Test: separate expression build and showing it

possible

.drone.yml

@@ -0,0 +1,18 @@
+kind: pipeline
+name: default
+
+steps:
+  - name: testing
+    image: python
+    commands:
+      - pip install -r requirements.txt
+      - pytest --doctest-modules ./mapytex/
+  - name: Publish
+    image: plugins/pypi
+    settings:
+      username:
+        from_secret: pypi_username
+      password:
+        from_secret: pypi_password
+    when:
+      event: tag

.gitignore

@@ -4,5 +4,7 @@ dist/
 build/
 *.egg-info/
 documentation/build/
+documentation/source/_build/
 cache/
 venv/
+.nox

README.md

@@ -1,4 +1,5 @@
 # Mapytex
+[![Build Status](https://drone.opytex.org/api/badges/lafrite/Mapytex/status.svg)](https://drone.opytex.org/lafrite/Mapytex)
 
 Formal calculus with explanation python module and exercises creation tools.
 

mapytex/__init__.py

@@ -1,9 +1,9 @@
 #!/usr/bin/env python
 # encoding: utf-8
 
-from .calculus import Expression#, Polynom, Fraction, random_str, txt, Equation
+from .calculus import Expression, Integer, Decimal, random_list
 
-#Expression.set_render('tex')
+# Expression.set_render('tex')
 
 from .stat import Dataset, WeightedDataset
 from .geometry import random_pythagore

mapytex/calculus/API/__init__.py

@@ -84,19 +84,20 @@ x^7
 >>> e = Expression.from_str("1+2x^2+3x+4+5x")
 >>> e_simplified = e.simplify()
 >>> e_simplified
-<Quadratic 5 + 2x^2 + 8x>
+<Quadratic 2x^2 + 8x + 5>
 >>> for s in e_simplified.explain():
 ...    print(s)
 1 + 2x^2 + 3x + 4 + 5x
-1 + 2x^2 + 3x + 4 + 5x
-1 + 4 + 2x^2 + 3x + 5x
-5 + 2x^2 + (3 + 5) * x
-5 + 2x^2 + 8x
+2x^2 + 3x + 1 + 4 + 5x
+2x^2 + 3x + 5x + 1 + 4
+2x^2 + (3 + 5) * x + 5
+2x^2 + 8x + 5
+
 
 >>> e = Expression.from_str("(2x+3)^2")
 >>> e_simplified = e.simplify()
 >>> e_simplified
-<Quadratic 12x + 4x^2 + 9>
+<Quadratic 4x^2 + 12x + 9>
 >>> for s in e_simplified.explain():
 ...    print(s)
 (2x + 3)^2
@@ -105,11 +106,13 @@ x^7
 2 * 2 * x^(1 + 1) + 3 * 2 * x + 3 * 2 * x + 9
 6x + 6x + 4x^2 + 9
 (6 + 6) * x + 4x^2 + 9
-12x + 4x^2 + 9
+4x^2 + 12x + 9
+
 
 """
 
 from .expression import Expression
+from .tokens.number import Integer, Decimal
 
 if __name__ == "__main__":
     e = Expression.from_str("1+2/3/4/5")

mapytex/calculus/API/expression.py

@@ -10,10 +10,17 @@
 Expression
 
 """
+from functools import partial
 from ..core import AssocialTree, Tree, compute, typing, TypingError
-from ..core.random import extract_rdleaf, extract_rv, random_generator, compute_leafs, replace_rdleaf
+from ..core.random import (
+    extract_rdleaf,
+    extract_rv,
+    random_generator,
+    compute_leafs,
+    replace_rdleaf,
+)
 from ..core.MO import moify
-from .tokens import factory, Token
+from .tokens import factory
 from .renders import renders
 
 
@@ -67,12 +74,14 @@ class Expression(object):
         2 + 3 \\times 4
         >>> e = Expression.from_str("2+3/4")
         >>> print(e)
-        2 + \\frac{3}{4}
+        2 + \\dfrac{3}{4}
         >>> es = e.simplify()
         >>> print(es)
-        \\frac{11}{4}
+        \\dfrac{11}{4}
         >>> Expression.set_render('txt')
         """
+        from .tokens.token import Token
+
         Token.set_render(render)
         cls.RENDER = render
 
@@ -95,15 +104,14 @@ class Expression(object):
         <Linear 2x + 1>
         >>> e = Expression.from_str("2x + 1 + 5x^2")
         >>> e
-        <Quadratic 2x + 1 + 5x^2>
+        <Quadratic 5x^2 + 2x + 1>
         >>> e = Expression.from_str("2x + 1 + 5x")
         >>> e
         <Exp: 2x + 1 + 5x>
-
         """
         t = Tree.from_str(string)
         if typing:
-            return cls._post_precessing(t)
+            return cls._post_processing(t)
 
         return cls(t)
 
@@ -128,9 +136,11 @@ class Expression(object):
         :returns: TODO
 
         :example:
-        >>> Expression.random("{a}/{a*k}") # doctest: +SKIP
+        >>> e = Expression.random("{a}/{a*k}")
+        >>> e # doctest: +SKIP
         <Exp: -3 / -15>
-        >>> Expression.random("{a}/{a*k} - 3*{b}", variables_scope={'a':{'min_max':(10, 30)}}) # doctest: +SKIP
+        >>> e = Expression.random("{a}/{a*k} - 3*{b}", variables_scope={'a':{'min_max':(10, 30)}})
+        >>> e # doctest: +SKIP
         <Exp: 18 / 108 - 3 * 9>
         >>> e = Expression.random("{a}*x + {b}*x + 3", ["a>b"], rejected=[0, 1])
         >>> ee = e.simplify()
@@ -152,10 +162,10 @@ class Expression(object):
         if shuffle:
             raise NotImplemented("Can't suffle expression yet")
 
-        return cls._post_precessing(t)
+        return cls._post_processing(t)
 
     @classmethod
-    def _post_precessing(cls, t):
+    def _post_processing(cls, t):
         """ Post process the tree by typing it """
         tt = cls(t)._typing()
         try:
@@ -437,6 +447,65 @@ class Expression(object):
         else:
             yield self
 
+    def __call__(self, value):
+        """ Call a Expression to evaluate itself on value 
+
+        :param value: evaluate the Expression with this value
+        :return: Expression simplified if the value is not a string with a length greater than 1.
+
+        :examples:
+        >>> f = Expression.from_str("3*x^2 + 2x + 1")
+        >>> for s in f(2).explain():
+        ...     print(s)
+        3 * 2^2 + 2 * 2 + 1
+        3 * 4 + 4 + 1
+        12 + 5
+        17
+        >>> f(f(2))
+        <Integer 902>
+        >>> f(17)
+        <Integer 902>
+        >>> f("n")
+        <Quadratic 3n^2 + 2n + 1>
+        >>> f("u_n")
+        <Exp: 3u_n^2 + 2u_n + 1>
+        >>> f(f)
+        <Polynomial 27x^4 + 36x^3 + 36x^2 + 16x + 6>
+        """
+        tree = self._tree
+        variable = (set(tree.get_leafs(extract_variable)) - {None}).pop()
+
+        try:
+            dest = value._mo
+        except AttributeError:
+            dest = moify(value)
+        replace_var = partial(replace, origin=variable, dest=dest)
+        tree = tree.map_on_leaf(replace_var)
+
+        if isinstance(value, str) and len(value) > 1:
+            return Expression(tree)
+        return Expression(tree).simplify()
+
+
+def extract_variable(leaf):
+    try:
+        return leaf.variable
+    except AttributeError:
+        return None
+
+
+def replace(leaf, origin, dest):
+    """ Recursively replace origin to dest in leaf """
+    try:
+        leaf.tree
+    except AttributeError:
+        if leaf == origin:
+            return dest
+        return leaf
+
+    replace_var = partial(replace, origin=origin, dest=dest)
+    return leaf.tree.map_on_leaf(replace_var)
+
 
