The Resultant, Episode 3: Inside the Episode

So we have, at long last, several expressions for the resultant:

The Resultant, Episode 3: Inside the Episode

So we have, at long last, several expressions for the resultant:

Filed under Algebraic Geometry

I first learned as a kid that “there are only 17 basically different wallpapers” from W.W.Sawyer’s Prelude to Mathematics. (The quote appears on p.102. Aside: this remains an excellent gift for a youngster with a yen for math.) I remember my father pointing out the absurdity of this claim: are all mural wallpapers of van Gogh’s paintings basically the same?

The Resultant, Episode 3

Last time the linear operator

Φ: *K _{n}*[

Φ(

made its grand entrance, clothed in the *Sylvester matrix*. (Recall that *K _{n}*[

Filed under Algebraic Geometry

The Resultant, Episode 2

By now you know the characters: the polynomials *E*(*x*) (degree *m*) and *F*(*x*) (degree *n*) with coefficients in an integral domain *R*, its fraction field *K*, and the extension field *L* of *K* in which *E* and *F* split completely:

Filed under Algebraic Geometry

The Resultant, Episode 1: Inside the Episode

In Episode 1 of our miniseries, “The Resultant”, the characters were introduced: integral domain *R* with fraction field *K* and extension field *L*, and polynomials *E*(*x*) and *F*(*x*) in *R*[*x*], factoring completely in *L* as *a*(*x–u*_{1})···(*x–u _{m}*) and

Filed under Algebraic Geometry

The Resultant, Episode 1

Time to discuss the resultant; we’ll need it for Kendig’s proof of Bézout’s theorem, but it has other uses too. The story will take several episodes, plus extras. Like a miniseries!

Filed under Algebraic Geometry

Filed under Algebraic Geometry