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Roots of unity serve as solutions to polynomial equations and have the special algebraic property that raising them to a certain power gives 1.Tetrahedron Solutions Finally Proved Decades After Computer Search|Kevin Hartnett|February 2, 2021|Quanta Magazine
Fittingly, the group structure of homology was discovered in the 1920s by Emmy Noether, a pioneer of the study of groups and other algebraic structures.
Hilbert’s 13th problem asks whether seventh-degree equations can be solved using a composition of addition, subtraction, multiplication and division plus algebraic functions of two variables, tops.
Resolvent degree, Farb said, offers a way to categorize these problems by a kind of algebraic complexity, rather like grouping optimization problems in complexity classes.
The theorem established a kind of bridge between distant mathematical continents, with certain algebraic equations on one side and a kind of symmetric organization of geometric tilings on the other.
A locus or curve may be algebraically specified in another way; viz.
The electro-motive changes induced at the two sides now became algebraically summated.
The effects of gravity and of light become algebraically summated under their simultaneous action.
But if the self-displacements be averaged algebraically, certain very definite tendencies toward constant errors are revealed.Vocational Psychology: Its Problems and Methods|Harry L. Hollingworth
Find algebraically the real difference of latitude, meridional difference of latitude and the difference of longitude.Lectures in Navigation|Ernest Gallaudet Draper