Divisor

About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.

Method for judging prime number, and device therefor

Abstract: PROBLEM TO BE SOLVED: To avoid calculation of repeated multiple length by calculating to find the remainder of a random integer when element of a prime number table required for the sieve method defined as modulus by using values of an increase value remainder table. SOLUTION: A remainder when a multiple length integer for increasing prime number candidates rejected by the sieve method is defined as dividend and elements of a prime table are defined as divisor, is calculated beforehand, and this value is held as an increase value remainder table. And, remainders corresponding to generated elements of a group are taken from a storage means. Next, a calculation for determining the remainders of the random integers when the element of the prime number table required for the sieve method is defined as modulus is performed by using the increase value remainder table (S303). In this case, if a size of the elements of the prime number table is made smaller than a word by several bits, the size of the elements of the increase value remainder table also becomes smaller than a word by several bits. Thus, the calculation is executable in a word.

Fractional type indexing device

Abstract: PURPOSE:To eliminate that phenomenon which likely to occur in processing a gear etc., where dividing errors are concentrated to one groove by making integer equal division of the circumference with an integer multiple of the remainder angle, which has been left when the circumference was divided by an integer. CONSTITUTION:In this gear speed reducer 11 of constant rotation type coupled with a meshing clutch capable of transmitting a certain rotational component to a constant angle rotating output shaft which can convert the resolution ability with a replacement gear train Gn, first the given number of division is resolved into a compound fraction which does not have a common measure. Then the table is turned at steps of the angle {(360 deg.)X(denominator/divisor)}, and the clutch is disengaged to permit the replacement gear to idle for a certain angle. When the table is stopped, the work thereon is processed. This procedure is repeated, and processing with all divisors is completed when the table has turned for an angle corresponding to the denominator. By this arrangement, the surface of a disc, cylinder, etc. can be divisionally processed into the number of arbitrary integer.

Rounding of binary integers

Abstract: Methods and apparatus to provide rounding of a binary integer are described. In one embodiment, a value that indicates whether a divisor divides a binary integer is extracted from a product of the binary integer and a scaled approximate reciprocal of the divisor.

Diviseurs de la forme 2D-G sans sections et rang de la multiplication dans les corps finis (Divisors of the form 2D-G without sections and bilinear complexity of multiplication in finite fields)

Abstract: Let X be an algebraic curve, defined over a perfect field, and G a divisor on X. If X has sufficiently many points, we show how to construct a divisor D on X such that l(2D-G)=0, of essentially any degree such that this is compatible the Riemann-Roch theorem. We also generalize this construction to the case of a finite number of constraints, l(k_i.D-G_i)=0, where |k_i|\leq 2. Such a result was previously claimed by Shparlinski-Tsfasman-Vladut, in relation with the Chudnovsky-Chudnovsky method for estimating the bilinear complexity of the multiplication in finite fields based on interpolation on curves; unfortunately, as noted by Cascudo et al., their proof was flawed. So our work fixes the proof of Shparlinski-Tsfasman-Vladut and shows that their estimate m_q\leq 2(1+1/(A(q)-1)) holds, at least when A(q)\geq 5. We also fix a statement of Ballet that suffers from the same problem, and then we point out a few other possible applications.

Electronic computer capable of repeatedly displaying the results of a quotient/remainder calculation

Abstract: An improved electronic computer which can produce a quotient/remainder calculation The computer has first and second memories for storing respectively a dividend and a divisor which are input for execution of division A quotient/remainder calculation is carried out using the dividend and divisor stored respectively in the first and second memories The computer further includes third and fourth memories for storing respectively a quotient and a remainder which are obtained in the division calculation A detector is provided for detecting which of the contents of the third memory or the contents of the fourth memory are displayed The contents of the third memory or the contents of the fourth memory which have not been detected as being displayed are displayed in response to a predetermined input operation