From a02d62a62febbdd204413b74a755a1bd96bd8dff Mon Sep 17 00:00:00 2001
From: lafrite <lafrite@poneyworld.net>
Date: Tue, 10 Dec 2013 21:22:15 +0100
Subject: [PATCH] Frac gene ok

---
 add_frac.py | 219 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 219 insertions(+)
 create mode 100644 add_frac.py

diff --git a/add_frac.py b/add_frac.py
new file mode 100644
index 0000000..c6fed12
--- /dev/null
+++ b/add_frac.py
@@ -0,0 +1,219 @@
+#!/usr/bin/env python
+# encoding: utf-8
+
+from random import randint, random
+
+
+
+"""Classe which generate randomly fractions sums
+
+Types of sums
+
+1 -> b / a + c / a
+2 -> b / a + c / ka
+3 -> b / a + e / d
+4 -> f + b / a or b / a + f
+
+where:
+    a integer > 2
+    b integer different from 0 (could be coprime with a)
+    c integer different from 0 (could be coprime with a or ka)
+    e integer different from 0 (could be coprime with d)
+    d integer > 2 ( a not divisible by d and d not divisible by a)
+    k integer > 2
+    f integer different from 0
+
+Signs can be mod 
+    
+
+"""
+
+def a(min_ = 2, max_ = 10):
+    """Generate randomly a
+
+    :param min_: minimum value for a
+    :param max_: maximum value for a
+    :returns: a value
+
+    """
+    return randint(min_, max_)
+
+def k(min_ = 2, max_ = 5):
+    """Generate randomly k
+
+    :param min_: minimum value for k
+    :param max_: maximum value for k
+    :returns: k value
+
+    """
+    return randint(min_, max_)
+
+def b(a_ = 0, min_ = -20, max_ = 20):
+    """Generate randomly b
+
+    :param a: the value of a if b has to be coprime with a (default 0 which means not necessarily coprime)
+    :param min_: minimum value for b (default -20)
+    :param max_: maximum value for b (default 20)
+    :returns: b value
+
+    """
+    b_ = 0
+    while b_ == 0 or not coprime:
+        b_ = randint(min_, max_)
+        if a_ == 0:
+            coprime = 1
+        elif b_ != 0:
+            gcd_ = gcd(abs(a_),abs(b_))
+            coprime = (gcd_ == 1)
+
+    return b_
+
+def c(a_ = 0, k_ = 1, min_ = -20, max_ = 20):
+    """Generate randomly c
+
+    :param a: the value of a if c has to be coprime with a (default 0 which means not necessarily coprime)
+    :param k: the value of a if c has to be coprime with ak (default 0 which means not necessarily coprime)
+    :param min_: minimum value for c (default -20)
+    :param max_: maximum value for c (default 20)
+    :returns: c value
+
+    """
+    return b(a_ = a_*k_, min_ = min_, max_ = max_)
+
+def e(d_ = 0, min_ = -20, max_ = 20):
+    """Generate randomly e
+
+    :param d: the value of a if e has to be coprime with a (default 0 which means not necessarily coprime)
+    :param min_: minimum value for e (default -20)
+    :param max_: maximum value for e (default 20)
+    :returns: e value
+
+    """
+    return b(a_ = d_, min_ = min_, max_ = max_)
+
+def d(a_, min_ = 2, max_ = 10):
+    """Generate randomly d
+
+    :param a: the value of a
+    :param min_: minimum value for d
+    :param max_: maximum value for d
+    :returns: d value
+
+    """
+    d_ = randint(min_, max_)
+    div = (not a_ % d_) or (not d_ % a_)
+    while div:
+        d_ = randint(min_, max_)
+        div = (not a_ % d_) or (not d_ % a_)
+
+    return d_
+
+def f(min_ = -10, max_ = 10):
+    """Generate randomly f
+
+    :param min_: minimum value for f
+    :param max_: maximum value for f
+    :returns: f value
+
+    """
+    f_ = randint(min_, max_)
+    while f_ == 0:
+        f_ = randint(min_, max_)
+
+    return f_
+
+def plusOrMinus(p = 0.5):
+    """Return plus with prob p and minus otherwise
+    """
+    pm = random()
+    return "+"*(pm >= p) + "-"*(pm < p)
+
+def nothingOrMinus(p = 0.5):
+    """Return nothing with prob p and minus otherwise
+    """
+    pm = random()
+    return ""*(pm >= p) + "-"*(pm < p)
+
+def type1():
+    """@todo: Docstring for type1
+    :returns: @todo
+
+    """
+    a_ = a()
+    b_ = b(a_=a_)
+    c_ = c(a_=a_)
+    
+    return nothingOrMinus() + "\\frac{" + str(b_) + "}{" + str(a_) + "}" + plusOrMinus() + "\\frac{" + str(c_) + "}{" + str(a_) + "}"
+
+def type2():
+    """@todo: Docstring for type2
+    :returns: @todo
+
+    """
+    a_ = a()
+    b_ = b(a_=a_)
+    k_ = k()
+    c_ = c(a_=a_, k_ = k_)
+    
+    return nothingOrMinus() + "\\frac{" + str(b_) + "}{" + str(a_) + "}" + plusOrMinus() + "\\frac{" + str(c_) + "}{" + str(k_*a_) + "}"
+
+def type3():
+    """@todo: Docstring for type3
+    :returns: @todo
+
+    """
+    a_ = a()
+    b_ = b(a_=a_)
+    c_ = c(a_=a_)
+    d_ = d(a_)
+    
+    return nothingOrMinus() + "\\frac{" + str(b_) + "}{" + str(a_) + "}" + plusOrMinus() + "\\frac{" + str(c_) + "}{" + str(d_) + "}"
+
+def type4():
+    """@todo: Docstring for type4
+    :returns: @todo
+
+    """
+    a_ = a()
+    b_ = b(a_=a_)
+    f_ = f()
+    
+    return str(f_) +  plusOrMinus() +  "\\frac{" + str(b_) + "}{" + str(a_) + "}"
+
+def gcd(a_, b_):
+        """Compute gcd(a,b)
+
+        :param a: first number
+        :param b: second number
+        :returns: the gcd
+
+        """
+        if a_ > b_:
+            c_ = a_ % b_
+        else:
+            c_ = b_ % a_
+
+        if c_ == 0:
+            return min(a_,b_)
+        elif a_ == 1:
+            return b_
+        elif b_ == 1:
+            return a_
+        else:
+            return gcd(min(a_,b_), c_)
+
+if __name__ == '__main__':
+    # print(a())
+    # print(b())
+    # print(c())
+    # print(d(3))
+    # print(e())
+    # print(f())
+    print(type1())
+    print(type2())
+    print(type3())
+    print(type4())
+
+# Reglages pour 'vim'
+# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
+# cursor: 16 del