial systems using continuation.
Appl. Math. Comput., 44(3):225-239, 1991.

106
J. Verschelde and R. Cools.
Symbolic homotopy construction.
Applicable Algebra in Engineering, Communication and Computing, 4(3):169-183, 1993.

107
J. Verschelde and R. Cools.
Symmetric homotopy construction.
J. Comput. Appl. Math., 50:575-592, 1994.

108
J. Verschelde and K. Gatermann.
Symmetric Newton polytopes for solving sparse polynomial systems.
Adv. Appl. Math., 16(1):95-127, 1995.

109
J. Verschelde and A. Haegemans.
The GBQ-Algorithm for constructing start systems of homotopies for polynomial systems.
SIAM J. Numer. Anal., 30(2):583-594, 1993.

110
J. Verschelde, P. Verlinden, and R. Cools.
Homotopies exploiting Newton polytopes for solving sparse polynomial systems.
SIAM J. Numer. Anal., 31(3):915-930, 1994.

111
J. Verschelde.
PHC and MVC: two programs for solving polynomial systems by homotopy continuation.
In J.C. Faugère, J. Marchand, and R. Rioboo, editors, Proceedings of the PoSSo Workshop on Software. Paris, March 1-4, 1995, pages 165-175, 1995.

112
J. Verschelde, K. Gatermann, and R. Cools.
Mixed-volume computation by dynamic lifting applied to polynomial system solving.
Discrete Comput. Geom., 16(1):69-112, 1996.

113
J. Verschelde.
Homotopy Continuation Methods for Solving Polynomial Systems.
PhD thesis, K.U.Leuven, Dept. of Computer Science, 1996.
Postscript version available from the author's web pages.

114
J. Verschelde.
Numerical evidence for a conjecture in real algebraic geometry.
MSRI Preprint #1998-064, 1998.
Accepted for publication in Experimental Mathematics. Paper and software available at the author's web-pages.

115
J. Verschelde.
PHCpack: A general-purpose solver for polynomial systems by homotopy continuation.
Accepted for publication in ACM Trans. Math. Softw.. Paper and software available at the author's web-pages., 1999.

116
J. Verschelde.
Toric Newton method for polynomial homotopies.
MSRI Preprint #1999-005, 1999.
Revised for special issue of J. Symbolic Computation.

117
A. Wallack, I.Z. Emiris, and D. Manocha.
MARS: A Maple/Matlab/C resultant-based solver.
In O. Gloor, editor, Proceedings of ISSAC-98, pages 244-251, Rostock, Germany, 1998. ACM.

118
C.W. Wampler, A.P. Morgan, and A.J. Sommese.
Numerical continuation methods for solving polynomial systems arising in kinematics.
ASME J. of Mechanical Design, 112(1):59-68, 1990.

119
C.W. Wampler, A.P. Morgan, and A.J. Sommese.
Complete solution of the nine-point path synthesis problem for four-bar linkages.
ASME J. of Mechanical Design, 114(1):153-159, 1992.

120
C.W. Wampler.
Bezout number calculations for multi-homogeneous polynomial systems.
Appl. Math. Comput., 51(2-3):143-157, 1992.

121
C.W. Wampler.
Isotropic coordinates, circularity and Bezout numbers: planar kinematics from a new perspective.
Proceedings of the 1996 ASME Design Engineering Technical Conference. Irvine, CA, Aug 18-22, 1996. Available on CD-ROM.

122
X. Wang, M.S. Ravi, and J. Rosenthal.
Algebraic and combinatorial aspects of the dynamic pole assignment problem.
In U. Helmke, R. Mennicken, and J. Saurer, editors, Systems and Networks: Mathematical Theory and Applications, volume 79 of Mathematical Research, pages 547-550. Akademie Verlag, Berlin, 1994.
Proc. of the International Symposium MTNS 93 held in Regensburg Germany. Vol II: Invited and contributed papers.

123
L.T. Watson.
Numerical linear algebra aspects of globally convergent homotopy methods.
SIAM Rev., 28(4):529-545, 1986.

124
L.T. Watson, S.C. Billups, and A.P. Morgan.
Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms.
ACM Trans. Math. Softw., 13(3):281-310, 1987.

125
L.T. Watson.
Globally convergent homotopy methods: a tutorial.
Appl. Math. Comput., 31(Spec. Issue):369-396, 1989.

126
L.T. Watson, M. Sosonkina, R.C. Melville, A.P. Morgan, and H.F. Walker.
HOMPACK90: A suite of Fortran 90 codes for globally convergent homotopy algorithms.
ACM Trans. Math. Softw., 23(4):514-549, 1997.
Available at http://www.cs.vt.edu/~ltw/.

127
A. Weil.
Foundations of Algebraic Geometry, volume XXIX of AMS Colloquium Publications.
AMS, Providence, Rhode Island, 1962.
Revised and Enlarged Edition.

128
S.M. Wise, A.J. Sommese, and L.T. Watson.
POLSYS_PLP: A partitioned linear product homotopy code for solving polynomial systems of equations.
Available at http://www.cs.vt.edu/~ltw/, 1998.

129
A.H. Wright.
Finding all solutions to a system of polynomial equations.
Math. Comp., 44(169):125-133, 1985.

130
G.M. Ziegler.
Lectures on Polytopes, volume 152 of Graduate Texts in Mathematics.
Springer-Verlag, New York, 1995.

131
W. Zulehner.
A simple homotopy method for determining all isolated solutions to polynomial systems.
Math. Comp., 50(181):167-177, 1988.



Jan Verschelde
2001-04-08