In other words, an absolutely irreducible algebraic set is a synonym of an algebraic variety, which emphasizes that the coefficients of the defining equations may not belong to an algebraically closed field.
32.
A single defining equation shouldn't contain " one " quantity defining " all other " quantities in the " same equation ", otherwise contradictions arise again.
33.
In a language that supports lazy evaluation, like in Haskell, it is possible to define a fixed-point combinator using the defining equation of the fixed-point combinator which is conventionally named fix.
34.
Defining equations are normally formulated in terms of elementary algebra and calculus, complex-valued for theoretical advantage, but for a physical measurement the real part is relevant, the imaginary part can be discarded.
35.
If the negative Pell equation does have a solution for a particular " n ", its fundamental solution leads to the fundamental one for the positive case by squaring both sides of the defining equation:
36.
Notice that the scaling of \ mathbf { a } or \ mathbf { A } is not important ( except that it must be non-zero ) since the defining equations already allow for unknown scaling.
37.
A defining equation only defines how calculate the defined quantity, it " cannot " describe how the quantity varies as a function of other parameters since the function would vary from one application to another.
38.
Every algebraic plane curve has a degree, the degree of the defining equation, which is equal, in case of an algebraically closed field, to the number of intersections of the curve with a line in general position.
39.
Being a quadratic polynomial with no multiple root, the defining equation " 1 } } has " two " distinct solutions, which are equally valid and which happen to be additive and multiplicative inverses of each other.
40.
Unlike PRA, however, the elementary recursive functions can be characterized by the closure under composition and projection of a " finite " number of basis functions, and thus only a finite number of defining equations are needed.