 # -----------------------------
 # Reglages pour 'vim'

mapytex/calculus/API/tokens/__init__.py

@@ -10,22 +10,163 @@
 Tokens represents MathObject at API level
 
 """
-from ...core.MO import MO, MOnumber, MOstr
+from ...core.MO import MO, MOnumber, MOstr, moify
 from ...core.MO.fraction import MOFraction
 from ...core.MO.monomial import MOstrPower, MOMonomial
 from ...core.MO.polynomial import MOpolynomial
 from decimal import Decimal as _Decimal
-
-from .number import Integer, Decimal, Fraction
-from .polynomial import Polynomial, Linear, Quadratic
-
+from functools import wraps
 from .token import Token
 
 __all__ = ["factory"]
 
 
+def tokenify(mo, name="", ancestor=None):
+    """ Transform a MO or a python builtin to the appropriate token 
+
+    :param mo: the thing to turn into a Token
+    :param name: a virtual name of the toke
+    :param ancestor: its ancestor
+
+    :example:
+    >>> a = MOnumber(2)
+    >>> tokenify(a)
+    <Integer 2>
+    >>> tokenify(2)
+    <Integer 2>
+    >>> tokenify("x")
+    <Linear x>
+    >>> tokenify(_Decimal("2.2"))
+    <Decimal 2.2>
+    >>> tokenify("2.2")
+    <Decimal 2.2>
+    >>> tokenify(2.2)
+    <Decimal 2.20000000000000017763568394002504646778106689453125>
+
+    tokenify is idempotent on "mo" parameter
+
+    >>> a = MOnumber(2)
+    >>> ta = tokenify(a)
+    >>> ta == tokenify(ta)
+    True
+
+    """
+    if isinstance(mo, MO):
+        return _tokenify(mo, name, ancestor)
+
+    if isinstance(mo, Token):
+        if name == "":
+            _name = mo.name
+        else:
+            _name = name
+        if ancestor is None:
+            _ancestor = mo._ancestor
+        else:
+            _ancestor = ancestor
+        return _tokenify(mo._mo, _name, _ancestor)
+
+    return _tokenify(moify(mo), name, ancestor)
+
+
+def to_be_token(func):
+    """ Decorator to ensure that the return value is a Token """
+    @wraps(func)
+    def wrapped(*args, **kwds):
+        ans = func(*args, **kwds)
+        try:
+            return [tokenify(t) for t in ans]
+        except TypeError:
+            return tokenify(ans)
+    return wrapped
+
+
+def _tokenify(mo, name="", ancestor=None):
+    """ Transform a MO (from core) to the appropriate token (from API)
+
+    :example:
+    >>> a = MOnumber(2)
+    >>> _tokenify(a)
+    <Integer 2>
+    >>> a = MOnumber(2.5)
+    >>> _tokenify(a)
+    <Decimal 2.5>
+    >>> a = MOFraction(2, 5)
+    >>> _tokenify(a)
+    <Fraction 2 / 5>
+    >>> a = MOstr('x')
+    >>> _tokenify(a)
+    <Linear x>
+    >>> a = MOstrPower('x', 2)
+    >>> _tokenify(a)
+    <Quadratic x^2>
+    >>> a = MOstrPower('x', 3)
+    >>> _tokenify(a)
+    <Polynomial x^3>
+    >>> a = MOMonomial(3, 'x', 1)
+    >>> _tokenify(a)
+    <Linear 3x>
+    >>> a = MOMonomial(3, 'x', 2)
+    >>> _tokenify(a)
+    <Quadratic 3x^2>
+    >>> a = MOMonomial(3, 'x', 3)
+    >>> _tokenify(a)
+    <Polynomial 3x^3>
+    """
+    if isinstance(mo, MOnumber):
+        if isinstance(mo.value, int):
+            from .number import Integer
+
+            return Integer.from_mo(mo, name, ancestor)
+        elif isinstance(mo.value, _Decimal):
+            from .number import Decimal
+
+            return Decimal.from_mo(mo, name, ancestor)
+
+        raise TypeError(f"Can't build from MOnumber ({mo}) neither int nor decimal")
+
+    if isinstance(mo, MOFraction):
+        if isinstance(mo._denominator, MOnumber) and isinstance(
+            mo._numerator, MOnumber
+        ):
+            from .number import Fraction
+
+            return Fraction.from_mo(mo, name, ancestor)
+
+        raise TypeError(
+            f"Can't build from MOFraction ({mo}) numerator and denominator are not MOnumber"
+        )
+
+    if isinstance(mo, (MOstr, MOstrPower, MOMonomial, MOpolynomial)):
+        if not isinstance(mo._variable, (MOstr, str)):
+            raise TypeError(
+                f"Can't build Polynom over something else than a letter (got {mo._variable})"
+            )
+        if (
+            isinstance(mo, MOstr)
+            or (isinstance(mo, MOMonomial) and mo.power.value == 1)
+            or (isinstance(mo, MOpolynomial) and mo.power.value == 1)
+        ):
+            from .polynomial import Linear
+
+            return Linear.from_mo(mo, name, ancestor)
+        elif (
+            (isinstance(mo, MOstrPower) and mo.power.value == 2)
+            or (isinstance(mo, MOMonomial) and mo.power.value == 2)
+            or (isinstance(mo, MOpolynomial) and mo.power.value == 2)
+        ):
+            from .polynomial import Quadratic
+
+            return Quadratic.from_mo(mo, name, ancestor)
+        else:
+            from .polynomial import Polynomial
+
+            return Polynomial.from_mo(mo, name, ancestor)
+
+    raise TypeError(f"{type(mo)} is unknown MathObject")
+
+
 def factory(exp, name="", ancestor=None):
-    """ Transform a Expression with on MathObject (from core) to a appropriate token (from API)
+    """ Transform a Expression with on single MathObject (from core) to a appropriate token (from API)
 
     :example:
     >>> from ..expression import Expression
@@ -61,46 +202,7 @@ def factory(exp, name="", ancestor=None):
     if not isinstance(mo, MO):
         raise TypeError(f"Can't build Token from not computed Expression (got {mo})")
 
-    if isinstance(mo, MOnumber):
-        if isinstance(mo.value, int):
-            return Integer.from_mo(mo, name, ancestor)
-        elif isinstance(mo.value, _Decimal):
-            return Decimal.from_mo(mo, name, ancestor)
-
-        raise TypeError(f"Can't build from MOnumber ({mo}) neither int nor decimal")
-
-    elif isinstance(mo, MOFraction):
-        if isinstance(mo._denominator, MOnumber) and isinstance(
-            mo._numerator, MOnumber
-        ):
-            return Fraction.from_mo(mo, name, ancestor)
-
-        raise TypeError(
-            f"Can't build from MOFraction ({mo}) numerator and denominator are not MOnumber"
-        )
-
-    elif isinstance(mo, (MOstr, MOstrPower, MOMonomial, MOpolynomial)):
-        if not isinstance(mo._variable, (MOstr, str)):
-            raise TypeError(
-                f"Can't build Polynom over something else than a letter (got {mo._variable})"
-            )
-        if (
-            isinstance(mo, MOstr)
-            or (isinstance(mo, MOMonomial) and mo.power.value == 1)
-            or (isinstance(mo, MOpolynomial) and mo.power.value == 1)
-        ):
-            return Linear.from_mo(mo, name, ancestor)
-        elif (
-            (isinstance(mo, MOstrPower) and mo.power.value == 2)
-            or (isinstance(mo, MOMonomial) and mo.power.value == 2)
-            or (isinstance(mo, MOpolynomial) and mo.power.value == 2)
-        ):
-            return Quadratic.from_mo(mo, name, ancestor)
-        else:
-            return Polynomial.from_mo(mo, name, ancestor)
-
-    else:
-        raise TypeError(f"{type(mo)} is unknown MathObject")
+    return _tokenify(mo, name, ancestor)
 
 
 # -----------------------------

mapytex/calculus/API/tokens/number.py

@@ -16,6 +16,7 @@ from ...core.arithmetic import gcd
 from ...core.random.int_gene import filter_random
 from ...core.MO import MO, MOnumber
 from ...core.MO.fraction import MOFraction
+from random import random
 
 __all__ = ["Integer", "Decimal"]
 
@@ -242,6 +243,20 @@ class Fraction(Token):
     def denominator(self):
         return self._mo.denominator
 
