Feat: Remove references to random in API

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

@@ -1,7 +1,7 @@
 #!/usr/bin/env python
 # encoding: utf-8
 
-from .calculus import Expression#, Polynom, Fraction, random_str, txt, Equation
+from .calculus import Expression, render, random
 
 # Expression.set_render('tex')
 

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
@@ -105,26 +106,37 @@ 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
 
+>>> e = Expression.from_str("(2x-3)(-x+2)")
+>>> e_simplified = e.simplify()
+>>> e_simplified
+<Quadratic - 2x^2 + 7x - 6>
+>>> for s in e_simplified.explain():
+...    print(s)
+(2x - 3)(- x + 2)
+(2x - 3)(- x + 2)
+2x(- x) + 2x * 2 - 3(- x) - 3 * 2
+2(- 1) * x^(1 + 1) + 2 * 2 * x - 3(- 1) * x - 6
+4x + 3x - 2x^2 - 6
+(4 + 3) * x - 2x^2 - 6
+- 2x^2 + 7x - 6
 """
 
+from .renders import render
 from .expression import Expression
+from .tokens import Token
+from .tokens.polynomial import Polynomial
+from .tokens.number import Integer, Decimal, Fraction
+
 
 if __name__ == "__main__":
-    e = Expression.from_str("1+2/3/4/5")
-    et = e._typing()
-    print("typing")
-    print(e._tree)
-    e = et._order()
-    print("order")
-    print(e._tree)
-    e = e._optimize()
-    print("then optimize")
-    print(e._tree)
-    e = et._optimize()
-    print("optimize without order")
-    print(e._tree)
+    e = Expression.from_str("(2x-3)(-x+2)")
+    e_simplified = e.simplify()
+    e_simplified
+    for s in e_simplified.explain():
+        print(s._tree.map_on_leaf(lambda x: type(x)))
+        print(s)
 
 # -----------------------------
 # Reglages pour 'vim'

mapytex/calculus/API/expression.py

@@ -10,11 +10,11 @@
 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.MO import moify
-from .tokens import factory, Token
-from .renders import renders
+from .tokens import factory
+from .renders import render
 
 
 class Expression(object):
@@ -35,7 +35,6 @@ class Expression(object):
     14
     """
 
-    RENDER = "txt"
 
     def __init__(self, tree, ancestor=None):
         """
@@ -43,39 +42,6 @@ class Expression(object):
         self._tree = tree
         self._ancestor = ancestor
 
-    @classmethod
-    def set_render(cls, render):
-        """ Define default render function 
-
-        :param render: render name (txt or tex)
-
-        :example:
-        >>> e = Expression.from_str("2+3*4")
-        >>> print(e)
-        2 + 3 * 4
-        >>> e = Expression.from_str("2+3/4")
-        >>> print(e)
-        2 + 3 / 4
-        >>> es = e.simplify()
-        >>> print(es)
-        11 / 4
-        >>> Expression.set_render('tex')
-        >>> Expression.RENDER
-        'tex'
-        >>> e = Expression.from_str("2+3*4")
-        >>> print(e)
-        2 + 3 \\times 4
-        >>> e = Expression.from_str("2+3/4")
-        >>> print(e)
-        2 + \\frac{3}{4}
-        >>> es = e.simplify()
-        >>> print(es)
-        \\frac{11}{4}
-        >>> Expression.set_render('txt')
-        """
-        Token.set_render(render)
-        cls.RENDER = render
-
     @classmethod
     def from_str(cls, string, typing=True):
         """ Initiate the expression from a string
@@ -95,67 +61,19 @@ 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)
 
