Abstract
In this chapter we will consider a series of interrelated topics concerning polyhedral regions P in ℝn, the integer points in these regions, and piece-wise polynomial functions on subdivisions of such regions. In each case Gröbner basis techniques give important computational and conceptual tools to deal with problems of interest and practical importance. These topics are also closely related to the material on polytopes and toric varieties from Chapter 7, but we have tried to make this chapter as independent as possible from Chapter 7 so that it can be read separately.
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© 1998 Springer Science+Business Media New York
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Cox, D., Little, J., O’Shea, D. (1998). Integer Programming, Combinatorics, and Splines. In: Using Algebraic Geometry. Graduate Texts in Mathematics, vol 185. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-6911-1_8
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DOI: https://doi.org/10.1007/978-1-4757-6911-1_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98492-6
Online ISBN: 978-1-4757-6911-1
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