+    @property
+    def decimal(self):
+        """ return decimal approximation of the fraction
+
+        :example:
+        >>> f = Fraction("3/4")
+        >>> f.decimal
+        <Decimal 0.75>
+        >>> f = Fraction("1/3")
+        >>> f.decimal
+        <Decimal 0.3333333333333333333333333333>
+        """
+        return Decimal(_Decimal(self._mo.numerator._value) / _Decimal(self._mo.denominator._value))
+
 
 # -----------------------------
 # Reglages pour 'vim'

mapytex/calculus/API/tokens/polynomial.py

@@ -10,26 +10,32 @@
 Tokens representing polynomials functions 
 
 """
+from ..expression import Expression
 from .token import Token
+from . import to_be_token
 from ...core.MO import MO
+from ...core.MO.atoms import moify
 
 __all__ = ["Polynomial", "Quadratic", "Linear"]
 
 
 class Polynomial(Token):
 
-    """ Token representing a polynomial """
+    """ Token representing a polynomial 
+
+    :examples:
+    >>> from ...core.MO.polynomial import MOpolynomial
+    >>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
+    >>> P
+    <Polynomial 3x^2 + 2x + 1>
+    """
 
     def __init__(self, a, name="", ancestor=None):
+        """ Initiate Polynomial with a MO"""
         if not isinstance(a, MO):
-            if isinstance(a, str):
-                raise TypeError
-            else:
-                raise TypeError
-        else:
-            mo = a
+            raise TypeError
 
-        Token.__init__(self, mo, name, ancestor)
+        Token.__init__(self, a, name, ancestor)
         self._mathtype = "polynome"
 
     @classmethod
@@ -37,49 +43,257 @@ 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
+        raise NotImplementedError
+
+    @property
+    def raw(self):
+        raise NotImplementedError("Polynomial does not exists in python")
 
     def __setitem__(self, key, item):
         """ Use Polynomial like if they were a dictionnary to set coefficients """
-        pass
+        raise NotImplementedError("Can't set coefficient of a polynomial")
 
+    @to_be_token
     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]
+        <Integer 1>
+        >>> P[1]
+        <Integer 2>
+        >>> P[2]
+        <Integer 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 """
-        pass
+        """ Call a Polynomial to evaluate itself on value 
+
+        :examples:
+        >>> from ...core.MO.polynomial import MOpolynomial
+        >>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
+        >>> for s in P(2).explain():
+        ...     print(s)
+        3 * 2^2 + 2 * 2 + 1
+        3 * 4 + 4 + 1
+        12 + 5
+        17
+        """
+        return Expression(self._mo.tree)(value)
+
+    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 6x + 2>
+        >>> for s in P.differentiate().explain():
+        ...     print(s)
+        0 + 2 + 3 * 2x
+        2 + 3 * 2 * x
+        6x + 2
+        """
+        return Expression(self._mo.differentiate()).simplify()
+
+    @property
+    def roots(self):
+        """ Get roots of the Polynomial """
+        raise NotImplementedError("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
+    <Integer 2>
+    >>> P.b
+    <Integer 1>
+    >>> P.differentiate()
+    <Integer 2>
+    >>> 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"
 
     @classmethod
     def random(cls):
-        raise NotImplemented
+        raise NotImplementedError
+
+    @property
+    @to_be_token
+    def a(self):
+        return self[1]
+
+    @property
+    @to_be_token
+    def b(self):
+        return self[0]
+
+    @property
+    @to_be_token
+    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
+    <Integer 3>
+    >>> P.b
+    <Integer 2>
+    >>> P.c
+    <Integer 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.differentiate()
+    <Linear 6x + 2>
+    >>> 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"
 
     @classmethod
     def random(cls):
-        raise NotImplemented
+        raise NotImplementedError
+
+    @property
+    @to_be_token
+    def a(self):
+        try:
+            return self[2]
+        except KeyError:
+            return 0
+
+    @property
+    @to_be_token
+    def b(self):
+        try:
+            return self[1]
+        except KeyError:
+            return 0
+
+    @property
+    @to_be_token
+    def c(self):
+        try:
+            return self[0]
+        except KeyError:
+            return 0
+
+    @property
+    @to_be_token
+    def delta(self):
+        return Expression.from_str(f"{self.b}^2-4*{self.a}*{self.c}").simplify()
+
+    @property
+    @to_be_token
+    def roots(self):
+        """ Roots of the polynom
+
+        :example:
+        >>> from ...core.MO.polynomial import MOpolynomial
+        >>> P = Quadratic(MOpolynomial('x', [1, 0, 1]))
+        >>> P.roots
+        []
+        >>> P = Quadratic(MOpolynomial('x', [4, -4, 1]))
+        >>> P.roots
+        [<Integer 2>]
+        >>> P = Quadratic(MOpolynomial('x', [1, 0, -1]))
+        >>> P.roots
+        [<Integer - 1>, <Integer 1>]
+        """
+        if self.delta._mo < 0:
+            return []
+        elif self.delta._mo == 0:
+            # return [Expression.from_str(f"-{self.b}/(2*{self.a})").simplify()]
+            return [round(eval(f"-{self.b}/(2*{self.a})"), 2)]
+        else:
+            from math import sqrt
+
+            roots = [
+                str(eval(f"(-{self.b}-sqrt({self.delta}))/(2*{self.a})")),
+                str(eval(f"(-{self.b}+sqrt({self.delta}))/(2*{self.a})")),
+            ]
+            roots.sort()
+            return roots
 
 
 # -----------------------------

mapytex/calculus/API/tokens/token.py

@@ -11,6 +11,7 @@ Tokens: practical envelop of math object
 
 """
 from ..renders import renders
+from ...core.MO.atoms import moify
 
 
 class Token(object):
@@ -26,7 +27,11 @@ class Token(object):
         self._ancestor = ancestor
 
     @classmethod
-    def random(cls):
+    def random(
+        cls,
+        family="integer",
+        **kwds
+    ):
         raise NotImplemented
 
     @classmethod
@@ -69,7 +74,7 @@ class Token(object):
         else:
             raise ValueError(f"Unknow render {self.RENDER}")
 
-        #return renders[self.RENDER](self._mo)
+        # return renders[self.RENDER](self._mo)
 
     @property
     def __txt__(self):
@@ -79,20 +84,29 @@ class Token(object):
     def __tex__(self):
         return self._mo.__tex__
 
+    @property
+    def raw(self):
+        """ Get python's raw forme of the token  """
+        return self._mo.content
+
     def _operate(self, other, operation):
-        """ Make a operation between 2 Tokens, 
-        a Token and en Expression ora
-        a Token an a builtin type
-        """
+        """ Make a operation between 2 Tokens """
         from ..expression import Expression
         from ...core import Tree
         from . import factory
 
         if not isinstance(other, Token):
-            _other = factory(other)
+            try:
+                _other = factory(other)
+            except AttributeError:
+                _other = factory(Expression(moify(other)))
         else:
             _other = other
-        tree = Tree(operation, self._mo, _other._mo)
+
+        if operation == '-':
+            tree = Tree("+", self._mo, Tree("-", None,  _other._mo))
+        else:
+            tree = Tree(operation, self._mo, _other._mo)
         return Expression(tree).simplify()
 
     def __add__(self, other):
@@ -109,6 +123,18 @@ class Token(object):
         ...    print(i)
         3 + 7
         10
+        >>> a = Integer(3)
+        >>> c = a + 7
+        >>> c
+        <Integer 10>
+        >>> for i in c.explain():
+        ...    print(i)
+        3 + 7
+        10
+        >>> a = Integer(3)
+        >>> c = a + "x"
+        >>> c
+        <Linear x + 3>
         >>> from .number import Fraction 
         >>> a = Fraction("4/3")
         >>> b = Integer(7)
@@ -126,6 +152,32 @@ class Token(object):
         """
         return self._operate(other, "+")
 