     @classmethod
-    def random(
-        cls,
-        template,
-        conditions=[],
-        rejected=[0],
-        min_max=(-10, 10),
-        variables_scope={},
-        shuffle=False,
-    ):
-        """ Initiate randomly the expression
-
-        :param template: the template of the expression
-        :param conditions: conditions on randomly generate variable
-        :param rejected: Values to reject for all random variables
-        :param min_max: Min and max value for all random variables
-        :param variables_scope: Dictionnary for each random varaibles to fic rejected and min_max
-        :param shuffle: allowing to shuffle the tree
-        :returns: TODO
-
-        :example:
-        >>> Expression.random("{a}/{a*k}") # doctest: +SKIP
-        <Exp: -3 / -15>
-        >>> Expression.random("{a}/{a*k} - 3*{b}", variables_scope={'a':{'min_max':(10, 30)}}) # doctest: +SKIP
-        <Exp: 18 / 108 - 3 * 9>
-        >>> e = Expression.random("{a}*x + {b}*x + 3", ["a>b"], rejected=[0, 1])
-        >>> ee = e.simplify()
-        >>> print(e) # doctest: +SKIP
-        10x - 6x + 3
-        >>> print(ee) # doctest: +SKIP
-        4x + 3
-
-        """
-        rd_t = Tree.from_str(template, random=True)
-        leafs = extract_rdleaf(rd_t)
-        rd_varia = extract_rv(leafs)
-        generated = random_generator(
-            rd_varia, conditions, rejected, min_max, variables_scope
-        )
-        computed = compute_leafs(leafs, generated)
-        t = replace_rdleaf(rd_t, computed).map_on_leaf(moify)
-
-        if shuffle:
-            raise NotImplemented("Can't suffle expression yet")
-
-        return cls._post_precessing(t)
-
-    @classmethod
-    def _post_precessing(cls, t):
+    def _post_processing(cls, t):
         """ Post process the tree by typing it """
         tt = cls(t)._typing()
         try:
@@ -164,10 +82,10 @@ class Expression(object):
             return cls(t)
 
     def __str__(self):
-        return renders[self.RENDER](self._tree)
+        return render(self._tree)
 
     def __repr__(self):
-        return f"<Exp: {renders['txt'](self._tree)}>"
+        return f"<Exp: {render(self._tree, 'txt')}>"
 
     def _order(self, exclude_nodes=["*", "/", "**"]):
         """ Order the expression base on types
@@ -194,7 +112,8 @@ class Expression(object):
                     return type(leaf)
             else:
                 try:
-                    typed_leaf = typing(leaf.node, leaf.left_value, leaf.right_value)
+                    typed_leaf = typing(
+                        leaf.node, leaf.left_value, leaf.right_value)
                     return typed_leaf.signature
                 except (AttributeError, NotImplementedError, TypingError):
                     return type(leaf)
@@ -334,15 +253,15 @@ class Expression(object):
 
         comp_exp = opt_exp._compute()
 
-        if typed_exp == comp_exp:
-            typed_exp.set_ancestor(self._ancestor)
-            return typed_exp
-        else:
+        if typed_exp != comp_exp:
             comp_exp.set_ancestor(self)
             return comp_exp._simplify(optimize=optimize)
 
+        typed_exp.set_ancestor(self._ancestor)
+        return typed_exp
+
     def simplify(self, optimize=True):
-        """ Compute as much as possible the expression
+        """ Simplify the expression, keep the history and factory child
 
         :param optimize: bool to optimize tree when it's possible
         :return: an expression
@@ -437,6 +356,65 @@ 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/renders.py

@@ -12,34 +12,59 @@ Expression
 """
 from ..core import tree2txt, tree2tex
 
+class Render(object):
+    """ Object which render Expression or token """
 
-def _txt(mo_tree):
-    """ txt render for MOs or Trees"""
+    def __init__(self, default="txt"):
+        self._default = default
+        self._render = default
+        self.renders = {}
+
+    def register_render(self, name, func, attribute):
+        """ register a render """
         try:
-        return tree2txt(mo_tree)
+            self.renders[name]
+        except KeyError:
+            self.renders[name] = {"name": name, "func": func, "attribute": attribute}
+        else:
+            raise ValueError("This render name already exists")
+
+    @property
+    def render_name(self):
+        return self._render
+
+    @property
+    def render(self):
+        return self.renders[self._render]
+
+    def __call__(self, mo_tree, tmp_render=''):
+        if tmp_render:
+            r = self.renders[tmp_render]
+        else:
+            r = self.render
+
+        try:
+            return r["func"](mo_tree)
         except ValueError:
             pass
 
         try:
-        return mo_tree.__txt__
+            return getattr(mo_tree, r["attribute"])
         except AttributeError:
             return str(mo_tree)
 
-
-def _tex(mo_tree):
-    """ Tex render for MOs or Trees"""
-    try:
-        return tree2tex(mo_tree)
-    except ValueError:
-        pass
-
-    try:
-        return mo_tree.__tex__
-    except AttributeError:
-        return str(mo_tree)
+    def set_render(self, render):
+        """ Define the render """
+        if render in self.renders.keys():
+            self._render = render
+        else:
+            raise ValueError("This render does not exists")
 
