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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A chain rule for multivariable resultants


Authors: Charles Ching-an Cheng, James H. McKay and Stuart Sui Sheng Wang
Journal: Proc. Amer. Math. Soc. 123 (1995), 1037-1047
MSC: Primary 12D10; Secondary 13B25
MathSciNet review: 1227515
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Abstract: We present a chain rule for the multivariable resultant, which is similar to the familiar chain rule for the Jacobian matrix. Specifically, given two homogeneous polynomial maps $ {K^n} \to {K^n}$ for a commutative ring K, such that their composition is a homogeneous polynomial map, the resultant of the composition is the product of appropriate powers of resultants of the individual maps.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1227515-9
PII: S 0002-9939(1995)1227515-9
Keywords: Multivariable resultant, common zeros, generic polynomials, Jacobian Conjecture, chain rule, Nullstellensatz, discriminant, isobaric property, invariant
Article copyright: © Copyright 1995 American Mathematical Society