+    def __sub__(self, other):
+        """ Subing 2 Tokens or a Token and a Expression
+
+        :example:
+        >>> from .number import Integer 
+        >>> a = Integer(3)
+        >>> b = Integer(7)
+        >>> c = a - b
+        >>> c
+        <Integer - 4>
+        >>> for i in c.explain():
+        ...    print(i)
+        3 - 7
+        3 - 7
+        - 4
+        >>> a = Integer(3)
+        >>> c = a - 7
+        >>> c
+        <Integer - 4>
+        >>> a = Integer(3)
+        >>> c = a - "x"
+        >>> c
+        <Linear - x + 3>
+        """
+        return self._operate(other, "-")
+
     def __mul__(self, other):
         """ Multiply 2 Tokens or a Token and a Expression
 
@@ -140,6 +192,12 @@ class Token(object):
         ...    print(i)
         3 * 7
         21
+        >>> c = a * 7
+        >>> c
+        <Integer 21>
+        >>> c = a * "x"
+        >>> c
+        <Linear 3x>
         >>> from .number import Fraction 
         >>> a = Fraction("4/3")
         >>> b = Integer(7)
@@ -167,6 +225,9 @@ class Token(object):
         >>> for i in c.explain():
         ...    print(i)
         3 / 7
+        >>> c = a / 7
+        >>> c
+        <Fraction 3 / 7>
         >>> from .number import Fraction 
         >>> a = Fraction("4/3")
         >>> b = Integer(7)
@@ -182,6 +243,129 @@ class Token(object):
         """
         return self._operate(other, "/")
 
+    def __pow__(self, other):
+        """ Token powered by an other
+
+        :example:
+        >>> from .number import Integer 
+        >>> a = Integer(3)
+        >>> b = Integer(7)
+        >>> c = a ** b
+        >>> c
+        <Integer 2187>
+        >>> c = a ** 7
+        >>> c
+        <Integer 2187>
+        >>> from .number import Decimal 
+        >>> a = Decimal('2.3')
+        >>> c = a ** 2
+        >>> c
+        <Decimal 5.29>
+
+    """
+        return self._operate(other, "^")
+
+
+    def _roperate(self, other, operation):
+        """ Make a operation between 2 Tokens """
+        from ..expression import Expression
+        from ...core import Tree
+        from . import factory
+
+        if not isinstance(other, Token):
+            try:
+                _other = factory(other)
+            except AttributeError:
+                _other = factory(Expression(moify(other)))
+        else:
+            _other = other
+        if operation == '-':
+            tree = Tree("+", _other._mo, Tree("-", None,  self._mo))
+        else:
+            tree = Tree(operation, _other._mo, self._mo)
+        return Expression(tree).simplify()
+
+    def __radd__(self, other):
+        """ Adding 2 Tokens or a Token and a Expression
+
+        :example:
+        >>> from .number import Integer 
+        >>> a = Integer(3)
+        >>> c = 7 + a
+        >>> c
+        <Integer 10>
+        >>> c = "x" + a
+        >>> c
+        <Linear x + 3>
+        """
+        return self._roperate(other, "+")
+
+    def __rsub__(self, other):
+        """ Subing 2 Tokens or a Token and a Expression
+
+        :example:
+        >>> from .number import Integer 
+        >>> a = Integer(3)
+        >>> c = 7 - a
+        >>> c
+        <Integer 4>
+        >>> a = Integer(3)
+        >>> c = "x" - a
+        >>> c
+        <Linear x - 3>
+        """
+        return self._roperate(other, "-")
+    def __rmul__(self, other):
+        """ Multiply 2 Tokens or a Token and a Expression
+
+        :example:
+        >>> from .number import Integer 
+        >>> a = Integer(3)
+        >>> c = 7 * a
+        >>> c
+        <Integer 21>
+        >>> c = "x" * a
+        >>> c
+        <Linear 3x>
+        """
+        return self._roperate(other, "*")
+
+    def __rtruediv__(self, other):
+        """ Divising 2 Tokens or a Token and a Expression
+
+        :example:
+        >>> from .number import Integer 
+        >>> a = Integer(3)
+        >>> c = 7 / a
+        >>> c
+        <Fraction 7 / 3>
+        """
+        return self._roperate(other, "/")
+
+
+    def _get_soul(self, other=None):
+        """ Get the builtin soul of self or other """
+        if isinstance(other, Token):
+            return other._mo._value
+        elif not other is None:
+            return other
+        return self._mo._value
+
+    def __eq__(self, other):
+        return self._get_soul() == self._get_soul(other)
+
+    def __gt__(self, other):
+        return self._get_soul() > self._get_soul(other)
+
+    def __lt__(self, other):
+        return self._get_soul() < self._get_soul(other)
+
+    def __ge__(self, other):
+        return self._get_soul() >= self._get_soul(other)
+
+    def __le__(self, other):
+        return self._get_soul() <= self._get_soul(other)
+
 
 # -----------------------------
 # Reglages pour 'vim'

mapytex/calculus/__init__.py

@@ -30,7 +30,11 @@ Expression is the classe wich handle all calculus. It can randomly generate or i
 
 """
 
-from .API import Expression
+from .API import Expression, Integer, Decimal
+from .core import random_list
+from decimal import getcontext
+#getcontext().prec = 2
+
 
 __all__ = ["Expression"]
 

mapytex/calculus/core/MO/atoms.py

@@ -26,6 +26,7 @@ def moify(token):
     except MOError:
         return token
 
+
 @coroutine
 def moify_cor(target):
     """ Coroutine which try to convert a parsed token into an MO 
@@ -91,6 +92,12 @@ class MOnumber(Atom):
         >>> MOnumber(Decimal("-23.3"))
         <MOnumber - 23.3>
 
+        Or directly passe a decimal string
+        >>> MOnumber("23.3")
+        <MOnumber 23.3>
+        >>> MOnumber("-23.3")
+        <MOnumber - 23.3>
+
         MOnumber initialisation is idempotent
 
         >>> a = MOnumber(23)
@@ -100,7 +107,7 @@ class MOnumber(Atom):
         >>> MOnumber("a")
         Traceback (most recent call last):
             ...
-        mapytex.calculus.core.MO.exceptions.MOError: ('The value of an MOnumber need to be a int, a float or a Decimal', "(got <class 'str'>)")
+        mapytex.calculus.core.MO.exceptions.MOError: ('The value of an MOnumber need to be a int, a float, a Decimal or a decimal string', "(got <class 'str'>)")
 
         Atoms specific property and methods
 
@@ -117,15 +124,26 @@ class MOnumber(Atom):
         """
         if isinstance(value, Atom) and isinstance(value.value, (int, Decimal, float)):
             Atom.__init__(self, value.value)
-        elif isinstance(value, (int, Decimal)):
+        elif isinstance(value, (float, Decimal)):
+            if int(value) == value:
+                Atom.__init__(self, int(value))
+            else:
+                Atom.__init__(self, Decimal(value))
+        elif isinstance(value, int):
             Atom.__init__(self, value)
-        elif isinstance(value, float):
-            Atom.__init__(self, Decimal(value))
         else:
-            raise MOError(
-                "The value of an MOnumber need to be a int, a float or a Decimal",
-                f"(got {type(value)})",
-            )
+            try:
+                v = float(value)
+            except (ValueError, TypeError):
+                raise MOError(
+                    "The value of an MOnumber need to be a int, a float, a Decimal or a decimal string",
+                    f"(got {type(value)})",
+                )
+            else:
+                if int(v) == v:
+                    Atom.__init__(self, int(v))
+                else:
+                    Atom.__init__(self, Decimal(value))
 
         self._signature = "scalar"
 
@@ -154,7 +172,7 @@ class MOnumber(Atom):
         >>> MOnumber(-3).__tex__
         '- 3'
         """
-        if self.value > 0:
+        if self.value >= 0:
             return str(self.value)
 
         return f"- {abs(self.value)}"
@@ -166,6 +184,16 @@ 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 +288,16 @@ 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'

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"]
 
@@ -34,7 +35,7 @@ class MOFraction(Molecule):
         >>> print(f.__txt__)
         2 / 3
         >>> print(f.__tex__)
-        \\frac{2}{3}
+        \\dfrac{2}{3}
         >>> print(f)
         2 / 3
         >>> f = MOFraction(2, 3, negative = True)
@@ -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'

mapytex/calculus/core/MO/mo.py

@@ -97,6 +97,9 @@ class MO(ABC):
         """
         return self._signature
 
+    def differentiate(self):
+        raise NotImplementedError
+
 
 class Atom(MO):
 

mapytex/calculus/core/MO/monomial.py

@@ -111,6 +111,22 @@ class MOstrPower(Molecule):
         """
         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 +274,31 @@ 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'

mapytex/calculus/core/MO/polynomial.py

@@ -6,6 +6,7 @@
 #
 # Distributed under terms of the MIT license.
 