 
-renders = {"txt": _txt, "tex": _tex}
+
+render = Render()
+render.register_render("txt", tree2txt, "__txt__")
+render.register_render("tex", tree2tex, "__tex__")
 
 # -----------------------------
 # 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

@@ -13,11 +13,10 @@ Tokens representing interger and decimal
 from decimal import Decimal as _Decimal
 from .token import Token
 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
 
-__all__ = ["Integer", "Decimal"]
+__all__ = ["Integer", "Decimal", "Fraction"]
 
 
 class Integer(Token):
@@ -53,23 +52,6 @@ class Integer(Token):
 
         return cls(mo, name, ancestor)
 
-    @classmethod
-    def random(
-        cls, name="", min_value=-10, max_value=10, rejected=[0, 1], accept_callbacks=[]
-    ):
-        """ Generate a random Integer
-
-        :param name: name of the Integer
-        :param min_value: minimum value
-        :param max_value: maximum value
-        :param rejected: rejected values
-        :param accept_callbacks: list of function for value acceptation
-
-        """
-        candidate = filter_random(min_value, max_value, rejected, accept_callbacks)
-
-        return Integer(candidate, name)
-
 
 class Decimal(Token):
 
@@ -107,40 +89,10 @@ class Decimal(Token):
 
         return cls(mo, name, ancestor)
 
-    @classmethod
-    def random(
-        cls,
-        name="",
-        min_value=-10,
-        max_value=10,
-        digits=2,
-        rejected=[0, 1],
-        reject_callbacks=[],
-    ):
-        """ Generate a random Decimal
-
-        :param name: name of the Integer
-        :param min_value: minimum value
-        :param max_value: maximum value
-        :param digits: digits after comas
-        :param rejected: rejected values
-        :param reject_callbacks: list of function for value rejection
-
-        """
-        conditions = [lambda x: x in rejected] + reject_callbacks
-
-        float_cand = (max_value - min_value) * random() + min_value
-        candidate = _Decimal(f"{float_cand:.{digits}f}")
-        while any(c(candidate) for c in conditions):
-            float_cand = (max_value - min_value) * random() + min_value
-            candidate = _Decimal(f"{float_cand:.{digits}f}")
-
-        return Decimal(candidate, name)
-
 
 class Fraction(Token):
 
-    """ Token representing a fraction
+    """ Token representing a fraction of numbers
 
     :example:
     >>> Fraction("3/4")
@@ -171,76 +123,92 @@ class Fraction(Token):
 
         return cls(mo, name, ancestor)
 
-    @classmethod
-    def random(
-        cls,
-        name="",
-        fix_num="",
-        min_num=-10,
-        max_num=10,
-        rejected_num=[0],
-        accept_num_callbacks=[],
-        fix_denom="",
-        min_denom=-10,
-        max_denom=10,
-        rejected_denom=[0, 1, -1],
-        accept_denom_callbacks=[],
-        irreductible=False,
-        not_integer=True,
-    ):
-        """ Generate a random Fraction
-
-        :param name: Name of the fraction
-        :param fix_num: if set, the numerator will get this value
-        :param min_num: minimum value for the numerator
-        :param max_num: maximum value for the numerator
-        :param rejected_num: rejected values for the numerator
-        :param accept_num_callbacks: list of function for numerator rejection
-        :param fix_denom: if set, the denomerator will get this value
-        :param min_denom: minimum value for the denominator
-        :param max_denom: maximum value for the denominator
-        :param rejected_denom: rejected values for the denominator
-        :param accept_denom_callbacks: list of function for denomerator rejection
-        :param irreductible: is the generated fraction necessary irreductible
-        :param not_integer: can the generated fraction be egal to an interger
-        """
-        if fix_num == "":
-            num = filter_random(min_num, max_num, rejected_num, accept_num_callbacks)
-        else:
-            num = fix_num
-
-        if fix_denom == "":
-            accept_callbacks = accept_denom_callbacks
-
-            if irreductible:
-
-                def prime_with_num(denom):
-                    return gcd(num, denom) == 1
-
-                accept_callbacks.append(prime_with_num)
-            if not_integer:
-
-                def not_divise_num(denom):
-                    return num % denom != 0
-
-                accept_callbacks.append(not_divise_num)
-
-            denom = filter_random(
-                min_denom, max_denom, rejected_denom, accept_callbacks
-            )
-        else:
-            denom = fix_denom
-
-        frac = MOFraction(num, denom)
-        return cls(frac, name)
-
     @property
     def numerator(self):
-        return self._mo.numerator
+        """ Get numerator of the fraction
+
+        :example:
+        >>> a = Fraction("3/4")
+        >>> a.numerator
+        <Integer 3>
+        """
+        return Integer(self._mo.numerator)
 
