Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am trying to find a minimal set of invariants for the binary homogenous form $$\displaystyle ax^7 + bx^{6}y + cx^{5}y^{2} + dx^{4}y^{3} + ex^{3}y^{4} + fx^{2}y^{5} + gxy^{6} + hy^{7}$$ What is the basis for all of the invariants for this form? Is there an easier way like using properties of symmetry without going through the crazy calculation? I've already calculated the binary form when the leading term's degree is 2,3 and 4 using the software SAGE.

share|improve this question
    
If people are unsure about what they are going to talk about, they usually don't talk. Given this fact, this title is superfluous. Please consider editing the title to put in something more informative. Regards, –  user21436 Apr 15 '12 at 10:54
    
Sorry Kannappan, I will make my questions clearer next time –  Low Scores Apr 20 '12 at 0:26

1 Answer 1

up vote 4 down vote accepted
  • Dixmier, Jacques; Lazard, D. (1988), "Minimum number of fundamental invariants for the binary form of degree 7", Journal of Symbolic Computation 6 (1): 113–115

    Abstract. The minimal number of fundamental invariants for the binary form of degree 7 was a problem left open since last century. It has been solved partly by computer algebra, partly by hand computations.

This looks promising.

Also see "On complete system of invariants for the binary form of degree 7", Leonid Bedratyuk.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.