split polynom with abstract_polynom

pymath/abstract_polynom.py

@@ -0,0 +1,571 @@
+#!/usr/bin/env python
+# encoding: utf-8
+
+from .explicable import Explicable
+from .expression import Expression
+from .operator import op
+from .generic import spe_zip, expand_list, isNumber, transpose_fill, flatten_list, isPolynom, isNumerand
+from .render import txt,tex
+from itertools import chain
+from functools import wraps
+
+def power_cache(fun):
+    """Decorator which cache calculated powers of polynoms """
+    cache  = {}
+    @wraps(fun)
+    def cached_fun(self, power):
+        #print("cache -> ", cache)
+        if (tuple(self._coef), power) in cache.keys():
+            return cache[(tuple(self._coef), power)]
+        else:
+            poly_powered = fun(self, power)
+            cache[(tuple(self._coef), power)] = poly_powered
+            return poly_powered
+    return cached_fun
+
+class AbstractPolynom(Explicable):
+
+    """The mathematic definition of a polynom. It will be the parent class of Polynom (classical polynoms) and later of SquareRoot polynoms"""
+
+    def __init__(self, coefs = [1], letter = "x", name = "P"):
+        """Initiate the polynom
+
+        :param coef: coefficients of the polynom (ascending degree sorted)
+            3 possibles type of coefficent:
+                - a : simple "number". [1,2] designate 1 + 2x
+                - [a,b,c]: list of coeficient for same degree. [1,[2,3],4] designate 1 + 2x + 3x + 4x^2
+                - a: a Expression. [1, Expression("2+3"), 4] designate 1 + (2+3)x + 4x^2
+        :param letter: the string describing the unknown
+        :param name: Name of the polynom
+
+        >>> P = AbstractPolynom([1, 2, 3])
+        >>> P.mainOp
+        '+'
+        >>> P.name
+        'P'
+        >>> P._letter
+        'x'
+        >>> AbstractPolynom([1]).mainOp
+        '*'
+        >>> AbstractPolynom([0, 0, 3]).mainOp
+        '*'
+        >>> AbstractPolynom([1, 2, 3])._letter
+        'x'
+        >>> AbstractPolynom([1, 2, 3], "y")._letter
+        'y'
+        >>> AbstractPolynom([1, 2, 3], name = "Q").name
+        'Q'
+        """
+        super(AbstractPolynom, self).__init__()
+        self.feed_coef(coefs)
+        self._letter = letter
+        self.name = name
+        
+        if self.is_monom():
+            self.mainOp = op.mul
+        else:
+            self.mainOp = op.add
+
+        self._isPolynom = 1
+
+    def feed_coef(self, l_coef):
+        """Feed coef of the polynom. Manage differently whether it's a number or an expression
+        
+        :l_coef: list of coef
+        """
+        self._coef = []
+        for coef in l_coef:
+            if type(coef) == list and len(coef)==1:
+                self._coef.append(coef[0])
+            else:
+                self._coef.append(coef)
+
+    @property
+    def degree(self):
+        """Getting the degree fo the polynom
+
+        :returns: the degree of the polynom
+
+        >>> AbstractPolynom([1, 2, 3]).degree
+        2
+        >>> AbstractPolynom([1]).degree
+        0
+        """
+        return len(self._coef) - 1
+
+    def is_monom(self):
+        """is the polynom a monom (only one coefficent)
+
+        :returns: 1 if yes 0 otherwise
+
+        >>> AbstractPolynom([1, 2, 3]).is_monom()
+        0
+        >>> AbstractPolynom([1]).is_monom()
+        1
+        """
+        if len([i for i in self._coef if i != 0])==1:
+            return 1
+        else:
+            return 0
+
+    def give_name(self, name):
+        self.name = name
+
+    def __str__(self):
+        return str(Expression(self.postfix_tokens))
+
+    def __repr__(self):
+        return  "< " + str(self.__class__) + " " + str(self._coef) + ">"
+
+    def __txt__(self):
+        return txt(self.postfix_tokens)
+
+    def __tex__(self):
+        return tex(self.postfix_tokens)
+
+    def coef_postfix(self, a, i):
+        """Return the postfix display of a coeficient
+
+        :param a: value for the coeficient (/!\ as a postfix list)
+        :param i: power
+        :returns: postfix tokens of coef
+
+        >>> p = AbstractPolynom()
+        >>> p.coef_postfix([3],2)
+        [3, 'x', 2, '^', '*']
+        >>> p.coef_postfix([0],1)
+        []
+        >>> p.coef_postfix([3],0)
+        [3]
+        >>> p.coef_postfix([3],1)
+        [3, 'x', '*']
+        >>> p.coef_postfix([1],1)
+        ['x']
+        >>> p.coef_postfix([1],2)
+        ['x', 2, '^']
+
+        """
+        # TODO: Couille certaine avec txt à qui il fait donner des opérateurs tout beau! |mar. nov. 11 13:08:35 CET 2014
+        ans =[] 
+        if a == [0]:
+            pass
+        elif i == 0:
+            ans = a
+        elif i == 1:
+            ans = a * (a!=[1]) + [self._letter] + [op.mul] *  (a!=[1]) 
+        else:
+            ans = a * (a!=[1]) + [self._letter, i, op.pw] + [op.mul] *  (a!=[1]) 
+        
+        return ans
+
+    @property
+    def postfix_tokens(self):
+        """Return the postfix form of the polynom
+
+        :returns: the postfix list of polynom's tokens
+
+        >>> p = AbstractPolynom([1, 2])
+        >>> p.postfix_tokens
+        [2, 'x', '*', 1, '+']
+        >>> p = AbstractPolynom([1, -2])
+        >>> p.postfix_tokens
+        [2, 'x', '*', '-', 1, '+']
