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Find a rational approximation of x to within the tolerance defined by tol.
If unspecified, the default tolerance is 1e-6 * norm (x(:), 1)
.
When called with one output argument, return a string containing a continued fraction expansion (multiple terms).
When called with two output arguments, return numeric matrices for the
numerator and denominator of a fractional representation of x such
that x = n ./ d
.
For example:
s = rat (pi) ⇒ s = 3 + 1/(7 + 1/16) [n, d] = rat (pi) ⇒ n = 355 ⇒ d = 113 n / d - pi ⇒ 0.00000026676
Programming Note: With one output rat
produces a string which is a
continued fraction expansion. To produce a string which is a simple
fraction (one numerator, one denominator) use rats
.
Convert x into a rational approximation represented as a string.
The string can be converted back into a matrix as follows:
r = rats (hilb (4)); x = str2num (r)
The optional second argument defines the maximum length of the string representing the elements of x. By default len is 9.
If the length of the smallest possible rational approximation exceeds len, an asterisk (*) padded with spaces will be returned instead.