+from collections import OrderedDict
 from mapytex.calculus.core.tree import Tree
 from . import MO, MOstr
 from .mo import Molecule
@@ -57,8 +58,9 @@ class MOpolynomial(Molecule):
             raise TypeError("Coefs needs to be a dictionnary or a list")
         self._coefs = _coefs
 
-        monomials = {}
-        for deg, coef in self._coefs.items():
+        monomials = OrderedDict()
+        for deg in sorted(self._coefs.keys()):
+            coef = self._coefs[deg]
             if deg == 0:
                 monomials[deg] = coef
             elif deg == 1 and coef == 1:
@@ -120,12 +122,34 @@ class MOpolynomial(Molecule):
         :example:
         >>> p = MOpolynomial('x', [1, 2, 3])
         >>> p.monomials
-        {<MOnumber 0>: <MOnumber 1>, <MOnumber 1>: <MOMonomial 2x>, <MOnumber 2>: <MOMonomial 3x^2>}
+        OrderedDict([(<MOnumber 0>, <MOnumber 1>), (<MOnumber 1>, <MOMonomial 2x>), (<MOnumber 2>, <MOMonomial 3x^2>)])
         >>> p.monomials.values()
-        dict_values([<MOnumber 1>, <MOMonomial 2x>, <MOMonomial 3x^2>])
+        odict_values([<MOnumber 1>, <MOMonomial 2x>, <MOMonomial 3x^2>])
         """
         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'

mapytex/calculus/core/__init__.py

@@ -66,6 +66,7 @@ from .tree import Tree, AssocialTree
 from .compute import compute
 from .typing import typing, TypingError
 from .renders import tree2txt, tree2tex
+from .random import list_generator as random_list
 
 
 # -----------------------------

mapytex/calculus/core/compute/add.py

@@ -70,6 +70,9 @@ def monumber_monumber(left, right):
     >>> b = MOnumber(6)
     >>> add(a, b)
     <MOnumber 10>
+    >>> b = MOnumber('2.3')
+    >>> add(a, b)
+    <MOnumber 6.3>
 
     """
     return MO.factory(left.value + right.value)

mapytex/calculus/core/random/__init__.py

@@ -47,8 +47,8 @@ Tree with RdLeaf replaced by generated values
 >>> leafs
 ['a', 'a*k']
 >>> rd_varia = extract_rv(leafs)
->>> rd_varia # doctest: +SKIP
-{'a', 'k'}
+>>> sorted(list(rd_varia))
+['a', 'k']
 >>> generated = random_generator(rd_varia, conditions=['a%2+1'])
 >>> generated # doctest: +SKIP
 {'a': 7, 'k': 4}
@@ -61,8 +61,18 @@ Tree with RdLeaf replaced by generated values
  > 7
  > 28
 
+List generator
+--------------
+
+This function ignores tree structure and works with lists
+
+>>> values = list_generator(["a", "a*b", "b", "c"], conditions=["b%c==1"])
+>>> values # doctest: +SKIP
+{'a': -8, 'a*b': -40, 'b': 5, 'c': 4}
 """
 
+__all__ = ["list_generator"]
+
 from random import choice
 from functools import reduce
 from .leaf import RdLeaf
@@ -244,3 +254,35 @@ def build_variable_scope(rd_variables, rejected, min_max, variables_scope):
             except KeyError:
                 complete_scope[v]["min_max"] = min_max
     return complete_scope
+
+    
+def list_generator(var_list, conditions=[], rejected=[0], min_max=(-10, 10), variables_scope={}, dictionnary=False):
+    """ Generate random computed values from the list
+
+    :param rd_variables: list of random variables to generate (can be computed value - "a*b")
+    :param conditions: condition over variables
+    :param rejected: Rejected values for the generator (default [0])
+    :param min_max: (min, max) limits in between variables will be generated
+    :param variables_scope: rejected and min_max define for individual variables
+    :param dictionnary: the return value will be a dictionnary with var_list as keys (default False)
+    :return: dictionnary of generated variables
+
+    :example:
+    >>> a, ab, b, c = list_generator(["a", "a*b", "b", "c"])
+    >>> a, ab, b, c # doctest: +SKIP
+    (5, -20, -4, -3)
+    >>> a * b == ab
+    True
+    >>> ab # doctest: +SKIP
+    -20
+    >>> a, b # doctest: +SKIP
+    5, -4
+    >>> list_generator(["a", "a*b", "b", "c"], dictionnary=True) # doctest: +SKIP
+    {'a': -3, 'a*b': 18, 'b': -6, 'c': -4}
+    """
+    rv = extract_rv(var_list)
+    rv_gen = random_generator(rv, conditions, rejected, min_max, variables_scope)
+    generated = compute_leafs(var_list, rv_gen)
+    if dictionnary:
+        return generated
+    return [generated[v] for v in var_list]

mapytex/calculus/core/renders/__init__.py

@@ -10,7 +10,7 @@
 Tree renders
 """
 
-__all__ = ["tree2txt"]
+__all__ = ["tree2txt", "tree2tex"]
 
 from .tree2txt import tree2txt
 from .tree2tex import tree2tex

mapytex/calculus/core/renders/tree2tex.py

@@ -117,17 +117,17 @@ def div2tex(left, right):
 
     >>> from ..MO import MO
     >>> div2tex(MO.factory(2), MO.factory(3))
-    '\\frac{2}{3}'
+    '\\dfrac{2}{3}'
     >>> from ..tree import Tree
     >>> t = Tree.from_str("1/2")
     >>> div2tex(t, MO.factory(3))
-    '\\frac{\\frac{1}{2}}{3}'
+    '\\dfrac{\\dfrac{1}{2}}{3}'
     >>> t = Tree.from_str("1+2")
     >>> div2tex(t, MO.factory(3))
-    '\\frac{1 + 2}{3}'
+    '\\dfrac{1 + 2}{3}'
     >>> t = Tree.from_str("1*2")
     >>> div2tex(MO.factory(3), t)
-    '\\frac{3}{1 \\times 2}'
+    '\\dfrac{3}{1 \\times 2}'
     """
     try:
         left_ = tree2tex(left)
@@ -138,7 +138,7 @@ def div2tex(left, right):
     except (AttributeError, ValueError):
         right_ = right.__tex__
 
-    return "\\frac{" + left_ + "}{" + right_ + "}"
+    return "\\dfrac{" + left_ + "}{" + right_ + "}"
 
 
 def pow2tex(left, right):
@@ -196,7 +196,10 @@ def render_with_parenthesis(subtree, operator):
                 subtree_need_parenthesis = True
         except (AttributeError, KeyError):
             pass
-        subtree_ = subtree.__tex__
+        try:
+            subtree_ = subtree.__tex__
+        except AttributeError:
+            subtree_ = str(subtree)
     else:
         if OPERATORS[subtree.node]["precedence"] < OPERATORS[operator]["precedence"]:
             subtree_need_parenthesis = True

mapytex/calculus/core/renders/tree2txt.py

@@ -200,7 +200,10 @@ def render_with_parenthesis(subtree, operator):
                 subtree_need_parenthesis = True
         except (AttributeError, KeyError):
             pass
-        subtree_ = subtree.__txt__
+        try:
+            subtree_ = subtree.__txt__
+        except AttributeError:
+            subtree_ = str(subtree)
     else:
         if OPERATORS[subtree.node]["precedence"] < OPERATORS[operator]["precedence"]:
             subtree_need_parenthesis = True

mapytex/calculus/core/str2.py

@@ -15,7 +15,7 @@ from decimal import Decimal, InvalidOperation
 from .coroutine import *
 from .operator import is_operator
 from .MO import moify_cor
-from .random.leaf import look_for_rdleaf
+from .random.leaf import look_for_rdleaf, RdLeaf
 
