From 9d9224fcba36e9407f761814bb2db1dfcdda4afa Mon Sep 17 00:00:00 2001
From: Bertrand Benjamin <benjamin.bertrand@opytex.org>
Date: Mon, 15 Jul 2019 17:48:59 +0200
Subject: [PATCH] Feat: Polynoms can be differentiate!!!!

---
 mapytex/calculus/API/tokens/polynomial.py | 22 +++++++++++++
 mapytex/calculus/core/MO/atoms.py         | 20 ++++++++++++
 mapytex/calculus/core/MO/fraction.py      | 17 ++++++++++
 mapytex/calculus/core/MO/mo.py            |  4 +++
 mapytex/calculus/core/MO/monomial.py      | 38 +++++++++++++++++++++++
 mapytex/calculus/core/MO/polynomial.py    | 22 +++++++++++++
 6 files changed, 123 insertions(+)

diff --git a/mapytex/calculus/API/tokens/polynomial.py b/mapytex/calculus/API/tokens/polynomial.py
index 30a75de..3b09f8a 100644
--- a/mapytex/calculus/API/tokens/polynomial.py
+++ b/mapytex/calculus/API/tokens/polynomial.py
@@ -101,6 +101,24 @@ class Polynomial(Token):
         tree = tree.map_on_leaf(replace_var)
 
         return Expression(tree).simplify()
+    
+    def differentiate(self):
+        """ Differentiate a polynome
+
+        :example:
+        >>> from ...core.MO.polynomial import MOpolynomial
+        >>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
+        >>> P
+        <Polynomial 3x^2 + 2x + 1>
+        >>> P.differentiate()
+        <Linear 2 + 6x>
+        >>> for s in P.differentiate().explain():
+        ...     print(s)
+        0 + 2 + 3 * 2x
+        2 + 3 * 2 * x
+        2 + 6x
+        """
+        return Expression(self._mo.differentiate()).simplify()
     @property
     def roots(self):
         """ Get roots of the Polynomial """
@@ -120,6 +138,8 @@ class Linear(Polynomial):
     <MOnumber 2>
     >>> P.b
     <MOnumber 1>
+    >>> P.differentiate()
+    <Integer 2>
     >>> P.roots
     [<Fraction - 2 / 1>]
 
@@ -194,6 +214,8 @@ class Quadratic(Polynomial):
     4 - 12 * 1
     4 - 12
     - 8
+    >>> P.differentiate()
+    <Linear 2 + 6x>
     >>> P.roots
     []
 
diff --git a/mapytex/calculus/core/MO/atoms.py b/mapytex/calculus/core/MO/atoms.py
index 6f8df1d..6f5eba8 100644
--- a/mapytex/calculus/core/MO/atoms.py
+++ b/mapytex/calculus/core/MO/atoms.py
@@ -166,6 +166,16 @@ class MOnumber(Atom):
         except AttributeError:
             return self.value < other
 
+    def differentiate(self):
+        """ differentiate a number and get 0
+
+        :example:
+        >>> a = MOnumber(3)
+        >>> a.differentiate()
+        <MOnumber 0>
+        """
+        return MOnumber(0)
+
 
 class MOstr(Atom):
 
@@ -260,6 +270,16 @@ class MOstr(Atom):
     def degree(self):
         return 1
 
+    def differentiate(self):
+        """ differentiate a variable and get 1
+
+        :example:
+        >>> a = MOstr("x")
+        >>> a.differentiate()
+        <MOnumber 1>
+        """
+        return MOnumber(1)
+
 
 # -----------------------------
 # Reglages pour 'vim'
diff --git a/mapytex/calculus/core/MO/fraction.py b/mapytex/calculus/core/MO/fraction.py
index eb338b2..16ee737 100644
--- a/mapytex/calculus/core/MO/fraction.py
+++ b/mapytex/calculus/core/MO/fraction.py
@@ -8,6 +8,7 @@
 
 from mapytex.calculus.core.tree import Tree
 from .mo import Molecule, MO
+from .atoms import MOnumber
 
