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Initialization: Load the package and set the display of special functions in output to typeset mathematical notation (textbook notation):
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Consider a list of complex number
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When doing numerical experimentation, interactively or within a program, it is frequently useful to see in which quadrants are the numbers located; for this purpose you can use QuadrantNumbers
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By convention, each quadrant contains the ending semi-axis, not the starting one
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To get an Array of four complex numbers around the origin, you can call QuadrantNumbers with no arguments
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The four numbers in this array are located in the four quadrants respectively.
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Note that each time you call this command it will return different numbers; they are chosen randomly.
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To get an Array of complex numbers with absolute value around the number 1 (where various special functions happen to be singular) use
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Consider the singularities of the linear differential equation behind the following AppellF4 function as a function of
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Get an Array of exact (not floating-point) complex number around these singularities
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Verify that the numbers in each of the arrays are located in the corresponding quadrant:
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Note that the absolute values of the numbers in each quadrant are equal or in between the absolute values of the singularities of F4 passed using around. For example, for the numbers in the first quadrant
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These numbers are equal or in between the absolute values of the singularities of F4
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