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single-valued, one makes a branch cut along the interval [0, 1] on the real axis, connecting the two branch points of the function. The same idea can be applied to the function √ z ; but in that case one has to perceive that the point at infinity is the appropriate 'other' branch point to connect to from 0, for example along the whole ...
The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4.The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1.
A more familiar principal branch function, limited to real numbers, is that of a positive real number raised to the power of 1/2. For example, take the relation y = x 1/2, where x is any positive real number. This relation can be satisfied by any value of y equal to a square root of x (either positive or negative).
Algebra is one of the main branches of mathematics, covering the study of structure, relation and quantity. Algebra studies the effects of adding and multiplying numbers , variables , and polynomials , along with their factorization and determining their roots .
Mathematics is a broad subject that is commonly divided in many areas or branches that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers .
Here the polynomial z 2 − 1 vanishes when z = ±1, so g evidently has two branch points. We can "cut" the plane along the real axis, from −1 to 1 , and obtain a sheet on which g ( z ) is a single-valued function.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
Branches found under larger branches can be called underbranches. Some branches from specific trees have their own names, such as osiers and withes or withies , which come from willows . Often trees have certain words which, in English, are naturally collocated , such as holly and mistletoe , which usually employ the phrase "sprig of" (as in, a ...