 __all__ = ["str2"]
 
@@ -395,8 +395,10 @@ def missing_times(target):
                     elif not is_operator(tok) and tok != ")":
                         target_.send("*")
 
-            if isinstance(tok, int) or (
-                isinstance(tok, str) and not is_operator(tok) and not tok == "("
+            if (
+                isinstance(tok, int)
+                or (isinstance(tok, str) and not is_operator(tok) and not tok == "(")
+                or (isinstance(tok, RdLeaf))
             ):
                 previous = tok
 
@@ -818,31 +820,8 @@ def rdstr2(sink):
     >>> rdstr2list = rdstr2(list_sink)
     >>> rdstr2list("{a}+{a*b}-2")
     [<RdLeaf a>, '+', <RdLeaf a*b>, '+', <MOnumber - 2>]
-    """
-    lfop = lookfor(is_operator)
-    operator_corout = partial(concurent_broadcast, lookfors=[lfop])
-
-    def pipeline(expression):
-        str2_corout = look_for_rdleaf(
-            lookforNumbers(operator_corout(missing_times(moify_cor(pparser(sink)))))
-        )
-
-        for i in expression.replace(" ", ""):
-            str2_corout.send(i)
-        a = str2_corout.throw(STOOOP)
-
-        return a
-
-    return pipeline
-
-
-def rdstr2(sink):
-    """ Return a pipeline which parse random expression and with sink as endpoint
-
-    :example:
-    >>> rdstr2list = rdstr2(list_sink)
-    >>> rdstr2list("{a}+{a*b}-2")
-    [<RdLeaf a>, '+', <RdLeaf a*b>, '+', <MOnumber - 2>]
+    >>> rdstr2list("{a}({b}x+{c})")
+    [<RdLeaf a>, '*', [<RdLeaf b>, '*', <MOstr x>, '+', <RdLeaf c>]]
     """
     lfop = lookfor(is_operator)
     operator_corout = partial(concurent_broadcast, lookfors=[lfop])

mapytex/calculus/core/tree.py

@@ -77,13 +77,22 @@ class Tree:
          > *
          | > 3
          | > n
-        >>> t = Tree.from_str("2+{n}*x", random=True)
+        >>> t = Tree.from_str("2+{n}x", random=True)
         >>> print(t)
         +
          > 2
          > *
          | > {n}
          | > x
+        >>> t = Tree.from_str("{a}({b}x+{c})", random=True)
+        >>> print(t)
+        *
+         > {a}
+         > +
+         | > *
+         | | > {b}
+         | | > x
+         | > {c}
 
 
         """
@@ -954,7 +963,22 @@ class MutableTree(Tree):
          | | > 8
          | | > 3
          | > x
-
+        >>> t = MutableTree.from_str("{b}*x+{c}", random=True)
+        >>> print(t)
+        +
+         > *
+         | > {b}
+         | > x
+         > {c}
+        >>> t = MutableTree.from_str("{a}*({b}*x+{c})", random=True)
+        >>> print(t)
+        *
+         > {a}
+         > +
+         | > *
+         | | > {b}
+         | | > x
+         | > {c}
         """
         if random:
             str_2_mut_tree = rdstr2(cls.sink)

mapytex/calculus/core/typing/add.py

@@ -95,10 +95,10 @@ def moscalar_momonomial(left, right):
     >>> a = MOnumber(2)
     >>> b = MOMonomial(3, 'x', 4)
     >>> add(a, b)
-    <MOpolynomial 2 + 3x^4>
+    <MOpolynomial 3x^4 + 2>
     >>> a = MOFraction(1, 5)
     >>> add(a, b)
-    <MOpolynomial 1 / 5 + 3x^4>
+    <MOpolynomial 3x^4 + 1 / 5>
     """
     return MOpolynomial(right.variable, {right.power: right.coefficient, 0: left})
 
@@ -126,10 +126,10 @@ def moscalar_mopolynomial(left, right):
     >>> a = MOnumber(2)
     >>> b = MOpolynomial('x', [0, 2, 3])
     >>> add(a, b)
-    <MOpolynomial 2 + 3x^2 + 2x>
+    <MOpolynomial 3x^2 + 2x + 2>
     >>> a = MOFraction(1, 5)
     >>> add(a, b)
-    <MOpolynomial 1 / 5 + 3x^2 + 2x>
+    <MOpolynomial 3x^2 + 2x + 1 / 5>
     """
     if 0 in right.coefficients.keys():
         raise NotImplementedError(
@@ -237,7 +237,7 @@ def mostr_mopolynomial(left, right):
     >>> a = MOstr("x")
     >>> b = MOpolynomial('x', [1, 0, 3])
     >>> add(a, b)
-    <MOpolynomial x + 3x^2 + 1>
+    <MOpolynomial 3x^2 + x + 1>
     """
     if 1 in right.coefficients.keys():
         raise NotImplementedError("Polynomial with no constant, calculus to do")
@@ -255,7 +255,7 @@ def mopolynomial_mostr(left, right):
     >>> a = MOpolynomial('x', [1, 0, 3])
     >>> b = MOstr("x")
     >>> add(a, b)
-    <MOpolynomial 3x^2 + 1 + x>
+    <MOpolynomial 3x^2 + x + 1>
     """
     if 1 in left.coefficients.keys():
         raise NotImplementedError("Polynomial with no constant, calculus to do")
@@ -272,7 +272,7 @@ def mostrpower_mopolynomial(left, right):
     >>> a = MOstrPower("x", 2)
     >>> b = MOpolynomial('x', [1, 2, 0, 4])
     >>> add(a, b)
-    <MOpolynomial x^2 + 4x^3 + 2x + 1>
+    <MOpolynomial 4x^3 + x^2 + 2x + 1>
     """
     if left.power in right.coefficients.keys():
         raise NotImplementedError("Degree in common, need to compute")
@@ -290,7 +290,7 @@ def mopolynomial_mostrpower(left, right):
     >>> a = MOpolynomial('x', [1, 2, 0, 4])
     >>> b = MOstrPower("x", 2)
     >>> add(a, b)
-    <MOpolynomial 4x^3 + 2x + 1 + x^2>
+    <MOpolynomial 4x^3 + x^2 + 2x + 1>
     """
     if right.power in left.coefficients.keys():
         raise NotImplementedError("Degree in common, need to compute")
@@ -307,7 +307,7 @@ def momonomial_mopolynomial(left, right):
     >>> a = MOMonomial(3, "x", 2)
     >>> b = MOpolynomial('x', [1, 2, 0, 4])
     >>> add(a, b)
-    <MOpolynomial 3x^2 + 4x^3 + 2x + 1>
+    <MOpolynomial 4x^3 + 3x^2 + 2x + 1>
     """
     if left.power in right.coefficients.keys():
         raise NotImplementedError("Degree in common, need to compute")
@@ -325,7 +325,7 @@ def mopolynomial_momonomial(left, right):
     >>> a = MOpolynomial('x', [1, 2, 0, 4])
     >>> b = MOMonomial(3, "x", 2)
     >>> add(a, b)
-    <MOpolynomial 4x^3 + 2x + 1 + 3x^2>
+    <MOpolynomial 4x^3 + 3x^2 + 2x + 1>
     """
     if right.power in left.coefficients.keys():
         raise NotImplementedError("Degree in common, need to compute")
@@ -342,9 +342,9 @@ def mopolynomial_mopolynomial(left, right):
     >>> a = MOpolynomial('x', [1, 0, 3])
     >>> b = MOpolynomial('x', [0, 2, 0, 4])
     >>> add(a, b)
-    <MOpolynomial 3x^2 + 1 + 4x^3 + 2x>
+    <MOpolynomial 4x^3 + 3x^2 + 2x + 1>
     >>> add(b, a)
-    <MOpolynomial 4x^3 + 2x + 3x^2 + 1>
+    <MOpolynomial 4x^3 + 3x^2 + 2x + 1>
     """
     common_degree = set(left.monomials.keys()).intersection(right.monomials.keys())
     if common_degree:
@@ -361,7 +361,7 @@ def mostr_monomial(left, right):
     >>> a = MOstr('x')
     >>> b = MOMonomial(3, 'x', 4)
     >>> add(a, b)
-    <MOpolynomial x + 3x^4>
+    <MOpolynomial 3x^4 + x>
     """
     if right.power == 1:
         raise NotImplementedError("Monomial is deg 1, need to compute")
@@ -391,7 +391,7 @@ def mostrpower_monomial(left, right):
     >>> a = MOstrPower('x', 2)
     >>> b = MOMonomial(3, 'x', 4)
     >>> add(a, b)
-    <MOpolynomial x^2 + 3x^4>
+    <MOpolynomial 3x^4 + x^2>
     """
     if left.power == right.power:
         raise NotImplementedError(

mapytex/calculus/core/typing/multiply.py

@@ -15,6 +15,7 @@ from ..tree import Tree
 from ..MO import MO, MOnumber, MOstr
 from ..MO.fraction import MOFraction
 from ..MO.monomial import MOstrPower, MOMonomial
+from ..compute.filters import special_case
 
 multiply_doc = """ Multiply MOs
 
@@ -27,7 +28,38 @@ multiply_doc = """ Multiply MOs
 multiply = Dispatcher("multiply", doc=multiply_doc)
 
