formal (which should be called polynom...) are ok.No mult yet

expression.py

@@ -4,6 +4,8 @@
 from generic import Stack, flatten_list, expand_list
 from fraction import Fraction
 from render import txt_render, post2in_fix, tex_render
+from formal import FormalExp
+from formal import FormalExp
 
 class Expression(object):
     """A calculus expression. Today it can andle only expression with numbers later it will be able to manipulate unknown"""
@@ -32,7 +34,7 @@ class Expression(object):
 
     def render(self, render = lambda  x:str(x)):
         """ Same as __str__ but accept render as argument
-        @param render: function which render the list of token (postfix form) to string
+        :param render: function which render the list of token (postfix form) to string
 
         """
         # TODO: I don't like the name of this method |ven. janv. 17 12:48:14 CET 2014
@@ -44,7 +46,7 @@ class Expression(object):
     def simplify(self, render = lambda x:str(x)):
         """ Generator which return steps for computing the expression
 
-        @param render: function which render the list of token (postfix form now) to string
+        :param render: function which render the list of token (postfix form now) to string
 
         """
         if not self.can_go_further():
@@ -123,8 +125,10 @@ class Expression(object):
 
         for character in exp:
             if character.isdigit():
+                # for "big" numbers (like 2345)
                 if type(tokens[-1]) == int:
                     tokens[-1] = tokens[-1]*10 + int(character)
+
                 # Special case for "-" at the begining of an expression or before "("
                 elif tokens[-1] == "-" and \
                         str(tokens[-2]) in " (":
@@ -133,16 +137,29 @@ class Expression(object):
                     tokens.append(int(character))
 
             elif character.isalpha():
-                if str(tokens[-1]).isalpha():
+                # If "3x", ")x" or "yx"
-                    tokens[-1] += character
+                if self.isNumber(tokens[-1]) \
+                        or tokens[-1] == ")" \
+                        or type(tokens[-1]) == FormalExp:
+                    tokens.append("*")
+                    tokens.append(FormalExp(letter = character))
+
+                # Special case for "-" at the begining of an expression or before "("
+                elif tokens[-1] == "-" \
+                        or str(tokens[-2]) in " (":
+                    tokens[-1] = - FormalExp(letter = character)
+
                 else:
-                    tokens.append(character)
+                    tokens.append(FormalExp(letter = character))
 
             elif character in "+-*/)":
                 tokens.append(character)
 
             elif character in "(":
-                if self.isNumber(tokens[-1]) or tokens[-1] == ")":
+                # If "3(", ")(" or "x("
+                if self.isNumber(tokens[-1]) \
+                        or tokens[-1] == ")" \
+                        or type(tokens[-1]) == FormalExp:
                     tokens.append("*")
                 tokens.append(character)
 
@@ -278,14 +295,19 @@ class Expression(object):
         :returns: string representing the result
 
         """
-        operations = {"+": "__add__", "-": "__sub__", "*": "__mul__"}
         if op == "/":
             ans = [Fraction(op1, op2)]
             ans += ans[0].simplify()
             return ans
         else:
+            if type(op2) != int:
+                operations = {"+": "__radd__", "-": "__rsub__", "*": "__rmul__"}
+                return getattr(op2,operations[op])(op1)
+            else:
+                operations = {"+": "__add__", "-": "__sub__", "*": "__mul__"}
                 return getattr(op1,operations[op])(op2)
 
+
     ## ---------------------
     ## Recognize numbers and operators
 
@@ -299,7 +321,7 @@ class Expression(object):
         """
         return type(exp) == int or \
                 type(exp) == Fraction or \
-                exp.isalpha()
+                type(exp) == FormalExp
 
     @staticmethod
     def isOperator(exp):
@@ -322,17 +344,17 @@ def test(exp):
     print("\n")
 
 if __name__ == '__main__':
-    exp = "1 + 3 * 5"
+    #exp = "1 + 3 * 5"
-    test(exp)
+    #test(exp)
 