     @property
     def denominator(self):
-        return self._mo.denominator
+        """ Get denominator of the fraction
+
+        :example:
+        >>> a = Fraction("3/4")
+        >>> a.denominator
+        <Integer 4>
+        """
+        return Integer(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(self._mo._value)
+
+    @property
+    def simplified(self):
+        """ Get the irreductible version of self
+
+        :example:
+        >>> f = Fraction("3/4")
+        >>> f.simplified
+        <Fraction 3 / 4>
+        >>> f = Fraction("12/9")
+        >>> f.simplified
+        <Fraction 4 / 3>
+        >>> f = Fraction("12/4")
+        >>> f.simplified
+        <Integer 3>
+
+        """
+        simplified = self._mo.simplified()
+
+        if isinstance(simplified, MOnumber):
+            return Integer(simplified)
+
+        return Fraction(simplified)
+
+    def simplify(self):
+        """ Itself or its simplified version
+
+        :example:
+        >>> f = Fraction("12/8")
+        >>> fs = f.simplify()
+        >>> for i in fs.explain():
+        ...    print(i)
+        12 / 8
+        3 / 2
+        >>> f = Fraction("5/8")
+        >>> fs = f.simplify()
+        >>> for i in fs.explain():
+        ...    print(i)
+        5 / 8
+        """
+        simplified = self.simplified
+        try:
+            if self.numerator == simplified.numerator:
+                return self
+        except AttributeError:
+            pass
+
+        simplified._ancestor = self
+        return simplified
+
+
 
 
 # -----------------------------

mapytex/calculus/API/tokens/polynomial.py

@@ -10,26 +10,33 @@
 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
+from ...core.MO.polynomial import MOpolynomial
 
 __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
 
-        Token.__init__(self, mo, name, ancestor)
+        Token.__init__(self, a, name, ancestor)
         self._mathtype = "polynome"
 
     @classmethod
@@ -38,48 +45,271 @@ class Polynomial(Token):
         return cls(mo, name, ancestor)
 
     @classmethod
-    def random(cls):
-        raise NotImplemented
+    def from_coefficients(cls, coefficients, variable_name="x", name=""):
+        """ Initiate polynomial from list of coefficients 
+
+        :examples:
+        >>> P = Polynomial.from_coefficients([1, 2, 3])
+        >>> P
+        <Polynomial 3x^2 + 2x + 1>
+        >>> P = Polynomial.from_coefficients([1, 2, -3])
+        >>> P
+        <Polynomial - 3x^2 + 2x + 1>
+        >>> P = Polynomial.from_coefficients([1, 2, 3], "y")
+        >>> P
+        <Polynomial 3y^2 + 2y + 1>
+        """
+        return cls(MOpolynomial(variable_name, coefficients), name)
+
+    @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
+    [<Integer - 2>]
+    >>> for i in P.roots[0].explain():
+    ...    print(i)
+    - 2 / 1
+    - 2
+
+    """
 
     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
+    @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
+        [<Integer - 2>]
+        >>> P = Linear(MOpolynomial('x', [2, 1]))
+        >>> P.roots
+        [<Fraction - 1 / 2>]
+        >>> for i in P.roots[0].explain():
+        ...    print(i)
+        - 1 / 2
+        >>> P = Linear(MOpolynomial('x', [10, 6]))
+        >>> P.roots
+        [<Fraction - 3 / 5>]
+        >>> for i in P.roots[0].explain():
+        ...    print(i)
+        - 6 / 10
+        - 3 / 5
+        """
+
+        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
+    @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

@@ -10,33 +10,20 @@
 Tokens: practical envelop of math object
 
 """
-from ..renders import renders
+from ..renders import render
+from ...core.MO.atoms import moify
 
 
 class Token(object):
 
     """ Token: practical envelop of an math object """
 
-    RENDER = "txt"
-
     def __init__(self, mo, name="", ancestor=None):
         self._mo = mo
         self.name = name
         self._mathtype = None
         self._ancestor = ancestor
 
-    @classmethod
-    def random(cls):
-        raise NotImplemented
-
-    @classmethod
-    def set_render(cls, render):
-        """ Define default render function
-
-        :param render: render name (txt or tex)
-        """
-        cls.RENDER = render
-
     def explain(self):
         """ Yield every calculus step which have lead to self
 