+        >>> p = AbstractPolynom([1,2,3])
+        >>> p.postfix_tokens
+        [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+']
+        >>> p = AbstractPolynom([1])
+        >>> p.postfix_tokens
+        [1]
+        >>> p = AbstractPolynom([0])
+        >>> p.postfix_tokens
+        [0]
+        >>> p = AbstractPolynom([1,[2,3]])
+        >>> p.postfix_tokens
+        [2, 'x', '*', 3, 'x', '*', '+', 1, '+']
+        >>> p = AbstractPolynom([1,[2,-3]])
+        >>> p.postfix_tokens
+        [2, 'x', '*', 3, 'x', '*', '-', 1, '+']
+        >>> p = AbstractPolynom([1,[-2,-3]])
+        >>> p.postfix_tokens
+        [2, 'x', '*', '-', 3, 'x', '*', '-', 1, '+']
+        >>> from pymath.expression import Expression
+        >>> from pymath.operator import op
+        >>> e = Expression([2,3,op.add])
+        >>> p = AbstractPolynom([1,e])
+        >>> p.postfix_tokens
+        [2, 3, '+', 'x', '*', 1, '+']
+
+        """
+        if self == 0:
+            return [0]
+        # TODO: Faudrait factoriser un peu tout ça..! |dim. déc. 21 16:02:34 CET 2014
+        postfix = []
+        for (i,a) in list(enumerate(self._coef))[::-1]:
+            operator = [op.add]
+            operator_sub1 = []
+            if type(a) == Expression:
+                # case coef is an arithmetic expression
+                c = self.coef_postfix(a.postfix_tokens,i)
+                if c != []:
+                    postfix.append(c)
+                    if len(postfix) > 1:
+                        postfix += operator
+
+            elif type(a) == list:
+                # case need to repeat the x^i
+                for b in a:
+                    operator = [op.add]
+                    operator_sub1 = []
+                    if len(postfix) == 0 and isNumber(b) and b < 0:
+                        try:
+                            b = [(-b)[-1]]
+                        except TypeError:
+                            b = [-b]
+                        operator_sub1 = [op.sub1]
+                    elif len(postfix) > 0 and isNumber(b) and b < 0:
+                        try:
+                            b = [(-b)[-1]]
+                        except TypeError:
+                            b = [-b]
+                        operator = [op.sub]
+                    else:
+                        b = [b]
+                    c = self.coef_postfix(b,i)
+                    if c != []:
+                        postfix.append(c)
+                        if len(postfix) > 1:
+                            postfix += operator_sub1
+                            postfix += operator
+                        postfix += operator_sub1
+
+            elif a != 0:
+                if len(postfix) == 0 and a < 0:
+                    try:
+                        a = [(-a)[-1]]
+                    except TypeError:
+                        a = [-a]
+                    operator_sub1 = [op.sub1]
+                elif len(postfix) > 0 and a < 0:
+                    try:
+                        a = [(-a)[-1]]
+                    except TypeError:
+                        a = [-a]
+                    operator = [op.sub]
+                else:
+                    a = [a]
+
+                c = self.coef_postfix(a,i)
+                if c != []:
+                    postfix.append(c)
+                    if len(postfix) > 1:
+                        postfix += operator_sub1
+                        postfix += operator
+                    postfix += operator_sub1
+
+        return flatten_list(postfix)
+
+    def conv2poly(self, other):
+        """Convert anything number into a polynom
+        
+        >>> P = AbstractPolynom([1,2,3])
+        >>> P.conv2poly(1)
+        < AbstractPolynom [1]>
+        >>> P.conv2poly(0)
+        < AbstractPolynom [0]>
+        
+        """
+        if isNumber(other) and not isPolynom(other):
+            return AbstractPolynom([other], letter = self._letter)
+        elif isPolynom(other):
+            return other
+        else:
+            raise ValueError(type(other) + " can't be converted into a polynom")
+    
+    def reduce(self):
+        """Compute coefficients which have same degree
+
+        :returns: new AbstractPolynom with numbers coefficients
+
+        >>> P = AbstractPolynom([1,2,3])
+        >>> Q = P.reduce()
+        >>> Q
+        < AbstractPolynom [1, 2, 3]>
+        >>> Q.steps
+        []
+        >>> P = AbstractPolynom([[1,2], [3,4,5], 6])
+        >>> Q = P.reduce()
+        >>> Q
+        < AbstractPolynom [3, 12, 6]>
+        >>> Q.steps
+        [< AbstractPolynom [< <class 'pymath.expression.Expression'> [1, 2, '+'] >, < <class 'pymath.expression.Expression'> [3, 4, '+', 5, '+'] >, 6]>, < AbstractPolynom [< <class 'pymath.expression.Expression'> [1, 2, '+'] >, < <class 'pymath.expression.Expression'> [7, 5, '+'] >, 6]>, < AbstractPolynom [3, < <class 'pymath.expression.Expression'> [7, 5, '+'] >, 6]>]
+        """
+    
+        # TODO: It doesn't not compute quick enough |ven. févr. 27 18:04:01 CET 2015
+
+        # gather steps for every coeficients
+        coefs_steps = []
+        for coef in self._coef:
+            coef_steps = []
+            if type(coef) == list:
+                # On converti en postfix avec une addition
