Some articles on totally real, real:
Cubic Field - Discriminant
... will be positive precisely when the field is totally real, and negative if it is a complex cubic field ... Given some real number N > 0 there are only finitely many cubic fields K whose discriminant DK satisfies
... will be positive precisely when the field is totally real, and negative if it is a complex cubic field ... Given some real number N > 0 there are only finitely many cubic fields K whose discriminant DK satisfies
Totally Real Number Field
... In number theory, a number field K is called totally real if for each embedding of K into the complex numbers the image lies inside the real numbers ... an integer polynomial P, all of the roots of P being real or that the tensor product algebra of K with the real field, over Q, is a product of copies of R ... For example, quadratic fields K of degree 2 over Q are either real (and then totally real), or complex, depending on whether the square root of a positive or ...
... In number theory, a number field K is called totally real if for each embedding of K into the complex numbers the image lies inside the real numbers ... an integer polynomial P, all of the roots of P being real or that the tensor product algebra of K with the real field, over Q, is a product of copies of R ... For example, quadratic fields K of degree 2 over Q are either real (and then totally real), or complex, depending on whether the square root of a positive or ...
Famous quotes containing the words real and/or totally:
“I’m not making light of prayers here, but of so-called school prayer, which bears as much resemblance to real spiritual experience as that freeze-dried astronaut food bears to a nice standing rib roast. From what I remember of praying in school, it was almost an insult to God, a rote exercise in moving your mouth while daydreaming or checking out the cutest boy in the seventh grade that was a far, far cry from soul-searching.”
—Anna Quindlen (b. 1952)
“It amazes me when I hear any person prefer blindness to deafness. Such a person must have a terrible dread of being alone. Blindness makes one totally dependent on others, and deprives us of every satisfaction that results from light.”
—Horace Walpole (1717–1797)
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