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The TI-84 Plus C Silver Edition was released in 2013 as the first Z80-based Texas Instruments graphing calculator with a color screen.It had a 320×240-pixel full-color screen, a modified version of the TI-84 Plus's 2.55MP operating system, a removable 1200 mAh rechargeable lithium-ion battery, and keystroke compatibility with existing math and programming tools. [6]
A modular multiplicative inverse of a modulo m can be found by using the extended Euclidean algorithm. The Euclidean algorithm determines the greatest common divisor (gcd) of two integers, say a and m. If a has a multiplicative inverse modulo m, this gcd must be 1. The last of several equations produced by the algorithm may be solved for this gcd.
The following table compares general and technical information for a selection of common and uncommon Texas Instruments graphing calculators. Many of the calculators in this list have region-specific models that are not individually listed here, such as the TI-84 Plus CE-T, a TI-84 Plus CE designed for non-French European markets.
Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm. That is: c = b e mod m = d −e mod m, where e < 0 and b ⋅ d ≡ 1 (mod m). Modular exponentiation is efficient to compute, even for very large integers.
TI-BASIC is the official [1] name of a BASIC-like language built into Texas Instruments' graphing calculators. TI-BASIC is a language family of three different and incompatible versions, released on different products: TI-BASIC 83 (on Z80 processor) for TI-83 series, TI-84 Plus series; TI-BASIC 89 (on 68k processor) for TI-89 series, TI-92 ...
Finally, given a, the multiplicative inverse of a modulo n is an integer x satisfying ax ≡ 1 (mod n). It exists precisely when a is coprime to n , because in that case gcd( a , n ) = 1 and by Bézout's lemma there are integers x and y satisfying ax + ny = 1 .
The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's method. In particular, if either exp {\displaystyle \exp } or log {\displaystyle \log } in the complex domain can be computed with some complexity, then that complexity is ...
In linear algebra, an invertible matrix is a square matrix which has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can be multiplied by an inverse to undo the operation. An invertible matrix multiplied by its inverse yields the identity matrix. Invertible matrices are the same size as their ...
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