     #exp = "2 * 3 * 3 * 5"
     #test(exp)
 
-    exp = "2 * 3 + 3 * 5"
+    #exp = "2 * 3 + 3 * 5"
-    test(exp)
+    #test(exp)
 
-    exp = "2 * ( 3 + 4 ) + 3 * 5"
+    #exp = "2 * ( 3 + 4 ) + 3 * 5"
-    test(exp)
+    #test(exp)
 
     #exp = "2 * ( 3 + 4 ) + ( 3 - 4 ) * 5"
     #test(exp)
@@ -352,25 +374,29 @@ if __name__ == '__main__':
     #exp = "( 2 + 5 ) * ( 3 * 4 )"
     #test(exp)
 
-    exp = "( 2 + 5 - 1 ) / ( 3 * 4 )"
+    #exp = "( 2 + 5 - 1 ) / ( 3 * 4 )"
-    test(exp)
+    #test(exp)
 
-    exp = "( 2 + 5 ) / ( 3 * 4 ) + 1 / 12"
+    #exp = "( 2 + 5 ) / ( 3 * 4 ) + 1 / 12"
-    test(exp)
+    #test(exp)
 
-    exp = "( 2+ 5 )/( 3 * 4 ) + 1 / 2"
+    #exp = "( 2+ 5 )/( 3 * 4 ) + 1 / 2"
-    test(exp)
+    #test(exp)
 
-    exp="(-2+5)/(3*4)+1/12+5*5"
+    #exp="(-2+5)/(3*4)+1/12+5*5"
-    test(exp)
+    #test(exp)
 
     exp="-2*4(12 + 1)(3-12)"
     test(exp)
 
-    exp="-2*a(12 + 1)(3-12)"
+    exp="-2+a+(12 + 1)(3-12) + 34a"
+    test(exp)
     e = Expression(exp)
     print(e)
 
+    #exp="-2*b+a(12 + 1)(3-12)"
+    #test(exp)
+
     # TODO: The next one doesn't work  |ven. janv. 17 14:56:58 CET 2014
     #exp="-2*(-a)(12 + 1)(3-12)"
     #e = Expression(exp)

formal.py

@@ -0,0 +1,128 @@
+#!/usr/bin/env python
+# encoding: utf-8
+
+from fraction import Fraction
+from generic import add_in_dict, remove_in_dict
+import re
+
+class FormalExp(object):
+    """A formal expression (similare to Symbol in Sympy"""
+
+    def __init__(self, coef = {}, letter = ""):
+        """Initiat the formal expression
+
+        :param coef: the dictionary representing the expression
+        :param letter:  minimum expression, a letter 
+
+        """
+
+        if coef != {} and letter != "":
+            raise ValueError("A FormalExp can't be initiate with dict_exp and a letter")
+        elif letter != "":
+            self._letter = letter
+            self._coef = {letter: 1}
+        elif coef != {}:
+            self._coef = coef
+        else:
+            raise ValueError("FormalExp needs a letter or dictionary of coeficients")
+
+        if len(self) != 1:
+            self.mainOp = "+"
+
+    def master_coef(self):
+        """Return the master coefficient
+        /!\ may not work pretty well if there is more than one indeterminate
+        :returns: a_n
+
+        """
+        pattern = "\w\*\*(\d*)"
+        finder = re.compile(pattern)
+        power = {}
+        for (k,v) in self._coef.items():
+            if k=="":
+                power[0] = v
+            else:
+                p = finder.findall(k)
+                if p == []:
+                    power[1] = v
+                else:
+                    power[int(p[0])] =  v
+
+        m_power = max(power)
+        return power[m_power]
+
+    def __add__(self, other):
+        if type(other) in [int, Fraction]:
+            d = {"":other}
+        elif type(other) == FormalExp:
+            d = other._coef
+        else:
+            raise ValueError("Can't add {type} with FormalExp".format(type=type(other)))
+
+        d = add_in_dict(self._coef, d)
+        d = remove_in_dict(d)
+        if list(d.keys()) == ['']:
+            return [d['']]
+        else:
+            return [FormalExp(d)]
+
+    def __radd__(self, other):
+        return self + other
+
+    def __sub__(self, other):
+        o_tmp = -other
+        return self + o_tmp
+
+    def __neg__(self):
+        d = {}
+        for k,v in self._coef.items():
+            d[k] = -v
+        return FormalExp(d)    
+
+    def __mul__(self, other):
+        pass
+    
+    def __rmul__(self, other):
+        pass
+
+    def __div__(self, other):
+        pass
+    
+    def __pow__(self, other):
+        pass
+
+    def __len__(self):
+        return len(list(self._coef.keys()))
+
+    def __str__(self):
+        return " + ".join([str(v) + str(k) for k,v in self._coef.items()])
+    
+if __name__ == '__main__':
+    #fe1 = FormalExp({"x": 1, "":2})    
+    #print(fe1)
+    #fe2 = FormalExp({"x**12": 5, "":2})    
+    #print(fe2)
+    #fe3 = fe1 + fe2
+    #for s in fe3:
+    #    print(s)
+    #fe4 = fe1 + 2
+    #for s in fe4:
+    #    print(s)
+
+    #print(fe1.master_coef())
+    #print(fe2.master_coef())
+    #print(fe3[0].master_coef())
+    #print(fe4[0].master_coef())
+
+    fe = FormalExp(letter = "a")
+    fe_ = -2 + fe
+    print(fe_[0])
+
+
+
+
+
+# -----------------------------
+# Reglages pour 'vim'
+# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
+# cursor: 16 del 

