From 50f77c4d6021b44344f13663b7acebd11404845a Mon Sep 17 00:00:00 2001
From: Bertrand Benjamin <benjamin.bertrand@opytex.org>
Date: Mon, 15 Jul 2019 11:59:28 +0200
Subject: [PATCH] Feat: coefficients, delta and some roots for polynomial,
 Linear and Quadratic

---
 mapytex/calculus/API/tokens/polynomial.py | 142 +++++++++++++++++++++-
 1 file changed, 137 insertions(+), 5 deletions(-)

diff --git a/mapytex/calculus/API/tokens/polynomial.py b/mapytex/calculus/API/tokens/polynomial.py
index e765a5e..020e47f 100644
--- a/mapytex/calculus/API/tokens/polynomial.py
+++ b/mapytex/calculus/API/tokens/polynomial.py
@@ -31,6 +31,7 @@ class Polynomial(Token):
     """
 
     def __init__(self, a, name="", ancestor=None):
+        """ Initiate Polynomial with a MO"""
         if not isinstance(a, MO):
             if isinstance(a, str):
                 raise TypeError
@@ -47,17 +48,37 @@ class Polynomial(Token):
 
         return cls(mo, name, ancestor)
 
+    @classmethod
+    def from_coefficients(cls, coefficients):
+        """ Initiate polynomial from list of coefficients """
+        pass
+
     @classmethod
     def random(cls):
         raise NotImplemented
 
     def __setitem__(self, key, item):
         """ Use Polynomial like if they were a dictionnary to set coefficients """
-        pass
+        raise NotImplemented("Can't set coefficient of a polynomial")
 
     def __getitem__(self, key):
-        """ Use Polynomial like if they were a dictionnary to get coefficients """
-        pass
+        """ Use Polynomial like if they were a dictionnary to get coefficients 
+
+        :examples:
+        >>> from ...core.MO.polynomial import MOpolynomial
+        >>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
+        >>> P[0]
+        <MOnumber 1>
+        >>> P[1]
+        <MOnumber 2>
+        >>> P[2]
+        <MOnumber 3>
+        >>> P[3]
+        Traceback (most recent call last):
+            ...
+        KeyError: 3
+        """
+        return self._mo.coefficients[key]
 
     def __call__(self, value):
         """ Call a Polynomial to evaluate itself on value 
@@ -80,14 +101,42 @@ class Polynomial(Token):
         tree = tree.map_on_leaf(replace_var)
 
         return Expression(tree).simplify()
+    @property
+    def roots(self):
+        """ Get roots of the Polynomial """
+        raise NotImplemented("Can't compute roots not specific polynomial")
 
 
 class Linear(Polynomial):
 
-    """ Token representing a linear """
+    """ Token representing a linear ax + b
+
+    :examples:
+    >>> from ...core.MO.polynomial import MOpolynomial, MOMonomial
+    >>> P = Linear(MOpolynomial('x', [1, 2]))
+    >>> P
+    <Linear 2x + 1>
+    >>> P.a
+    <MOnumber 2>
+    >>> P.b
+    <MOnumber 1>
+    >>> P.roots
+    [<Fraction - 2 / 1>]
+
+    """
 
     def __init__(self, mo, name="", ancestor=None):
+        """ Initiate Linear with MO
 
+        :examples:
+        >>> from ...core.MO.polynomial import MOpolynomial, MOMonomial
+        >>> P = Linear(MOpolynomial('x', [1, 2]))
+        >>> P
+        <Linear 2x + 1>
+        >>> Q = Linear(MOMonomial(3, 'x', 1))
+        >>> Q
+        <Linear 3x>
+        """
         Polynomial.__init__(self, mo, name, ancestor)
         self._mathtype = "affine"
 
@@ -95,12 +144,69 @@ class Linear(Polynomial):
     def random(cls):
         raise NotImplemented
 
+    @property
+    def a(self):
+        return self[1]
+
+    @property
+    def b(self):
+        return self[0]
+
+    @property
+    def roots(self):
+        """ Get the root of the polynomial
+
+        :examples:
+        >>> from ...core.MO.polynomial import MOpolynomial, MOMonomial
+        >>> P = Linear(MOpolynomial('x', [1, 2]))
+        >>> P.roots
+        [<Fraction - 2 / 1>]
+        >>> #P = Linear(MOpolynomial('x', [1, -2]))
+        >>> #P.roots
+        """
+
+        try:
+            return [Expression.from_str(f"-{self.a}/{self.b}").simplify()]
+        except AttributeError:
+            return [Expression.from_str(f"-{self.a}/{self.b}")]
+
 
 class Quadratic(Polynomial):
 
-    """ Token representing a quadratic """
+    """ Token representing a quadratic ax^2 + bx + c
+
+    :examples:
+    >>> from ...core.MO.polynomial import MOpolynomial
+    >>> P = Quadratic(MOpolynomial('x', [1, 2, 3]))
+    >>> P
+    <Quadratic 3x^2 + 2x + 1>
+    >>> P.a
+    <MOnumber 3>
+    >>> P.b
+    <MOnumber 2>
+    >>> P.c
+    <MOnumber 1>
+    >>> P.delta
+    <Integer - 8>
+    >>> for s in P.delta.explain():
+    ...    print(s)
+    2^2 - 4 * 3 * 1
+    4 - 12 * 1
+    4 - 12
+    - 8
+    >>> P.roots
+    []
+
+    """
 
     def __init__(self, mo, name="", ancestor=None):
+        """ Initiate Quadratic from MO
+
+        >>> from ...core.MO.polynomial import MOpolynomial
+        >>> P = Quadratic(MOpolynomial('x', [1, 2, 3]))
+        >>> P
+        <Quadratic 3x^2 + 2x + 1>
+        """
 
         Polynomial.__init__(self, mo, name, ancestor)
         self._mathtype = "polynome du 2nd degré"
@@ -109,6 +215,32 @@ class Quadratic(Polynomial):
     def random(cls):
         raise NotImplemented
 
+    @property
+    def a(self):
+        return self[2]
+
+    @property
+    def b(self):
+        return self[1]
+
+    @property
+    def c(self):
+        return self[0]
+
+    @property
+    def delta(self):
+        return Expression.from_str(f"{self.b}^2-4*{self.a}*{self.c}").simplify()
+
+    @property
+    def roots(self):
+        if self.delta._mo < 0:
+            return []
+        elif self.delta._mo == 0:
+            return [Expression.from_str(f"-{self.b}/(2*{self.a})").simplify()]
+        else:
+            raise NotImplemented("Todo!")
+
+
 
 def extract_variable(leaf):
     try: