1  Multiple-precision Rationals
 2  ============================
 3  
 4  gmpy2 provides a rational type call *mpq*. It should be a replacement for
 5  Python's fractions.Fraction module.
 6  
 7  ::
 8  
 9      >>> import gmpy2
10      >>> from gmpy2 import mpq
11      >>> mpq(1,7)
12      mpq(1,7)
13      >>> mpq(1,7) * 11
14      mpq(11,7)
15      >>> mpq(11,7)/13
16      mpq(11,91)
17  
18  mpq Methods
19  -----------
20  
21  **digits(...)**
22      x.digits([base=10]) returns a Python string representing *x* in the
23      given base (2 to 62, default is 10). A leading '-' is present if *x* < 0,
24      but no leading '+' is present if *x* >= 0.
25  
26  mpq Attributes
27  --------------
28  
29  **denominator**
30      x.denominator returns the denominator of *x*.
31  
32  **numerator**
33      x.numerator returns the numerator of *x*.
34  
35  mpq Functions
36  -------------
37  
38  **add(...)**
39      add(x, y) returns *x* + *y*. The result type depends on the input
40      types.
41  
42  **div(...)**
43      div(x, y) returns *x* / *y*. The result type depends on the input
44      types.
45  
46  **f2q(...)**
47      f2q(x[, err]) returns the best *mpq* approximating *x* to within
48      relative error *err*. Default is the precision of *x*. If *x* is not an
49      *mpfr*, it is converted to an *mpfr*. Uses Stern-Brocot tree to find the
50      best approximation. An *mpz* is returned if the denominator is 1. If
51      *err* < 0, then the relative error sought is 2.0 ** *err*.
52  
53  **mpq(...)**
54      mpq() returns an *mpq* object set to 0/1.
55  
56      mpq(n) returns an *mpq* object with a numeric value *n*. Decimal and
57      Fraction values are converted exactly.
58  
59      mpq(n, m) returns an *mpq* object with a numeric value *n* / *m*.
60  
61      mpq(s[, base=10]) returns an *mpq* object from a string *s* made up of
62      digits in the given base. *s* may be made up of two numbers in the same
63      base separated by a '/' character. If *base* == 10, then an embedded '.'
64      indicates a number with a decimal fractional part.
65  
66  **mul(...)**
67      mul(x, y) returns *x* \* *y*. The result type depends on the input
68      types.
69  
70  **qdiv(...)**
71      qdiv(x[, y=1]) returns *x/y* as *mpz* if possible, or as *mpq* if *x*
72      is not exactly divisible by *y*.
73  
74  **sub(...)**
75      sub(x, y) returns *x* - *y*. The result type depends on the input
76      types.
77  
78  
79  
80