User talk:D.Lazard

Archives

1, 2, 3, 4

This page has archives. Sections older than 10 days may be automatically archived by when more than 4 sections are present.

Primary Decomposition

You should check the talk page for primary decomposition. I fixed the example there. Can you add it onto the main page with the correct terminology?

Thanks and a question

Thank you for checking and reverting my mistaken edit of the Sylvester matrix article. I was going to revert it myself as $p_{m-n}^{m}\neq p_{n}^{m}$ , assuming your $p$ symbol meant number of permutations of m-n objects selected from a set of m objects. Please forgive my ignorance. What does your $p_{m}^{m-n}$ symbol stand for? If not number of permutations, then what? May I suggest that you add an explanation for ignorant people like me? Perhaps you meant the {m-n}th power of the highest coefficient, $p_{m}$ , of the first polynomial? If so, it would help readers like me not to see $p_{m}^{m-n}$ as a permutation symbol, if you could add a couple of words.

————————————————————————————————————————————————————————————————————————————————————————————————

Hi, D.Lazard,

Thanks for all the work you’ve put in on the math articles! And thanks for your recent answer at Talk:System of polynomial equations.

I have a question on that topic that I’ll ask here because it probably could not lead to any additions or clarifications in the article. If we have a system of polynomial equations in n variables, and we know one solution $(x_{0},y_{0},\dots ),$ is there some way to “divide out” the solution to obtain a lower-dimensional system, as we would for a single equation in a single unknown? Loraof (talk) 23:56, 1 November 2017 (UTC)[reply]

As asked, the answer is clearly no. However, if one knows that some component of the algebraic set of the solutions belong to an hypersurface, one may divide them out by saturation. This is widely used for eliminating the degenerate solutions that occur frequently in applications. D.Lazard (talk) 09:31, 2 November 2017 (UTC)[reply]

Thanks !

I just saw your edit on the Continuous function page and I wanted to thanks you for it as I was going to make a similar edit. Pyrrhonist05 (talk) 17:07, 9 November 2017 (UTC)[reply]

Hypersurface

Daniel, please respond to my talk entry to the Hypersurface article. Meilleurs vœux! Simiprof (talk) 20:17, 15 November 2017 (UTC)[reply]