 
+def multiply_filter(left, right):
+    """ Automatic multiply on MO
+
+    :param left: MO
+    :param right: MO
+    :returns: MO if it is a special case, nothing other wise
+    """
+    try:
+        if left == 0:
+            return left
+    except TypeError:
+        pass
+    try:
+        if right == 0:
+            return right
+    except TypeError:
+        pass
+
+    try:
+        if left == 1:
+            return right
+    except TypeError:
+        pass
+    try:
+        if right == 1:
+            return left
+    except TypeError:
+        pass
+
+
 @multiply.register((MOnumber, MOFraction), MOstr)
+@special_case(multiply_filter)
 def moscalar_mostr(left, right):
     """ Multiply a scalar with a letter to create a MOMonomial
 
@@ -43,6 +75,7 @@ def moscalar_mostr(left, right):
 
 
 @multiply.register(MOstr, (MOnumber, MOFraction))
+@special_case(multiply_filter)
 def mostr_moscalar(left, right):
     """ Multiply a scalar with a letter to create a MOMonomial
 
@@ -58,6 +91,7 @@ def mostr_moscalar(left, right):
 
 
 @multiply.register((MOnumber, MOFraction), MOstrPower)
+@special_case(multiply_filter)
 def moscalar_mostrpower(left, right):
     """ Multiply a scalar with a MOstrPower
 
@@ -65,12 +99,18 @@ def moscalar_mostrpower(left, right):
     >>> x = MOstrPower('x', 4)
     >>> multiply(a, x)
     <MOMonomial 4x^4>
-
+    >>> a = MOnumber(1)
+    >>> x = MOstrPower('x', 4)
+    >>> multiply(a, x)
+    <MOstrPower x^4>
     """
+    # if left == 1:
+    #    return right
     return MOMonomial(left, right)
 
 
 @multiply.register(MOstrPower, (MOnumber, MOFraction))
+@special_case(multiply_filter)
 def mostrpower_moscalar(left, right):
     """ Multiply a MOstrPower with a scalar
 

mapytex/geometry/__init__.py

@@ -6,4 +6,4 @@ from .pythagore import random_pythagore
 # -----------------------------
 # Reglages pour 'vim'
 # vim:set autoindent expandtab tabstop=4 shiftwidth=4:
-# cursor: 16 del 
+# cursor: 16 del

mapytex/geometry/pythagore.py

@@ -5,7 +5,7 @@
 from random import randint
 
 
-def random_pythagore(v_min = 1, v_max = 10, nbr_format = lambda x : x) :
+def random_pythagore(v_min=1, v_max=10, nbr_format=lambda x: x):
     """ Generate a pythagore triplet
     :returns: (a,b,c) such that a^2 = b^2 + c^2
 
@@ -14,10 +14,11 @@ def random_pythagore(v_min = 1, v_max = 10, nbr_format = lambda x : x) :
     while u == v:
         u, v = randint(v_min, v_max), randint(v_min, v_max)
     u, v = max(u, v), min(u, v)
-    triplet = (u**2+v**2, 2*u*v, u**2-v**2)
+    triplet = (u ** 2 + v ** 2, 2 * u * v, u ** 2 - v ** 2)
     formated_triplet = [nbr_format(i) for i in triplet]
     return formated_triplet
 
+
 # -----------------------------
 # Reglages pour 'vim'
 # vim:set autoindent expandtab tabstop=4 shiftwidth=4:

mapytex/stat/dataset.py

@@ -1,4 +1,4 @@
-#/usr/bin/env python
+# /usr/bin/env python
 # -*- coding:Utf-8 -*-
 
 #
@@ -32,11 +32,17 @@ class Dataset(list):
     """
 
     @classmethod
-    def random(cls, length, data_name="Valeurs",
-               distrib="gauss", rd_args=(0, 1),
-               nbr_format=lambda x: round(x, 2),
-               v_min=None, v_max=None,
-               exact_mean=None):
+    def random(
+        cls,
+        length,
+        data_name="Valeurs",
+        distrib="gauss",
+        rd_args=(0, 1),
+        nbr_format=lambda x: round(x, 2),
+        v_min=None,
+        v_max=None,
+        exact_mean=None,
+    ):
         """ Generate a random list of value
 
         :param length: length of the dataset
@@ -47,11 +53,9 @@ class Dataset(list):
         :param v_max: maximum accepted value
         :param exact_mean: if set, the last generated number will be create in order that the computed mean is exacly equal to "exact_mean"
         """
-        data = random_generator(length,
-                                distrib, rd_args,
-                                nbr_format,
-                                v_min, v_max,
-                                exact_mean)
+        data = random_generator(
+            length, distrib, rd_args, nbr_format, v_min, v_max, exact_mean
+        )
 
         return cls(data, data_name=data_name)
 
@@ -94,7 +98,7 @@ class Dataset(list):
     def deviation(self):
         """ Compute the deviation (not normalized) """
         mean = self.mean()
-        return sum([(x - mean)**2 for x in self])
+        return sum([(x - mean) ** 2 for x in self])
 
     @number_factory
     def variance(self):
@@ -120,7 +124,8 @@ class Dataset(list):
             self.quartile(1),
             self.quartile(2),
             self.quartile(3),
-            max(self))
+            max(self),
+        )
 
     @number_factory
     def quartile(self, quartile=1):
@@ -173,18 +178,21 @@ class Dataset(list):
         """ Latex code to display dataset as a tabular """
         d_per_line = self.effectif_total() // nbr_lines
         d_last_line = self.effectif_total() % d_per_line
-        splited_data = [self[x:x + d_per_line]
-                        for x in range(0, self.effectif_total(), d_per_line)]
+        splited_data = [
+            self[x : x + d_per_line]
+            for x in range(0, self.effectif_total(), d_per_line)
+        ]
         # On ajoute les éléments manquant pour la dernière line
         if d_last_line:
-            splited_data[-1] += [' '] * (d_per_line - d_last_line)
+            splited_data[-1] += [" "] * (d_per_line - d_last_line)
 
         # Construction du tableau
         latex = "\\begin{{tabular}}{{|c|*{{{nbr_col}}}{{c|}}}} \n".format(
-            nbr_col=d_per_line)
+            nbr_col=d_per_line
+        )
         latex += "\t\t \hline \n"
 
-        d_lines = [' & '.join(map(str, l)) for l in splited_data]
+        d_lines = [" & ".join(map(str, l)) for l in splited_data]
         latex += " \\\\ \n \\hline \n".join(d_lines)
 
         latex += " \\\\ \n \\hline \n"

mapytex/stat/number_tools.py

@@ -1,4 +1,4 @@
-#/usr/bin/env python
+# /usr/bin/env python
 # -*- coding:Utf-8 -*-
 
 from functools import wraps
@@ -6,6 +6,7 @@ from functools import wraps
 
 def number_factory(fun):
     """ Decorator which format returned value """
+
     @wraps(fun)
     def wrapper(*args, **kwargs):
         ans = fun(*args, **kwargs)
@@ -16,6 +17,7 @@ def number_factory(fun):
                 return round(ans, 2)
         except AttributeError:
             return ans
+
     return wrapper
 