@@ -59,39 +46,39 @@ class Token(object):
             yield self
 
     def __repr__(self):
-        return f"<{self.__class__.__name__} {self.__txt__}>"
+        try:
+            return f"<{self.__class__.__name__} {render(self._mo._tree, 'txt')}>"
+        except AttributeError:
+            return f"<{self.__class__.__name__} {render(self._mo, 'txt')}>"
 
     def __str__(self):
-        if self.RENDER == "tex":
-            return self.__tex__
-        elif self.RENDER == "txt":
-            return self.__txt__
-        else:
-            raise ValueError(f"Unknow render {self.RENDER}")
-
-        #return renders[self.RENDER](self._mo)
+        try:
+            return render(self._mo._tree)
+        except AttributeError:
+            return render(self._mo)
 
     @property
-    def __txt__(self):
-        return self._mo.__txt__
-
-    @property
-    def __tex__(self):
-        return self._mo.__tex__
+    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):
+            try:
                 _other = factory(other)
+            except AttributeError:
+                _other = factory(Expression(moify(other)))
         else:
             _other = other
+
+        if operation == '-':
+            tree = Tree("+", self._mo, Tree("-", None,  _other._mo))
+        else:
             tree = Tree(operation, self._mo, _other._mo)
         return Expression(tree).simplify()
 
@@ -109,6 +96,18 @@ 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 +125,32 @@ 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 +165,12 @@ 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 +198,9 @@ 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 +216,128 @@ 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

@@ -12,8 +12,7 @@ Make calculus as a student
 
 Expression is the classe wich handle all calculus. It can randomly generate or import calculus, simplify them and explain them as a student would do.
 
->>> from mapytex.calculus import Expression
->>> Expression.set_render("txt")
+>>> render.set_render("txt")
 >>> e = Expression.from_str("2x + 6 - 3x")
 >>> print(e)
 2x + 6 - 3x
@@ -27,12 +26,23 @@ Expression is the classe wich handle all calculus. It can randomly generate or i
 (2 - 3) * x + 6
 - x + 6
 
+Create random Expression
+========================
+
+>>> e = random.expression("{a} / {b} + {c} / {d}")
+>>> print(e) # doctest: +SKIP 
+- 3 / - 10 + 3 / 5
 
 """
 
-from .API import Expression
+from .API import render, Expression
+#from decimal import getcontext
+from . import random
 
-__all__ = ["Expression"]
+#getcontext().prec = 2
+
+
+__all__ = ["render",  "Expression", "random"]
 
 
 # -----------------------------

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)):
-            Atom.__init__(self, value)
-        elif isinstance(value, float):
-            Atom.__init__(self, Decimal(value))
+        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)
+        else:
+            try:
+                v = float(value)
+            except (ValueError, TypeError):
                 raise MOError(
-                "The value of an MOnumber need to be a int, a float or a Decimal",
+                    "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):
 
@@ -231,7 +259,8 @@ class MOstr(Atom):
                 f"An MOstr should be initiate with a single caracter string, got {val}"
             )
         if not val.isalpha():
-            raise MOError(f"An MOstr should be initiate with a alpha string, got {val}")
+            raise MOError(
+                f"An MOstr should be initiate with a alpha string, got {val}")
 
         Atom.__init__(self, val)
 
@@ -260,6 +289,16 @@ 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 +8,9 @@
 
 from mapytex.calculus.core.tree import Tree
 from .mo import Molecule, MO
+from .atoms import MOnumber
+from decimal import Decimal
+from ..arithmetic import gcd
 
 __all__ = ["MOFraction"]
 
@@ -31,10 +34,10 @@ class MOFraction(Molecule):
         >>> f = MOFraction(2, 3)
         >>> f
         <MOFraction 2 / 3>
-        >>> print(f.__txt__)
-        2 / 3
-        >>> print(f.__tex__)
-        \\frac{2}{3}
+        >>> print(f.tree)
+        /
+         > 2
+         > 3
         >>> print(f)
         2 / 3
         >>> f = MOFraction(2, 3, negative = True)
@@ -43,11 +46,13 @@ class MOFraction(Molecule):
         """
         _numerator = MO.factory(numerator)
         _denominator = MO.factory(denominator)
+
         base_tree = Tree("/", _numerator, _denominator)
         if negative:
             tree = Tree("-", None, base_tree)
         else:
             tree = base_tree
+
         Molecule.__init__(self, tree)
 
         self._numerator = _numerator
@@ -67,10 +72,61 @@ class MOFraction(Molecule):
     def denominator(self):
         return self._denominator
 
