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Some new canonical
forms for polynomials
Bruce Reznick |
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Vol. 266 (2013), No. 1, 185–220
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Abstract |
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We give some new canonical representations for forms over ℂ. For example, a general binary quartic form can be written as the square of a quadratic form plus the fourth power of a linear form. A general cubic form in (x1,…,xn) can be written uniquely as a sum of the cubes of linear forms ℓij(xi,…,xj), 1 ≤ i ≤ j ≤ n. A general ternary quartic form is the sum of the square of a quadratic form and three fourth powers of linear forms. The methods are classical and elementary. |
Keywords
canonical forms, sums of powers of polynomials
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Mathematical Subject Classification 2000
Primary: 11E76, 14N15
Secondary: 11E25, 11P05, 15A72
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Milestones
Received: 28 March 2012
Revised: 17 June 2013
Accepted: 19 June 2013
Published: 23 September 2013
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Authors |
| Bruce Reznick | |
| Department of Mathematics and Center
for Advanced Study University of Illinois at Urbana-Champaign 1409 W. Green Street 327 Altgeld Hall Urbana, IL 61801-2975 United States |
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