B-splines, Polytopes, and Their Characteristic D-modules

REFERENCES

• Borel , A. , Grivel , P.-P. , Kaup , B. , Haefliger , A. , Malgrange , B. , Ehlers , F. ( 1987 ). Algebraic D-Modules . Perspectives in Mathematics , Vol. 2 , Bostonv , MA : Academic Press Inc .
   Google Scholar
• Cohen , M. M. ( 1973 ). A Course in Simple-Homotopy Theory . Graduate Texts in Mathematics , Vol. 10 . New York : Springer-Verlag .
   Google Scholar
• Coutinho , S. C. ( 1995 ). A Primer of Algebraic D-Modules . London Mathematical Society Student Texts , Vol. 33 . Cambridge : Cambridge University Press .
   Google Scholar
• de Boor , C. , Höllig , K. ( 1982 ). Recurrence relations for multivariate B-splines . Proc. Amer. Math. Soc. 85 ( 3 ): 397 – 400 .
   Web of Science ®Google Scholar
• De Concini , C. , Procesi , C. ( 2011 ). Topics in Hyperplane Arrangements, Polytopes and Box-Splines . New York : Springer .
   Google Scholar
• Kashiwara , M. ( 1995 ). Algebraic study of systems of partial differential equations. Mém. Soc. Math. France (N.S.) (63):xiv+ 72 .
   Google Scholar
• Malgrange , B. ( 1993 ). De Rham complex and direct images of 𝒟-modules . In: Éléments de la théorie des systèmes différentiels. Images directes et constructibilité (Nice, 1990) . Travaux en Cours , Vol. 46 . Paris : Hermann , pp. 1 – 13 .
   Google Scholar
• Oaku , T. , Takayama , N. ( 2001 ). Algorithms for D-modules—restriction, tensor product, localization, and local cohomology groups . J. Pure Appl. Algebra 156 ( 2–3 ): 267 – 308 .
   Web of Science ®Google Scholar
• Oaku , T. , Takayama , N. , Walther , U. ( 2000 ). A localization algorithm for D-modules . J. Symbolic Comput. 29 ( 4–5 ): 721 – 728 , Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998) .
   Web of Science ®Google Scholar
• Pham , F. ( 1979 ). Singularités des Systèmes Différentiels de Gauss-Manin . Progress in Mathematics , Vol. 2 . Mass. : Birkhäuser Boston, With contributions by Lo Kam Chan, Philippe Maisonobe and Jean-Étienne Rombaldi .
   Google Scholar
• Communicated by V. Walther.
   Google Scholar