generic.py

@@ -99,6 +99,54 @@ def expand_list(list_list):
         ans = [list_list]
 
     return ans
+
+def add_in_dict(dict1, dict2):
+    """Merge dictionary keys and add the content from dict1 and dict2
+
+    :param dict1: first dictionary
+    :param dict2: second dictionary
+    :returns: merged and added dictionary
+
+    >>> add_in_dict({'a':1, 'b':2}, {'c':3, 'd': 4}) == {'d': 4, 'a': 1, 'c': 3, 'b': 2}
+    True
+    >>> add_in_dict({'a':1, 'b':2}, {'a':3, 'b': 4}) == {'a': 4, 'b': 6}
+    True
+    >>> add_in_dict({'a':1, 'b':2}, {'a':3, 'c': 4}) == {'a': 4, 'b': 2, 'c': 4}
+    True
+
+    """
+    new_dict = {}
+    new_dict.update(dict1)
+    for (k,v) in dict2.items():
+        if k in new_dict.keys():
+            new_dict[k] += v
+        else:
+            new_dict[k] = v
+
+    return new_dict
+
+def remove_in_dict(d, value = 0):
+    """ In a dictionary, remove keys which have certain value
+
+    :param d: the dictionary
+    :param value: value to remove
+    :returns: new dictionary whithout unwanted value
+
+    >>> remove_in_dict({'b': 1, 'a': 0}) == {'b': 1}
+    True
+    >>> remove_in_dict({'b': 1, 'a': 0}, 1) == {'a': 0}
+    True
+    """
+    new_dict = {}
+    for (k,v) in d.items():
+        if v != value:
+            new_dict[k] = v
+    return new_dict
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()
+
 # -----------------------------
 # Reglages pour 'vim'
 # vim:set autoindent expandtab tabstop=4 shiftwidth=4:

render.py

@@ -3,6 +3,7 @@
 
 from generic import Stack,flatten_list
 from fraction import Fraction
+from formal import FormalExp
 
         
 
@@ -16,7 +17,7 @@ class Render(object):
 
     PRIORITY = {"*" : 3, "/": 3, "+": 2, "-":2, "(": 1}
 
-    def __init__(self, op_infix = {}, op_postfix = {}, other = {}, join = " ", type_render = {int: str, Fraction: str, str: str}):
+    def __init__(self, op_infix = {}, op_postfix = {}, other = {}, join = " ", type_render = {int: str, Fraction: str, FormalExp: str}):
         """Initiate the render
         
