This package contains some functions connected
to the Number Theory
|
| Function |
Description |
| Cfe |
Cfe(x,eps)
Given the real number x and the optional error eps,
computes the first n terms of the Simple Continued Fraction Expansion
of x until the approximation error is less or equal to eps
(eps >= 1E-12)
Returns a n x 4 matrix containing {numer.|denom.|fract.val.|err}
Example: Cfe(pi,1E-6), Ans=
| 3 |
1 |
3 |
0.142 |
| 22 |
7 |
3.142857.. |
0.00126 |
| 333 |
106 |
3.141509.. |
8.3E-005 |
| 355 |
113 |
3.141592.. |
2.67E-007 |
|
| GCD |
GCD(a,b) or GCD(m)
Finds the Greatest Common Divisor.
a,b = numbers or vectors (must be of the same size)
or
m = matrix
Returns a number or a vector containing the GCDs
Examples :
GCD(56,98)=14
GCD({56|25},{98,40})={14|5}
GCD({56,98|25,40})={14|5} |
| LCM |
LCM(a,b) or LCM(m)
Finds the Least Common Multiple.
a,b = numbers or vectors (must be of the same size)
or
m = matrix
Returns a number or vector containing the LCMs
Examples :
LCM(56,98)=392
LCM({56|25},{98,40})={392|200}
LCM({56,98|25,40})={392|200} |
| XFactors |
XFactors(n)
Finds all the prime factors of a integer positive number.
In order to avoid errors in case n is computed, it indeed finds
the factors of int(abs(n)+.5)
Retuns a two columns matrix whose 1st column contains the prime
factors and the 2nd column the corresponding exponents.
Examples:
XFactors(648), ANS=
XFactors(2^3*3^4), ANS=
(it'd give a incorrect answer without the rounding)
Note: The main advantage of XFactors over the library script
factors is that it isn't limited to the first 32000 primes, on the
other hand it could take a long time to complete.
Reference:
The algorithm used is a modified version of the
one published in 1978 by Texas Instruments with the MU-09 Program
part of the Math/Utilities Solid State Software™ Module for
their TI Programmable 58/59 Calculators |
|