+                postfix_add = self.postfix_add([i for i in coef if i!=0])
+                # On converti en Expression
+                coef_exp = Expression(postfix_add)
+
+                with Expression.tmp_render():
+                    coef_steps = list(coef_exp.simplify().explain())
+
+                #print('\t 1.coef_steps -> ', coef_steps)
+
+            elif type(coef) == Expression:
+
+                with Expression.tmp_render():
+                    coef_steps = list(coef.simplify().explain())
+
+                #print('\t 2.coef_steps -> ', coef_steps)
+
+            else:
+                try:
+                    with Expression.tmp_render():
+                        coef_steps += coef.simplify().explain()
+                except AttributeError:
+                    coef_steps = [coef]
+
+                #print('\t 3.coef_steps -> ', coef_steps)
+            # On ajoute toutes ces étapes
+            coefs_steps.append(coef_steps)
+
+        #print('\t coefs_steps -> ', coefs_steps)
+
+        # On retourne la matrice
+        steps = []
+        for coefs in transpose_fill(coefs_steps):
+            steps.append(AbstractPolynom(coefs, self._letter))
+
+        ans, steps = steps[-1], steps[:-1]
+        ans.steps = steps
+            
+        return ans
+
+    def simplify(self):
+        """Same as reduce """
+        return self.reduce()
+
+    @staticmethod
+    def postfix_add(numbers):
+        """Convert a list of numbers into a postfix addition
+        
+        :numbers: list of numbers
+        :returns: Postfix list of succecive attition of number
+
+        >>> AbstractPolynom.postfix_add([1])
+        [1]
+        >>> AbstractPolynom.postfix_add([1, 2])
+        [1, 2, '+']
+        >>> AbstractPolynom.postfix_add([1, 2, 3])
+        [1, 2, '+', 3, '+']
+        >>> AbstractPolynom.postfix_add(1)
+        [1]
+        >>> AbstractPolynom.postfix_add([])
+        [0]
+        """
+        if not type(numbers) == list:
+            return [numbers]
+        elif numbers == []:
+            return [0]
+        else:
+            ans = [[a, op.add] if i!=0 else [a] for (i,a) in enumerate(numbers)]
+            return list(chain.from_iterable(ans))
+            
+    def __eq__(self, other):
+        try:
+            o_poly = self.conv2poly(other)
+            return self._coef == o_poly._coef
+        except TypeError:
+            return 0
+
+    def __add__(self, other):
+        """ Overload + 
+
+        >>> P = AbstractPolynom([1,2,3])
+        >>> Q = AbstractPolynom([4,5])
+        >>> R = P+Q
+        >>> R
+        < AbstractPolynom [5, 7, 3]>
+        >>> R.steps
+        [< <class 'pymath.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', 5, 'x', '*', 4, '+', '+'] >, < AbstractPolynom [< <class 'pymath.expression.Expression'> [1, 4, '+'] >, < <class 'pymath.expression.Expression'> [2, 5, '+'] >, 3]>, < AbstractPolynom [< <class 'pymath.expression.Expression'> [1, 4, '+'] >, < <class 'pymath.expression.Expression'> [2, 5, '+'] >, 3]>]
+        """
+        o_poly = self.conv2poly(other)
+
+        n_coef = spe_zip(self._coef, o_poly._coef)
+        p = AbstractPolynom(n_coef, letter = self._letter)
+
+        ini_step = [Expression(self.postfix_tokens + o_poly.postfix_tokens + [op.add])]
+        ans = p.simplify()
+        ans.steps = ini_step + ans.steps
+        return ans
+
+    def __radd__(self, other):
+        o_poly = self.conv2poly(other)
+        return o_poly.__add__(self)
+
+    def __neg__(self):
+        """ overload - (as arity 1 operator)
+
+        >>> P = AbstractPolynom([1,2,3])
+        >>> Q = -P
+        >>> Q
+        < AbstractPolynom [-1, -2, -3]>
+        >>> Q.steps
+        [< <class 'pymath.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', '-'] >]
+        """
+        ini_step = [Expression(self.postfix_tokens + [op.sub1])]
+        ans = AbstractPolynom([-i for i in self._coef], letter = self._letter).simplify()
+        ans.steps = ini_step + ans.steps
+        return ans
+
+    def __sub__(self, other):
+        """ overload -
+
+        >>> P = AbstractPolynom([1,2,3])
+        >>> Q = AbstractPolynom([4,5,6])
+        >>> R = P - Q
+        >>> R
+        < AbstractPolynom [-3, -3, -3]>
+        >>> R.steps
+        [< <class 'pymath.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', 6, 'x', 2, '^', '*', 5, 'x', '*', '+', 4, '+', '-'] >, < <class 'pymath.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', 6, 'x', 2, '^', '*', '-', 5, 'x', '*', '-', 4, '-', '+'] >, < AbstractPolynom [< <class 'pymath.expression.Expression'> [1, -4, '+'] >, < <class 'pymath.expression.Expression'> [2, -5, '+'] >, < <class 'pymath.expression.Expression'> [3, -6, '+'] >]>, < AbstractPolynom [< <class 'pymath.expression.Expression'> [1, -4, '+'] >, < <class 'pymath.expression.Expression'> [2, -5, '+'] >, < <class 'pymath.expression.Expression'> [3, -6, '+'] >]>]
+        """
+        o_poly = self.conv2poly(other)
+        ini_step = [Expression(self.postfix_tokens + o_poly.postfix_tokens + [op.sub])]
+        o_poly = -o_poly
+        #ini_step += o_poly.steps
+
+        ans = self + o_poly
+        ans.steps = ini_step + ans.steps
+
+        return ans
+
+    def __rsub__(self, other):
+        o_poly = self.conv2poly(other)
+        