         @param op_infix: the dictionnary of infix operator with how they have to be render
@@ -71,11 +72,12 @@ class Render(object):
             else:
                 operandeStack.push(token)
 
+            
         # Manip pour gerer les cas de listes imbriquées dans d'autres listes
         infix_tokens = operandeStack.pop()
         if type(infix_tokens) == list or type(infix_tokens) == flist:
             infix_tokens = flatten_list(infix_tokens)
-        elif self.isNumber(infix_tokens):
+        elif self.isNumerande(infix_tokens):
             infix_tokens = [infix_tokens]
 
         if self.join:
@@ -84,13 +86,13 @@ class Render(object):
             return infix_tokens
 
     def render_from_type(self, op):
-        """ If the op is a number, it transforms it with type_render conditions
+        """ If the op is a numerande, it transforms it with type_render conditions
 
         :param op: the operator
         :returns: the op transformed if it's necessary
 
         """
-        if self.isNumber(op):
+        if self.isNumerande(op):
             return self.type_render[type(op)](op)
         else:
             return op
@@ -108,9 +110,17 @@ class Render(object):
         :returns: bollean
         """
         if self.isNumber(operande) \
-                and type(operande) != str \
                 and operande < 0:
             return 1
+            
+        elif type(operande) == FormalExp:
+            if operator in ["*", "/"]:
+                if len(operande) > 1 \
+                        or operande.master_coef() < 0:
+                    return 1
+            else:
+                return 0
+
         elif not self.isNumber(operande):
             # Si c'est une grande expression ou un chiffre négatif
             stand_alone = self.get_main_op(operande)
@@ -155,17 +165,28 @@ class Render(object):
 
     @staticmethod
     def isNumber( exp):
-        """Check if the expression can be a number which means that it is not a operator
+        """Check if the expression can be a number which means int or Fraction
 
         :param exp: an expression
         :returns: True if the expression can be a number and false otherwise
 
         """
-        return type(exp) == int or \
+        return type(exp) == int \
-                type(exp) == Fraction or \
+                or type(exp) == Fraction
-                (type(exp) == str and exp.isalpha())
         #return type(exp) == int or type(exp) == Fraction
 
+    @staticmethod
+    def isNumerande(exp):
+        """Check if the expression can be a numerande (not an operator)
+
+        :param exp: an expression
+        :returns: True if the expression can be a number and false otherwise
+
+        """
+        return type(exp) == int \
+                or type(exp) == Fraction \
+                or type(exp) == FormalExp
+
     def isOperator(self, exp):
         """Check if the expression is in self.operators
 
@@ -202,9 +223,9 @@ post2in_fix = Render(p2i_infix, p2i_postfix, p2i_other, join = False)
 # A latex render
 
 def texSlash(op1, op2):
-    if not Render.isNumber(op1) and op1[0] == "(" and op1[-1] == ")":
+    if not Render.isNumerande(op1) and op1[0] == "(" and op1[-1] == ")":
         op1 = op1[1:-1]
-    if not Render.isNumber(op2) and op2[0] == "(" and op2[-1] == ")":
+    if not Render.isNumerande(op2) and op2[0] == "(" and op2[-1] == ")":
         op2 = op2[1:-1]
     return ["\\frac{" , op1 , "}{" , op2 , "}"]
 
@@ -214,7 +235,7 @@ def texFrac(frac):
 tex_infix = {"+": " + ", "-": " - ", "*": " \\times "}
 tex_postfix = {"/": texSlash}
 tex_other = {"(": "(", ")": ")"}
-tex_type_render = {int: str, Fraction: texFrac, str: str}
+tex_type_render = {int: str, Fraction: texFrac, FormalExp: str}
 
 tex_render = Render(tex_infix, tex_postfix, tex_other, type_render = tex_type_render)