Some new canonical forms for polynomials

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)185-220
Number of pages36
JournalPacific Journal of Mathematics
Issue number1
StatePublished - 2013


  • Canonical forms
  • Sums of powers of polynomials

ASJC Scopus subject areas

  • General Mathematics


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