modular arithmetic in a sentence
1) These proofs require some background in modular arithmetic .
2) This makes use of modular arithmetic for provisions especially attractive.
3) In modern times modular arithmetic is sometimes used in Digital signal processing.
modular arithmetic example sentences4) He further advanced modular arithmetic , greatly simplifying manipulations in number theory.
5) Modular arithmetic is convenient for calculating the check digit using modulus 11.
6) Modular arithmetic is often used to calculate checksums that are used within identifiers.
7) Why it is valid to "cancel" in the setting of modular arithmetic .
8) Standard properties of addition and multiplication familiar from the integers remain valid in modular arithmetic .
9) The notion of modular arithmetic is related to that of the remainder in Euclidean division.
10) Modular arithmetic , and in particular, modular exponentiation , comes to the rescue.
11) In modular arithmetic , some numbers have a multiplicative inverse with respect to the modulus.
12) This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic .
13) In this modular art article, one can learn more about applications of modular arithmetic in art.
14) Another way to find a solution is with basic algebra, modular arithmetic , and stepwise substitution.
15) Another advantage of this convention is in the use of modular arithmetic as implemented in modern computers.
example sentences with modular arithmetic16) It is used in polynomial factorization, a problem for which all known efficient algorithms use modular arithmetic .
17) The credit counters are modular counters, and the comparison of consumed credits to credit limit requires modular arithmetic .
18) A great convenience of modular arithmetic is that it is easy to multiply, though quite difficult to add.
19) This is well defined because addition and multiplication commute with the "mod" operator; see modular arithmetic .
20) Article 16 of Gauss' "Disquisitiones Arithmeticae" is an early modern statement and proof employing modular arithmetic .
21) In all cases, addition and subtraction of subscripts should be performed using modular arithmetic with modulus "n".
22) Using number-theoretic transforms instead of discrete Fourier transforms avoids rounding error problems by using modular arithmetic instead of floating-point arithmetic.
23) In computer algebra, modular arithmetics is commonly used to limit the size of integer coefficients in intermediate calculations and data.
24) In computer science, modular arithmetic is often applied in bitwise operations and other operations involving fixed-width, cyclic data structures.
25) Interesting cases are finite fields and modular arithmetics , for which the article root of unity modulo n contains some information.
26) In modular arithmetic , two integers are added and then the sum is divided by a positive integer called the "modulus.
27) The distinctive feature of prime numbers is the following: division is possible in modular arithmetic if and only if n is a prime.
28) By avoiding modular arithmetic , this method is much easier to implement and also runs significantly faster in practice (usually by at least a factor of four).
How to use modular arithmetic in a sentence29) For example, in modular arithmetic , a finite group of size n can be formed by partitioning the integers via the equivalence relation x~y iff x=y(mod n).
30) The base step, that 0 "p" ≡ 0 (mod "p"), is true for modular arithmetic because it is true for integers.
31) This is a simple consequence of the laws of modular arithmetic ; we are simply saying that we may first reduce "a" modulo "p".
32) In modular arithmetic , the set of integers modulo 12 has twelve elements; it inherits an addition operation from the integers that is central to musical set theory.
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