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The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations .
The Unicode Standard encodes almost all standard characters used in mathematics. [1] Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation. [1]
Lists are also supported through the use of six built-in lists, and user created lists with up to five characters as the name. They are capable of holding up to 999 elements. A list may hold entirely real numbers or entirely imaginary numbers. Some functions in the calculator are able to operate over entire lists, via Array programming.
Python supports normal floating point numbers, which are created when a dot is used in a literal (e.g. 1.1), when an integer and a floating point number are used in an expression, or as a result of some mathematical operations ("true division" via the / operator, or exponentiation with a negative exponent). Python also supports complex numbers ...
In mathematics, exponentiation, denoted b n, is an operation involving two numbers: the base, b, and the exponent or power, n. [1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [1] = ⏟.
The evident correspondence to Church numerals is non-coincidental, as that can be seen as a unary encoding, with natural numbers represented by lists of unit (i.e. non-important) values, e.g. [() ()], with the list's length serving as the representation of the natural number.
Range reduction (also argument reduction, domain-spltting) is the first step for any function, after checks for unusual values (infinity and NaN) are performed.The goal here is to reduce the domain of the argument for the polynomial to process, using the function's symmetry and periodicity (if any), setting flags to indicate e.g. whether to negate the result in the end (if needed).
The method is based on the observation that, for any integer >, one has: = {() /, /,. If the exponent n is zero then the answer is 1. If the exponent is negative then we can reuse the previous formula by rewriting the value using a positive exponent.