+        return o_poly.__sub__(self)
+    
+    def __mul__(self, other):
+        """ Overload *
+
+        >>> p = AbstractPolynom([1,2])
+        >>> p*3
+        < AbstractPolynom [3, 6]>
+        >>> (p*3).steps
+        [[< <class 'pymath.expression.Expression'> [2, 'x', '*', 1, '+', 3, '*'] >], < AbstractPolynom [3, < <class 'pymath.expression.Expression'> [2, 3, '*'] >]>, < AbstractPolynom [3, < <class 'pymath.expression.Expression'> [2, 3, '*'] >]>]
+        >>> q = AbstractPolynom([0,0,4])
+        >>> q*3
+        < AbstractPolynom [0, 0, 12]>
+        >>> (q*3).steps
+        [[< <class 'pymath.expression.Expression'> [4, 'x', 2, '^', '*', 3, '*'] >], < AbstractPolynom [0, 0, < <class 'pymath.expression.Expression'> [4, 3, '*'] >]>, < AbstractPolynom [0, 0, < <class 'pymath.expression.Expression'> [4, 3, '*'] >]>]
+        >>> r = AbstractPolynom([0,1])
+        >>> r*3
+        < AbstractPolynom [0, 3]>
+        >>> (r*3).steps
+        [[< <class 'pymath.expression.Expression'> ['x', 3, '*'] >]]
+        >>> p*q
+        < AbstractPolynom [0, 0, 4, 8]>
+        >>> (p*q).steps
+        [[< <class 'pymath.expression.Expression'> [2, 'x', '*', 1, '+', 4, 'x', 2, '^', '*', '*'] >], < AbstractPolynom [0, 0, 4, < <class 'pymath.expression.Expression'> [2, 4, '*'] >]>, < AbstractPolynom [0, 0, 4, < <class 'pymath.expression.Expression'> [2, 4, '*'] >]>]
+        >>> p*r
+        < AbstractPolynom [0, 1, 2]>
+        >>> P = AbstractPolynom([1,2,3])
+        >>> Q = AbstractPolynom([4,5,6])
+        >>> P*Q
+        < AbstractPolynom [4, 13, 28, 27, 18]>
+        """
+        # TODO: Je trouve qu'elle grille trop d'étapes... |ven. févr. 27 19:08:44 CET 2015
+        o_poly = self.conv2poly(other)
+
+        coefs = [0]*(self.degree + o_poly.degree + 1)
+        for (i,a) in enumerate(self._coef):
+            for (j,b) in enumerate(o_poly._coef):
+                if a == 0 or b == 0:
+                    elem = 0
+                elif a==1:
+                    elem = b
+                elif b==1:
+                    elem = a
+                else:
+                    elem = Expression([a, b, op.mul])
+
+                if coefs[i+j]==0:
+                    coefs[i+j] = elem
+                elif elem != 0:
+                    if type(coefs[i+j]) == list:
+                        coefs[i+j] += [elem]
+                    else:
+                        coefs[i+j] = [coefs[i+j] , elem]
+
+        p = AbstractPolynom(coefs, letter = self._letter)
+        ini_step = [Expression(self.postfix_tokens + o_poly.postfix_tokens + [op.mul])]
+        ans = p.simplify()
+
+        ans.steps = [ini_step] + ans.steps
+        return ans
+
+    def __rmul__(self, other):
+        o_poly = self.conv2poly(other)
+
+        return o_poly.__mul__(self)
+        
+    @power_cache
+    def __pow__(self, power):
+        """ Overload **
+
+        >>> p = AbstractPolynom([0,0,3])
+        >>> p**2
+        < AbstractPolynom [0, 0, 0, 0, 9]>
+        >>> (p**2).steps
+        [< <class 'pymath.expression.Expression'> [3, 'x', 2, '^', '*', 2, '^'] >, < AbstractPolynom [0, 0, 0, 0, < <class 'pymath.expression.Expression'> [3, 2, '^'] >]>, < AbstractPolynom [0, 0, 0, 0, < <class 'pymath.expression.Expression'> [3, 2, '^'] >]>]
+        >>> p = AbstractPolynom([1,2])
+        >>> p**2
+        < AbstractPolynom [1, 4, 4]>
+        >>> (p**2).steps
+        [< <class 'pymath.expression.Expression'> [2, 'x', '*', 1, '+', 2, '^'] >, [< <class 'pymath.expression.Expression'> [2, 'x', '*', 1, '+', 2, 'x', '*', 1, '+', '*'] >], < AbstractPolynom [1, < <class 'pymath.expression.Expression'> [2, 2, '+'] >, < <class 'pymath.expression.Expression'> [2, 2, '*'] >]>, < AbstractPolynom [1, < <class 'pymath.expression.Expression'> [2, 2, '+'] >, < <class 'pymath.expression.Expression'> [2, 2, '*'] >]>]
+        >>> p = AbstractPolynom([0,0,1])
+        >>> p**3
+        < AbstractPolynom [0, 0, 0, 0, 0, 0, 1]>
+        >>> p = AbstractPolynom([1,2,3])
+        >>> p**2
+        < AbstractPolynom [1, 4, 10, 12, 9]>
+
+        """
+        if not type(power):
+            raise ValueError("Can't raise {obj} to {pw} power".format(obj = self.__class__, pw = str(power)))
+
+        ini_step = [Expression(self.postfix_tokens + [power, op.pw])]
+
+        if self.is_monom():
+            if self._coef[self.degree] == 1:
+                coefs = [0]*self.degree*power + [1]
+                p = AbstractPolynom(coefs, letter = self._letter)
+                ans = p
+            else:
+                coefs = [0]*self.degree*power + [Expression([self._coef[self.degree] , power, op.pw])]
+                p = AbstractPolynom(coefs, letter = self._letter)
+                ans = p.simplify()
+        else:
+            if power == 2:
+                ans = self * self
+            else:
+                # TODO: faudrait changer ça c'est pas très sérieux |ven. févr. 27 22:08:00 CET 2015
+                raise AttributeError("__pw__ not implemented yet when power is greatter than 2")
+
+        ans.steps = ini_step + ans.steps
+        return ans
+
+    def __xor__(self, power):
+        return self.__pow__(power)
+
+
+
+# -----------------------------
+# Reglages pour 'vim'
+# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
+# cursor: 16 del 

