Create Equation and solutions methods

pymath/calculus/equation.py

@@ -0,0 +1,180 @@
+#!/usr/bin/env python
+# encoding: utf-8
+
+
+from .expression import Expression
+from .polynom import Polynom
+from .fraction import Fraction
+
+from .random_expression import RdExpression
+
+__all__ = ['Equation']
+
+
+class Equation(object):
+    """A calculus expression. Today it can andle only expression with numbers later it will be able to manipulate unknown"""
+
+#    @classmethod
+#    def random(self, form="", conditions=[], val_min=-10, val_max=10):
+#        """Create a random expression from form and with conditions
+#
+#        :param form: the form of the expression (/!\ variables need to be in brackets {})
+#        :param conditions: condition on variables (/!\ variables need to be in brackets {})
+#        :param val_min: min value for generate variables
+#        :param val_max: max value for generate variables
+#
+#        """
+#        random_generator = RdExpression(form, conditions)
+#        return Expression(random_generator(val_min, val_max))
+#
+
+    def __init__(self, exp_str = "", left_poly = Expression([0]), right_poly = Expression([0])):
+        """Create the equation
+
+        :param exp_str: the equality string which represent the equation
+        :param left_poly: the left polynom of the equation
+        :param right_poly: the right polynom of the equation
+
+        >>> e = Equation("2x+3 = 4x+5")
+        >>> e
+        < Equation [2 x + 3, 4 x + 5]>
+        >>> Pl = Polynom([1, 2])
+        >>> Pr = Polynom([3, 4])
+        >>> e = Equation(left_poly = Pl)
+        >>> e
+        < Equation [2 x + 1, 0]>
+        >>> e = Equation(right_poly = Pr)
+        >>> e
+        < Equation [0, 4 x + 3]>
+        >>> e = Equation(left_poly = Pl, right_poly = Pr)
+        >>> e
+        < Equation [2 x + 1, 4 x + 3]>
+
+        """
+        if exp_str:
+            l_part, r_part = exp_str.split("=")
+            self.l_exp = Expression(l_part)
+            self.r_exp = Expression(r_part)
+        else:
+            self.l_exp = left_poly
+            self.r_exp = right_poly
+
+        self.smpl_each_part()
+
+    def smpl_each_part(self):
+        """ Simplify left and right part, transform them into polynom and stock them in smpl_*_exp 
+        """
+        self.smpl_l_exp = self.l_exp.simplify()
+        self.smpl_r_exp = self.r_exp.simplify()
+
+        try:
+            self.smpl_r_exp = self.smpl_l_exp.conv2poly(self.smpl_r_exp) 
+        except AttributeError:
+            pass
+
+        try:
+            self.smpl_l_exp = self.smpl_r_exp.conv2poly(self.smpl_l_exp)
+        except AttributeError:
+            raise EquationError("None of left and right parts are polynoms. \
+                    Can't use it to make an equation.")
+
+        # TODO: On pourrait rajouter des tests sur les inconnues |mar. mars 22 10:17:12 EAT 2016
+
+    def __str__(self):
+        return str(self.l_exp) + " = " + str(self.r_exp)
+
+    def __repr__(self):
+        return "< {cls} [{l}, {r}]>".format(
+                cls = str(self.__class__).split('.')[-1][:-2],
+                l = self.l_exp,
+                r = self.r_exp,
+                )
+
+    def solve(self):
+        """Solve the equation but yielding each steps
+
+        """
+        pass
+
+    def solution(self):
+        """Return the solution of the equation
+
+        :returns: the solution
+
+        >>> e = Equation("2x + 1 = x + 2") 
+        >>> e.solution()
+        1
+        >>> e = Equation("2x + 1 = 1") 
+        >>> e.solution()
+        0
+        >>> e = Equation("1 = 2x + 1") 
+        >>> e.solution()
+        0
+        >>> e = Equation("3x = 2x") 
+        >>> e.solution()
+        0
+        >>> e = Equation("3x + 1 = 0") 
+        >>> e.solution()
+        < Fraction -1 / 3>
+        >>> e = Equation("6x + 2 = 0") 
+        >>> e.solution()
+        < Fraction -1 / 3>
+
+        """
+        num = self.smpl_r_exp._coef[0] - self.smpl_l_exp._coef[0]
+
+        try:
+            denom = self.smpl_l_exp._coef[1]
+        except IndexError:
+            denom = 0
+        try:
+            denom -= self.smpl_r_exp._coef[1]
+        except IndexError:
+            pass
+
+        if denom == 0 and num == 0:
+            raise EquationError("All number are solution")
+        elif denom == 0:
+            raise NoSolutionError("This equation has no solution")
+
+        return Fraction(num, denom).simplify()
+
+    def is_solution(self, num):
+        """ Tell if a number is a solution.
+
+        :param num: the number to test
+
+        >>> e = Equation("2x + 1 = x + 2")
+        >>> e.is_solution(2)
+        False
+        >>> e.is_solution(1)
+        True
+        >>> e = Equation("3x = 2x") 
+        >>> e.is_solution(1)
+        False
+        >>> e.is_solution(0)
+        True
+        >>> e = Equation("3x + 1 = 0") 
+        >>> e.is_solution(0)
+        False
+        >>> e.is_solution(Fraction(-1, 3))
+        True
+        >>> e.is_solution(Fraction(-2, 6))
+        True
+        
+        """
+        l_part = self.smpl_l_exp.replace_letter(num).simplify()
+        r_part = self.smpl_r_exp.replace_letter(num).simplify()
+        return l_part == r_part
+
+class EquationError(Exception):
+    pass
+
+
+class NoSolutionError(EquationError):
+    pass
+
+# -----------------------------
+# Reglages pour 'vim'
+# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
+# cursor: 16 del