Sentence examples for over the rational from inspiring English sources

The conjecture involves elliptic curves defined over the rational numbers.

"Authentic verse music is that mystery which brims over the rational texture of the line".

He presented a new foundation for and extended the arithmetic of semi-simple algebras over the rational number field.

We also provide algorithms to answer a number of structural questions for a nilpotent matrix group.The main algorithms have been implemented in GAP, for groups over the rational number field.

Everything I wrote was designed to appeal to the emotional over the rational, the knee-jerk over the considered, assumptions reinforced rather than challenged and all presented in an easily digestible style that celebrated its own triviality... Journalism is a form of storytelling, both being simulacra-building enterprises.

Algebraic number fields are of particular interest and play an important role in both mathematics and engineering since an algebraic number field can be viewed as a finite dimensional linear space over the rational number field Q. Algorithms using algebraic number fields can be efficiently implemented involving only integer arithmetics.

We then search for tractable instances of C among the subclasses of Horn disjunctive linear constraints over the rationals.

If the measure is positive, this condition is also necessary, and likewise if the positions of the masses are linearly independent over the rationals.

Wiles's proof of the modularity of semistable elliptic curves over the rationals uses, as a starting point, the Langlands-Tunnell theorem, which implies that the mod 3 Galois representation attached to an elliptic curve over the rationals arises from a modular form of weight one.

Baker's generalization states that, if α1,…, αk (≠ 0, 1) are algebraic, if 1, β1,…, βk are linearly independent over the rationals, and if all the βi are irrational algebraic numbers, then α1β1⋯αkβk is transcendental.

Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space.