pymath/polynom.py

@@ -3,34 +3,27 @@
 
 
 from .expression import Expression
-from .explicable import Explicable
 from .operator import op
-from .generic import spe_zip, expand_list, isNumber, transpose_fill, flatten_list, isPolynom, isNumerand
+from .generic import isNumerand
-from .render import txt,tex
 from .random_expression import RdExpression
-from itertools import chain
+from .abstract_polynom import AbstractPolynom
-from functools import wraps
 
 __all__ = ["Polynom"]
 
+class Polynom(AbstractPolynom):
 
-def power_cache(fun):
+    """Polynom view as a function.
-    """Decorator which cache calculated powers of polynoms """
-    cache  = {}
-    @wraps(fun)
-    def cached_fun(self, power):
-        #print("cache -> ", cache)
-        if (tuple(self._coef), power) in cache.keys():
-            return cache[(tuple(self._coef), power)]
-        else:
-            poly_powered = fun(self, power)
-            cache[(tuple(self._coef), power)] = poly_powered
-            return poly_powered
-    return cached_fun
     
-class Polynom(Explicable):
+    It can be initiate like a AbstractPolynom
+    # Put example
+    Randomly
+    # Put example
+    It can be evaluate
+    # Put example
+    And derivate
+    # Put example
 
-    """Docstring for Polynom. """
+    """
 
     @classmethod
     def random(self, coefs_form=[], conditions=[], letter = "x", degree = 0, name = "P"):
@@ -95,18 +88,7 @@ class Polynom(Explicable):
         >>> Polynom([1, 2, 3], name = "Q").name
         'Q'
         """
-        super(Polynom, self).__init__()
+        super(Polynom, self).__init__(coefs, letter, name)
-        self.feed_coef(coefs)
-        self._letter = letter
-        self.name = name
-
-        
-        if self.is_monom():
-            self.mainOp = op.mul
-        else:
-            self.mainOp = op.add
-
-        self._isPolynom = 1
 
     def __call__(self, value):
         """ Evaluate the polynom in value
@@ -135,285 +117,6 @@ class Polynom(Explicable):
 
         return Expression(postfix_exp).simplify()
 