 

mapytex/stat/random_generator.py

@@ -1,14 +1,18 @@
-#/usr/bin/env python
+# /usr/bin/env python
 # -*- coding:Utf-8 -*-
 
 from random import randint, uniform, gauss, choice
 
 
-def random_generator(length,
-                     distrib=gauss, rd_args=(0, 1),
-                     nbr_format=lambda x: round(x, 2),
-                     v_min=None, v_max=None,
-                     exact_mean=None):
+def random_generator(
+    length,
+    distrib=gauss,
+    rd_args=(0, 1),
+    nbr_format=lambda x: round(x, 2),
+    v_min=None,
+    v_max=None,
+    exact_mean=None,
+):
     """ Generate a random list of value
 
     :param length: length of the dataset
@@ -19,12 +23,18 @@ def random_generator(length,
     :param v_max: maximum accepted value
     :param exact_mean: if set, the last generated number will be create in order that the computed mean is exacly equal to "exact_mean"
 
-    >>> random_generator(10)
-    >>> random_generator(10, distrib = uniform, rd_args = (5, 10))
-    >>> random_generator(10, distrib = "uniform", rd_args = (5, 10))
-    >>> random_generator(10, v_min = 0)
-    >>> random_generator(10, exact_mean = 0)
-    >>> random_generator(10, distrib = gauss, rd_args = (50,20), nbr_format = int)
+    >>> random_generator(10) # doctest: +SKIP
+    [-0.76, 0.46, 0.19, 0.08, -1.13, -0.5, 0.47, -2.11, 0.16, -1.05]
+    >>> random_generator(10, distrib = uniform, rd_args = (5, 10)) # doctest: +SKIP
+    [9.01, 5.32, 5.59, 8.8, 7.36, 6.9, 6.05, 7.44, 9.47, 6.95]
+    >>> random_generator(10, distrib = "uniform", rd_args = (5, 10)) # doctest: +SKIP
+    [7.85, 9.01, 5.32, 5.59, 8.8, 7.36, 6.9, 6.05, 7.44, 9.47]
+    >>> random_generator(10, v_min = 0) # doctest: +SKIP
+    [0.46, 0.19, 0.08, 0.47, 0.16, 0.87, 0.17, 1.79, 0.19, 1.12]
+    >>> random_generator(10, exact_mean = 0) # doctest: +SKIP
+    [-0.76, 0.46, 0.19, 0.08, -1.13, -0.5, 0.47, -2.11, 0.16, 3.14]
+    >>> random_generator(10, distrib = gauss, rd_args = (50,20), nbr_format = int) # doctest: +SKIP
+    [34, 59, 53, 51, 27, 40, 59, 7, 53, 28]
 
     """
     # if exact_mean is set, we create automaticaly only length-1 value
@@ -47,7 +57,8 @@ def random_generator(length,
         "gauss": gauss,
         "uniform": uniform,
         "randint": randint,
-        "choice": choice}
+        "choice": choice,
+    }
     try:
         distrib(*rd_args)
     except TypeError:
@@ -67,11 +78,13 @@ def random_generator(length,
         last_v = nbr_format((length + 1) * exact_mean - sum(data))
         if not validate(last_v):
             raise ValueError(
-                "Can't build the last value. Conflict between v_min/v_max and exact_mean")
+                "Can't build the last value. Conflict between v_min/v_max and exact_mean"
+            )
         data.append(last_v)
 
     return data
 
+
 # -----------------------------
 # Reglages pour 'vim'
 # vim:set autoindent expandtab tabstop=4 shiftwidth=4:

mapytex/stat/weightedDataset.py

@@ -1,4 +1,4 @@
-#/usr/bin/env python
+# /usr/bin/env python
 # -*- coding:Utf-8 -*-
 
 """
@@ -12,9 +12,11 @@ from .dataset import Dataset
 from itertools import chain
 from .number_tools import number_factory
 
+
 def flatten_list(l):
     return list(chain(*l))
 
+
 class WeightedDataset(dict):
     """ A weighted dataset with statistics and latex rendering methods
 
@@ -37,11 +39,8 @@ class WeightedDataset(dict):
     """
 
     def __init__(
-            self,
-            datas=[],
-            data_name="Valeurs",
-            weights=[],
-            weight_name="Effectifs"):
+        self, datas=[], data_name="Valeurs", weights=[], weight_name="Effectifs"
+    ):
         """
         Initiate the WeightedDataset
         """
@@ -84,7 +83,7 @@ class WeightedDataset(dict):
     def deviation(self):
         """ Compute the deviation (not normalized) """
         mean = self.mean()
-        return sum([v * (k - mean)**2 for (k, v) in self.items()])
+        return sum([v * (k - mean) ** 2 for (k, v) in self.items()])
 
     @number_factory
     def variance(self):
@@ -109,11 +108,13 @@ class WeightedDataset(dict):
         (1, 3, 4, 5, 5)
 
         """
-        return (min(self.keys()),
-                self.quartile(1),
-                self.quartile(2),
-                self.quartile(3),
-                max(self.keys()))
+        return (
+            min(self.keys()),
+            self.quartile(1),
+            self.quartile(2),
+            self.quartile(3),
+            max(self.keys()),
+        )
 
     @number_factory
     def quartile(self, quartile=1):
@@ -146,8 +147,9 @@ class WeightedDataset(dict):
         position = self.posi_quartile(quartile) - 1
         expanded_values = flatten_list([v * [k] for (k, v) in self.items()])
         if position.is_integer():
-            return (expanded_values[int(position)] +
-                    expanded_values[int(position) + 1]) / 2
+            return (
+                expanded_values[int(position)] + expanded_values[int(position) + 1]
+            ) / 2
         else:
             return expanded_values[ceil(position)]
 
@@ -167,7 +169,8 @@ class WeightedDataset(dict):
     def tabular_latex(self):
         """ Latex code to display dataset as a tabular """
         latex = "\\begin{{tabular}}{{|c|*{{{nbr_col}}}{{c|}}}} \n".format(
-            nbr_col=len(self.keys()))
+            nbr_col=len(self.keys())
+        )
         latex += "\t \hline \n"
         data_line = "\t {data_name} ".format(data_name=self.data_name)
         weight_line = "\t {weight_name} ".format(weight_name=self.weight_name)

noxfile.py

@@ -0,0 +1,35 @@
+#!/usr/bin/env python
+
+
+import nox
+
+
+@nox.session
+def lint(session):
+    session.install("black")
+    session.run("black", "mapytex", "noxfile.py", "setup.py")
+
+
+@nox.session
+def test(session):
+    session.install("-r", "requirements.txt")
+    session.install("pytest")
+    session.run("pytest", "mapytex")
+
+
+@nox.session
+def docs(session):
+    """Build the documentation."""
+    session.run("rm", "-rf", "documentation/_build", external=True)
+    session.install("sphinx", "sphinx-autobuild", "sphinx_rtd_theme")
+    session.install(".")
+    session.cd("documentation/source")
+    sphinx_args = ["-b", "html", "-W", "-d", "_build/doctrees", ".", "_build/html"]
+
+    if not session.interactive:
+        sphinx_cmd = "sphinx-build"
+    else:
+        sphinx_cmd = "sphinx-autobuild"
+        sphinx_args.insert(0, "--open-browser")
+
+        session.run(sphinx_cmd, *sphinx_args)

setup.py

@@ -6,17 +6,14 @@ except ImportError:
     from distutils.core import setup
 
 setup(
-    name='mapytex',
-    version='2.1',
-    description='Computing like a student',
-    author='Benjamin Bertrand',
-    author_email='programming@opytex.org',
-    url='http://git.opytex.org/lafrite/Mapytex',
-    #packages=['mapytex'],
+    name="mapytex",
+    version="2.3.2",
+    description="Computing like a student",
+    author="Benjamin Bertrand",
+    author_email="programming@opytex.org",
+    url="http://git.opytex.org/lafrite/Mapytex",
+    # packages=['mapytex'],
     packages=find_packages(),
-    include_package_data = True,
-    install_requires=[
-        'multipledispatch',
-        'tabulate',
-    ],
-    )
+    include_package_data=True,
+    install_requires=["multipledispatch", "tabulate"],
+)