- algebraically independent
- niezależny algebraicznie

*English-Polish dictionary for engineers.
2013.*

- algebraically independent
- niezależny algebraicznie

*English-Polish dictionary for engineers.
2013.*

**Independent equation**— An independent equation is an equation in a system of simultaneous equations which cannot be derived algebraically from the other equations.ee also*Linear algebra *Indeterminate systemReferences … Wikipedia**Algebraic independence**— In abstract algebra, a subset S of a field L is algebraically independent over a subfield K if the elements of S do not satisfy any non trivial polynomial equation with coefficients in K . This means that for every finite sequence α1, ..., α n of … Wikipedia**Transcendence degree**— In abstract algebra, the transcendence degree of a field extension L / K is a certain rather coarse measure of the size of the extension. Specifically, it is defined as the largest cardinality of an algebraically independent subset of L over K .A … Wikipedia**Glossary of field theory**— Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.) Definition of a field A field is a commutative ring… … Wikipedia**Field extension**— In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… … Wikipedia**Lindemann–Weierstrass theorem**— In mathematics, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states that if α1,...,α n are algebraic numbers which are linearly independent over the rational numbers Q, then… … Wikipedia**Transcendence theory**— In mathematics, transcendence theory is a branch of number theory that investigates transcendental numbers, in both qualitative and quantitative ways.TranscendenceThe fundamental theorem of algebra tells us that if we have a non zero polynomial… … Wikipedia**E-function**— In mathematics, E functions are a type of power series that satisfy particular systems of linear differential equations.DefinitionA function f ( x ) is called of type E , or an E function [Carl Ludwig Siegel, Transcendental Numbers , p.33,… … Wikipedia**Elementary symmetric polynomial**— In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial P can be expressed as a polynomial in elementary… … Wikipedia**Transcendental function**— A transcendental function is a function that does not satisfy a polynomial equation whose coefficients are themselves polynomials, in contrast to an algebraic function, which does satisfy such an equation. In other words a transcendental function … Wikipedia**Auxiliary function**— In mathematics, auxiliary functions are an important construction in transcendental number theory. They are functions which appear in most proofs in this area of mathematics and that have specific, desirable properties, such as taking the value… … Wikipedia