An algorithm for constructing a basis for -spline modules over polynomial rings

Authors:
Satya Deo and Lipika Mazumdar

Journal:
Math. Comp. **67** (1998), 1107-1120

MSC (1991):
Primary 41A15; Secondary 13C10

DOI:
https://doi.org/10.1090/S0025-5718-98-00943-0

MathSciNet review:
1459386

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Abstract: Let be a polyhedral complex embedded in the euclidean space and , , denote the set of all -splines on . Then is an -module where is the ring of polynomials in several variables. In this paper we state and prove the existence of an algorithm to write down a free basis for the above -module in terms of obvious linear forms defining common faces of members of . This is done for the case when consists of a finite number of parallelopipeds properly joined amongst themselves along the above linear forms.

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Additional Information

**Satya Deo**

Affiliation:
Department of Mathematics and Computer Science, R.D. University, Jabalpur - 482 001, India

Email:
sdt@rdunijb.ren.nic.in

**Lipika Mazumdar**

Affiliation:
Department of Mathematics and Computer Science, R.D. University, Jabalpur - 482 001, India

DOI:
https://doi.org/10.1090/S0025-5718-98-00943-0

Received by editor(s):
December 15, 1994

Received by editor(s) in revised form:
March 3, 1997

Additional Notes:
The first author was supported by the UGC research project no. F 8-5/94 (SR-I)

The second author was supported by the CSIR(JRF) no. 9/97(36)/92/EMR-I

Article copyright:
© Copyright 1998
American Mathematical Society