-    def feed_coef(self, l_coef):
-        """Feed coef of the polynom. Manage differently whether it's a number or an expression
-        
-        :l_coef: list of coef
-        """
-        self._coef = []
-        for coef in l_coef:
-            if type(coef) == list and len(coef)==1:
-                self._coef.append(coef[0])
-            else:
-                self._coef.append(coef)
-
-    @property
-    def degree(self):
-        """Getting the degree fo the polynom
-
-        :returns: the degree of the polynom
-
-        >>> Polynom([1, 2, 3]).degree
-        2
-        >>> Polynom([1]).degree
-        0
-        """
-        return len(self._coef) - 1
-
-    def is_monom(self):
-        """is the polynom a monom (only one coefficent)
-
-        :returns: 1 if yes 0 otherwise
-
-        >>> Polynom([1, 2, 3]).is_monom()
-        0
-        >>> Polynom([1]).is_monom()
-        1
-        """
-        if len([i for i in self._coef if i != 0])==1:
-            return 1
-        else:
-            return 0
-
-    def give_name(self, name):
-        self.name = name
-
-    def __str__(self):
-        return str(Expression(self.postfix_tokens))
-
-    def __repr__(self):
-        return  "< Polynom " + str(self._coef) + ">"
-
-    def __txt__(self):
-        return txt(self.postfix_tokens)
-
-    def __tex__(self):
-        return tex(self.postfix_tokens)
-
-    def coef_postfix(self, a, i):
-        """Return the postfix display of a coeficient
-
-        :param a: value for the coeficient (/!\ as a postfix list)
-        :param i: power
-        :returns: postfix tokens of coef
-
-        >>> p = Polynom()
-        >>> p.coef_postfix([3],2)
-        [3, 'x', 2, '^', '*']
-        >>> p.coef_postfix([0],1)
-        []
-        >>> p.coef_postfix([3],0)
-        [3]
-        >>> p.coef_postfix([3],1)
-        [3, 'x', '*']
-        >>> p.coef_postfix([1],1)
-        ['x']
-        >>> p.coef_postfix([1],2)
-        ['x', 2, '^']
-
-        """
-        # TODO: Couille certaine avec txt à qui il fait donner des opérateurs tout beau! |mar. nov. 11 13:08:35 CET 2014
-        ans =[] 
-        if a == [0]:
-            pass
-        elif i == 0:
-            ans = a
-        elif i == 1:
-            ans = a * (a!=[1]) + [self._letter] + [op.mul] *  (a!=[1]) 
-        else:
-            ans = a * (a!=[1]) + [self._letter, i, op.pw] + [op.mul] *  (a!=[1]) 
-        
-        return ans
-
-    @property
-    def postfix_tokens(self):
-        """Return the postfix form of the polynom
-
-        :returns: the postfix list of polynom's tokens
-
-        >>> p = Polynom([1, 2])
-        >>> p.postfix_tokens
-        [2, 'x', '*', 1, '+']
-        >>> p = Polynom([1, -2])
-        >>> p.postfix_tokens
-        [2, 'x', '*', '-', 1, '+']
-        >>> p = Polynom([1,2,3])
-        >>> p.postfix_tokens
-        [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+']
-        >>> p = Polynom([1])
-        >>> p.postfix_tokens
-        [1]
-        >>> p = Polynom([0])
-        >>> p.postfix_tokens
-        [0]
-        >>> p = Polynom([1,[2,3]])
-        >>> p.postfix_tokens
-        [2, 'x', '*', 3, 'x', '*', '+', 1, '+']
-        >>> p = Polynom([1,[2,-3]])
-        >>> p.postfix_tokens
-        [2, 'x', '*', 3, 'x', '*', '-', 1, '+']
-        >>> p = Polynom([1,[-2,-3]])
-        >>> p.postfix_tokens
-        [2, 'x', '*', '-', 3, 'x', '*', '-', 1, '+']
-        >>> from pymath.expression import Expression
-        >>> from pymath.operator import op
-        >>> e = Expression([2,3,op.add])
-        >>> p = Polynom([1,e])
-        >>> p.postfix_tokens
-        [2, 3, '+', 'x', '*', 1, '+']
-
-        """
-        if self == 0:
-            return [0]
-        # TODO: Faudrait factoriser un peu tout ça..! |dim. déc. 21 16:02:34 CET 2014
-        postfix = []
-        for (i,a) in list(enumerate(self._coef))[::-1]:
-            operator = [op.add]
-            operator_sub1 = []
-            if type(a) == Expression:
-                # case coef is an arithmetic expression
-                c = self.coef_postfix(a.postfix_tokens,i)
-                if c != []:
-                    postfix.append(c)
-                    if len(postfix) > 1:
-                        postfix += operator
-
-            elif type(a) == list:
-                # case need to repeat the x^i
-                for b in a:
-                    operator = [op.add]
-                    operator_sub1 = []
-                    if len(postfix) == 0 and isNumber(b) and b < 0:
-                        try:
-                            b = [(-b)[-1]]
-                        except TypeError:
-                            b = [-b]
-                        operator_sub1 = [op.sub1]
-                    elif len(postfix) > 0 and isNumber(b) and b < 0:
-                        try:
-                            b = [(-b)[-1]]
-                        except TypeError:
-                            b = [-b]
-                        operator = [op.sub]
-                    else:
-                        b = [b]
-                    c = self.coef_postfix(b,i)
-                    if c != []:
-                        postfix.append(c)
-                        if len(postfix) > 1:
-                            postfix += operator_sub1
-                            postfix += operator
-                        postfix += operator_sub1
-
-            elif a != 0:
-                if len(postfix) == 0 and a < 0:
-                    try:
-                        a = [(-a)[-1]]
-                    except TypeError:
-                        a = [-a]
-                    operator_sub1 = [op.sub1]
-                elif len(postfix) > 0 and a < 0:
-                    try:
-                        a = [(-a)[-1]]
-                    except TypeError:
-                        a = [-a]
-                    operator = [op.sub]
-                else:
-                    a = [a]
-
-                c = self.coef_postfix(a,i)
-                if c != []:
-                    postfix.append(c)
-                    if len(postfix) > 1:
-                        postfix += operator_sub1
-                        postfix += operator
-                    postfix += operator_sub1
-
-        return flatten_list(postfix)
-
-    def conv2poly(self, other):
-        """Convert anything number into a polynom
-        
-        >>> P = Polynom([1,2,3])
-        >>> P.conv2poly(1)
-        < Polynom [1]>
-        >>> P.conv2poly(0)
-        < Polynom [0]>
-        
-        """
-        if isNumber(other) and not isPolynom(other):
-            return Polynom([other], letter = self._letter)
-        elif isPolynom(other):
-            return other
-        else:
-            raise ValueError(type(other) + " can't be converted into a polynom")
-    
-    def reduce(self):
-        """Compute coefficients which have same degree
-
-        :returns: new Polynom with numbers coefficients
-
-        >>> P = Polynom([1,2,3])
-        >>> Q = P.reduce()
-        >>> Q
-        < Polynom [1, 2, 3]>
-        >>> Q.steps
-        []
-        >>> P = Polynom([[1,2], [3,4,5], 6])
-        >>> Q = P.reduce()
-        >>> Q
-        < Polynom [3, 12, 6]>
-        >>> Q.steps
-        [< Polynom [< <class 'pymath.expression.Expression'> [1, 2, '+'] >, < <class 'pymath.expression.Expression'> [3, 4, '+', 5, '+'] >, 6]>, < Polynom [3, < <class 'pymath.expression.Expression'> [7, 5, '+'] >, 6]>]
-        """
-    
-        # TODO: It doesn't not compute quick enough |ven. févr. 27 18:04:01 CET 2015
-
-        # gather steps for every coeficients
-        coefs_steps = []
-        for coef in self._coef:
-            coef_steps = []
-            if type(coef) == list:
-                # On converti en postfix avec une addition
-                postfix_add = self.postfix_add([i for i in coef if i!=0])
-                # On converti en Expression
-                coef_exp = Expression(postfix_add)
-
-                with Expression.tmp_render():
-                    coef_steps = list(coef_exp.simplify().explain())
-
-                #print('\t 1.coef_steps -> ', coef_steps)
-
-            elif type(coef) == Expression:
-
-                with Expression.tmp_render():
-                    coef_steps = list(coef.simplify().explain())
-
-                #print('\t 2.coef_steps -> ', coef_steps)
-
-            else:
-                try:
-                    with Expression.tmp_render():
-                        coef_steps += coef.simplify().explain()
-                except AttributeError:
-                    coef_steps = [coef]
-
-                #print('\t 3.coef_steps -> ', coef_steps)
-            # On ajoute toutes ces étapes
-            coefs_steps.append(coef_steps)
-
-        #print('\t coefs_steps -> ', coefs_steps)
-
-        # On retourne la matrice
-        steps = []
-        for coefs in transpose_fill(coefs_steps):
-            steps.append(Polynom(coefs, self._letter))
-
-        ans, steps = steps[-1], steps[:-1]
-        ans.steps = steps
-            
-        return ans
-
     def derivate(self):
         """ Return the derivated polynom 
         