 __all__ = ["MOFraction"]
 
@@ -71,6 +72,22 @@ class MOFraction(Molecule):
         """ return the inverse fraction """
         return MOFraction(self._denominator, self._numerator, self.negative)
 
+    def differentiate(self):
+        """ differentiate a fraction and get something!
+
+        :example:
+        >>> a = MOFraction(2, 3)
+        >>> a.differentiate()
+        <MOnumber 0>
+        """
+        d_num = self.numerator.differentiate()
+        d_denom = self.denominator.differentiate()
+
+        if d_num == 0 and d_denom == 0:
+            return MOnumber(0)
+        else:
+            raise NotImplementedError
+
 
 # -----------------------------
 # Reglages pour 'vim'
diff --git a/mapytex/calculus/core/MO/mo.py b/mapytex/calculus/core/MO/mo.py
index 91c043c..1729498 100644
--- a/mapytex/calculus/core/MO/mo.py
+++ b/mapytex/calculus/core/MO/mo.py
@@ -97,6 +97,10 @@ class MO(ABC):
         """
         return self._signature
 
+    def differentiate(self):
+        raise NotImplementedError
+
+
 
 class Atom(MO):
 
diff --git a/mapytex/calculus/core/MO/monomial.py b/mapytex/calculus/core/MO/monomial.py
index f9d7017..41eaeed 100644
--- a/mapytex/calculus/core/MO/monomial.py
+++ b/mapytex/calculus/core/MO/monomial.py
@@ -110,6 +110,19 @@ class MOstrPower(Molecule):
         'monome2'
         """
         return f"monome{self.power}"
+    def differentiate(self):
+        """ differentiate a MOstrPower and get a tree
+
+        :example:
+        >>> a = MOstrPower('x', 3)
+        >>> print(a.differentiate())
+        *
+         > 3
+         > x^2
+        """
+        if self._power > 2:
+            return Tree('*', self.power, MOstrPower(self.variable, self._power._value-1))
+        return Tree('*', self.power, MOstr(self.variable))
 
 
 class MOMonomial(Molecule):
@@ -258,6 +271,31 @@ class MOMonomial(Molecule):
         """
         return f"monome{self.power}"
 
+    def differentiate(self):
+        """ Differentiate a MOMonomial and get a tree
+
+        :example:
+        >>> x = MOstr('x')
+        >>> m = MOMonomial(4, x)
+        >>> m
+        <MOMonomial 4x>
+        >>> print(m.differentiate())
+        4
+        >>> m = MOMonomial(4, 'x', 2)
+        >>> m
+        <MOMonomial 4x^2>
+        >>> print(m.differentiate())
+        *
+         > 4
+         > *
+         | > 2
+         | > x
+
+        """
+        if self.power == 1:
+            return self.coefficient
+        return Tree("*", self.coefficient, self.strpower.differentiate())
+
 
 # -----------------------------
 # Reglages pour 'vim'
diff --git a/mapytex/calculus/core/MO/polynomial.py b/mapytex/calculus/core/MO/polynomial.py
index bb286df..dd74b92 100644
--- a/mapytex/calculus/core/MO/polynomial.py
+++ b/mapytex/calculus/core/MO/polynomial.py
@@ -126,6 +126,28 @@ class MOpolynomial(Molecule):
         """
         return self._monomials
 
+    def differentiate(self):
+        """ Differentiate a MOMonomial and get a tree
+
+        :example:
+        >>> p = MOpolynomial('x', [1, 2, 3])
+        >>> print(p)
+        3x^2 + 2x + 1
+        >>> print(p.differentiate())
+        +
+         > 0
+         > +
+         | > 2
+         | > *
+         | | > 3
+         | | > *
+         | | | > 2
+         | | | > x
+
+        """
+        monomials_d = [m.differentiate() for m in self.monomials.values()]
+        return Tree.from_list("+", monomials_d)
+
 
 # -----------------------------
 # Reglages pour 'vim'