First presenter Co-presenter(s)
Name :  Marc Moreno Maza * Name:   
E-mail: E-mail:  
Affiliation: Massachusetts Institute of Technology Name:   
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Country: USA Name:   
13-08  E-mail:    
Session: 13- Symbolic and numeric approaches to dynamical modeling and simulation Schedule:
Thursday, 11:00
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Title of
Regular Chains and Differential Elimination
Files of this talk (zip)

Files of this talk (zip)

Regular chains are one of the major tools for solving polynomial systems. For systems of algebraic equations, they provide a convenient way to describe complex solutions and a step toward isolation of real roots or decomposition into irreducible components. Combined with other techniques, they are used for these purposes by several computer algebra systems.

For systems of partial differential equations, they provide a popular way for determining a symbolic description of the solution set. Moreover, thanks to Rosenfeld's Lemma, techniques from the algebraic case apply to the differential one

In this talk, we first review the fundamental differential operations that, in practice, rely directly on this reduction to the algebraic case, namely pseudo-division, regularity test, regular GCDs and ranking conversions in some cases. Then, we discuss how the recent improvements of the algebraic operations (based on modular methods, fast polynomial arithmetic, parallel algorithms) can benefit to their differential counterparts.