@@ -436,225 +139,6 @@ class Polynom(Explicable):
         ans.name = self.name + "'"
         return ans
 
-    @staticmethod
-    def postfix_add(numbers):
-        """Convert a list of numbers into a postfix addition
-        
-        :numbers: list of numbers
-        :returns: Postfix list of succecive attition of number
-
-        >>> Polynom.postfix_add([1])
-        [1]
-        >>> Polynom.postfix_add([1, 2])
-        [1, 2, '+']
-        >>> Polynom.postfix_add([1, 2, 3])
-        [1, 2, '+', 3, '+']
-        >>> Polynom.postfix_add(1)
-        [1]
-        >>> Polynom.postfix_add([])
-        [0]
-        """
-        if not type(numbers) == list:
-            return [numbers]
-        elif numbers == []:
-            return [0]
-        else:
-            ans = [[a, op.add] if i!=0 else [a] for (i,a) in enumerate(numbers)]
-            return list(chain.from_iterable(ans))
-            
-    def simplify(self):
-        """Same as reduce """
-        return self.reduce()
-
-    def __eq__(self, other):
-        try:
-            o_poly = self.conv2poly(other)
-            return self._coef == o_poly._coef
-        except TypeError:
-            return 0
-
-    def __add__(self, other):
-        """ Overload + 
-
-        >>> P = Polynom([1,2,3])
-        >>> Q = Polynom([4,5])
-        >>> R = P+Q
-        >>> R
-        < Polynom [5, 7, 3]>
-        >>> R.steps
-        [< <class 'pymath.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', 5, 'x', '*', 4, '+', '+'] >, < Polynom [< <class 'pymath.expression.Expression'> [1, 4, '+'] >, < <class 'pymath.expression.Expression'> [2, 5, '+'] >, 3]>]
-        """
-        o_poly = self.conv2poly(other)
-
-        n_coef = spe_zip(self._coef, o_poly._coef)
-        p = Polynom(n_coef, letter = self._letter)
-
-        ini_step = [Expression(self.postfix_tokens + o_poly.postfix_tokens + [op.add])]
-        ans = p.simplify()
-        ans.steps = ini_step + ans.steps
-        return ans
-
-    def __radd__(self, other):
-        o_poly = self.conv2poly(other)
-        return o_poly.__add__(self)
-
-    def __neg__(self):
-        """ overload - (as arity 1 operator)
-
-        >>> P = Polynom([1,2,3])
-        >>> Q = -P
-        >>> Q
-        < Polynom [-1, -2, -3]>
-        >>> Q.steps
-        [< <class 'pymath.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', '-'] >]
-        """
-        ini_step = [Expression(self.postfix_tokens + [op.sub1])]
-        ans = Polynom([-i for i in self._coef], letter = self._letter).simplify()
-        ans.steps = ini_step + ans.steps
-        return ans
-
-    def __sub__(self, other):
-        """ overload -
-
-        >>> P = Polynom([1,2,3])
-        >>> Q = Polynom([4,5,6])
-        >>> R = P - Q
-        >>> R
-        < Polynom [-3, -3, -3]>
-        >>> R.steps
-        [< <class 'pymath.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', 6, 'x', 2, '^', '*', 5, 'x', '*', '+', 4, '+', '-'] >, < <class 'pymath.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', 6, 'x', 2, '^', '*', '-', 5, 'x', '*', '-', 4, '-', '+'] >, < Polynom [< <class 'pymath.expression.Expression'> [1, -4, '+'] >, < <class 'pymath.expression.Expression'> [2, -5, '+'] >, < <class 'pymath.expression.Expression'> [3, -6, '+'] >]>]
-        """
-        o_poly = self.conv2poly(other)
-        ini_step = [Expression(self.postfix_tokens + o_poly.postfix_tokens + [op.sub])]
-        o_poly = -o_poly
-        #ini_step += o_poly.steps
-
-        ans = self + o_poly
-        ans.steps = ini_step + ans.steps
-
-        return ans
-
-    def __rsub__(self, other):
-        o_poly = self.conv2poly(other)
-        
-        return o_poly.__sub__(self)
-    
-    def __mul__(self, other):
-        """ Overload *
-
-        >>> p = Polynom([1,2])
-        >>> p*3
-        < Polynom [3, 6]>
-        >>> (p*3).steps
-        [[< <class 'pymath.expression.Expression'> [2, 'x', '*', 1, '+', 3, '*'] >], < Polynom [3, < <class 'pymath.expression.Expression'> [2, 3, '*'] >]>]
-        >>> q = Polynom([0,0,4])
-        >>> q*3
-        < Polynom [0, 0, 12]>
