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Then the discriminant is the product of the a i, which is well-defined as a class in K/(K ×) 2. Geometrically, the discriminant of a quadratic form in three variables is the equation of a quadratic projective curve. The discriminant is zero if and only if the curve is decomposed in lines (possibly over an algebraically closed extension of the ...
The discriminant of K is 49 = 7 2. Accordingly, the volume of the fundamental domain is 7 and K is only ramified at 7. In mathematics, the discriminant of an algebraic number field is a numerical invariant that, loosely speaking, measures the size of the (ring of integers of the) algebraic number field.
Explicitly it is the modular discriminant Δ ( z , q ) , {\displaystyle \Delta (z,q),} which represents (up to a normalizing constant ) the discriminant of the cubic on the right side of the Weierstrass equation of an elliptic curve ; and the 24-th power of the Dedekind eta function .
For this converse the field discriminant is needed. This is the Dedekind discriminant theorem. In the example above, the discriminant of the number field () with x 3 − x − 1 = 0 is −23, and as we have seen the 23-adic place ramifies. The Dedekind discriminant tells us it is the only ultrametric place that does.
Let D be the discriminant of the field, n be the degree of K over , and = be the number of complex embeddings where is the number of real embeddings.Then every class in the ideal class group of K contains an integral ideal of norm not exceeding Minkowski's bound
December 2, 2024 at 12:45 PM. The Marburg virus, which causes bleeding from the eyes, nose, and mouth, can be fatal in up to 90% of those infected. Science Photo Library/Getty.
For solving the cubic equation x 3 + m 2 x = n where n > 0, Omar Khayyám constructed the parabola y = x 2 /m, the circle that has as a diameter the line segment [0, n/m 2] on the positive x-axis, and a vertical line through the point where the circle and the parabola intersect above the x-axis.
A Trump spokesperson responded to the DA's letter by calling it "a total and definitive victory for President Trump and the American People who elected him in a landslide."
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