-        >>> (q*3).steps
-        [[< <class 'pymath.expression.Expression'> [4, 'x', 2, '^', '*', 3, '*'] >], < Polynom [0, 0, < <class 'pymath.expression.Expression'> [4, 3, '*'] >]>]
-        >>> r = Polynom([0,1])
-        >>> r*3
-        < Polynom [0, 3]>
-        >>> (r*3).steps
-        [[< <class 'pymath.expression.Expression'> ['x', 3, '*'] >]]
-        >>> p*q
-        < Polynom [0, 0, 4, 8]>
-        >>> (p*q).steps
-        [[< <class 'pymath.expression.Expression'> [2, 'x', '*', 1, '+', 4, 'x', 2, '^', '*', '*'] >], < Polynom [0, 0, 4, < <class 'pymath.expression.Expression'> [2, 4, '*'] >]>]
-        >>> p*r
-        < Polynom [0, 1, 2]>
-        >>> P = Polynom([1,2,3])
-        >>> Q = Polynom([4,5,6])
-        >>> P*Q
-        < Polynom [4, 13, 28, 27, 18]>
-        """
-        # TODO: Je trouve qu'elle grille trop d'étapes... |ven. févr. 27 19:08:44 CET 2015
-        o_poly = self.conv2poly(other)
-
-        coefs = [0]*(self.degree + o_poly.degree + 1)
-        for (i,a) in enumerate(self._coef):
-            for (j,b) in enumerate(o_poly._coef):
-                if a == 0 or b == 0:
-                    elem = 0
-                elif a==1:
-                    elem = b
-                elif b==1:
-                    elem = a
-                else:
-                    elem = Expression([a, b, op.mul])
-
-                if coefs[i+j]==0:
-                    coefs[i+j] = elem
-                elif elem != 0:
-                    if type(coefs[i+j]) == list:
-                        coefs[i+j] += [elem]
-                    else:
-                        coefs[i+j] = [coefs[i+j] , elem]
-
-        p = Polynom(coefs, letter = self._letter)
-        ini_step = [Expression(self.postfix_tokens + o_poly.postfix_tokens + [op.mul])]
-        ans = p.simplify()
-
-        ans.steps = [ini_step] + ans.steps
-        return ans
-
-    def __rmul__(self, other):
-        o_poly = self.conv2poly(other)
-
-        return o_poly.__mul__(self)
-
-    @power_cache
-    def __pow__(self, power):
-        """ Overload **
-
-        >>> p = Polynom([0,0,3])
-        >>> p**2
-        < Polynom [0, 0, 0, 0, 9]>
-        >>> (p**2).steps
-        [< <class 'pymath.expression.Expression'> [3, 'x', 2, '^', '*', 2, '^'] >, < Polynom [0, 0, 0, 0, < <class 'pymath.expression.Expression'> [3, 2, '^'] >]>]
-        >>> p = Polynom([1,2])
-        >>> p**2
-        < Polynom [1, 4, 4]>
-        >>> (p**2).steps
-        [< <class 'pymath.expression.Expression'> [2, 'x', '*', 1, '+', 2, '^'] >, [< <class 'pymath.expression.Expression'> [2, 'x', '*', 1, '+', 2, 'x', '*', 1, '+', '*'] >], < Polynom [1, < <class 'pymath.expression.Expression'> [2, 2, '+'] >, < <class 'pymath.expression.Expression'> [2, 2, '*'] >]>]
-        >>> p = Polynom([0,0,1])
-        >>> p**3
-        < Polynom [0, 0, 0, 0, 0, 0, 1]>
-        >>> p = Polynom([1,2,3])
-        >>> p**2
-        < Polynom [1, 4, 10, 12, 9]>
-
-        """
-        if not type(power):
-            raise ValueError("Can't raise Polynom to {} power".format(str(power)))
-
-        ini_step = [Expression(self.postfix_tokens + [power, op.pw])]
-
-        if self.is_monom():
-            if self._coef[self.degree] == 1:
-                coefs = [0]*self.degree*power + [1]
-                p = Polynom(coefs, letter = self._letter)
-                ans = p
-            else:
-                coefs = [0]*self.degree*power + [Expression([self._coef[self.degree] , power, op.pw])]
-                p = Polynom(coefs, letter = self._letter)
-                ans = p.simplify()
-        else:
-            if power == 2:
-                ans = self * self
-            else:
-                # TODO: faudrait changer ça c'est pas très sérieux |ven. févr. 27 22:08:00 CET 2015
-                raise AttributeError("__pw__ not implemented yet when power is greatter than 2")
-
-        ans.steps = ini_step + ans.steps
-        return ans
-
-    def __xor__(self, power):
-        return self.__pow__(power)
-
-
-
-
 def test(p,q):
     print("---------------------")
     print("---------------------")