+    @property
+    def _value(self):
+        return Decimal(self._numerator._value) / Decimal(self._denominator._value)
+
     def inverse(self):
         """ 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
+
+    def simplified(self):
+        """ Simplified version of self 
+
+        :examplex
+        >>> f = MOFraction(2, 3)
+        >>> f
+        <MOFraction 2 / 3>
+        >>> f.simplified()
+        <MOFraction 2 / 3>
+        >>> f = MOFraction(2, 6)
+        >>> f
+        <MOFraction 2 / 6>
+        >>> f.simplified()
+        <MOFraction 1 / 3>
+        >>> f = MOFraction(32, 24)
+        >>> f.simplified()
+        <MOFraction 4 / 3>
+        >>> f = MOFraction(32, 8)
+        >>> f.simplified()
+        <MOnumber 4>
+        """
+        frac_gcd = gcd(self.numerator._value, self.denominator._value) 
+        new_num = self.numerator._value / frac_gcd
+        new_denom = self.denominator._value / frac_gcd
+
+        if new_denom == 1:
+            return MOnumber(new_num)
+
+        return MOFraction(new_num, new_denom)
+
+
 
 # -----------------------------
 # Reglages pour 'vim'

mapytex/calculus/core/MO/mo.py

@@ -57,20 +57,12 @@ class MO(ABC):
         pass
 
     def __repr__(self):
-        return f"<{self.__class__.__name__} {self.__txt__}>"
+        return f"<{self.__class__.__name__} {self.__str__()}>"
 
     @abstractmethod
     def __str__(self):
         pass
 
-    @abstractmethod
-    def __txt__(self):
-        pass
-
-    @abstractmethod
-    def __tex__(self):
-        pass
-
     def __hash__(self):
         try:
             return self._tree.__hash__()
@@ -97,6 +89,9 @@ class MO(ABC):
         """
         return self._signature
 
+    def differentiate(self):
+        raise NotImplementedError
+
 
 class Atom(MO):
 
@@ -158,21 +153,21 @@ class Molecule(MO):
 
     It is a wrapping of tree
 
-    Its wrapping tree can be access throw .tree property
+    Its wrapping tree can be access through .tree property
     """
 
     MAINOP = None
 
-    def __init__(self, value):
+    def __init__(self, tree):
         """ Initiate the MO
 
         It should be idempotent.
 
         """
         try:
-            self._tree = value._tree
+            self._tree = tree._tree
         except AttributeError:
-            self._tree = value
+            self._tree = tree
 
         self.is_scalar = True
         self._signature = None
@@ -183,18 +178,10 @@ class Molecule(MO):
 
     @property
     def content(self):
-        return self._tree
+        return self.tree
 
     def __str__(self):
-        return str(self.__txt__)
-
-    @property
-    def __txt__(self):
-        return tree2txt(self._tree)
-
-    @property
-    def __tex__(self):
-        return tree2tex(self._tree)
+        return tree2txt(self.tree)
 
 
 # -----------------------------

mapytex/calculus/core/MO/monomial.py

@@ -31,10 +31,10 @@ class MOstrPower(Molecule):
         <MOstrPower x^2>
         >>> print(s)
         x^2
-        >>> print(s.__txt__)
-        x^2
-        >>> print(s.__tex__)
-        x^{2}
+        >>> print(s.tree)
+        ^
+         > x
+         > 2
         >>> MOstrPower(3, 1)
         Traceback (most recent call last):
         ...
@@ -59,7 +59,8 @@ class MOstrPower(Molecule):
         """
         _variable = MO.factory(variable)
         if not isinstance(_variable, MOstr):
-            raise MOError("The variable of a monomial should be convertible into MOstr")
+            raise MOError(
+                "The variable of a monomial should be convertible into MOstr")
         self._variable = _variable
 
         _power = MO.factory(power)
@@ -111,6 +112,23 @@ 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):
 
@@ -131,22 +149,20 @@ class MOMonomial(Molecule):
         <MOMonomial 4x>
         >>> print(m)
         4x
-        >>> print(m.__txt__)
-        4x
-        >>> print(m.__tex__)
-        4x
+        >>> print(m.tree)
+        *
+         > 4
+         > x
         >>> x = MOstrPower('x', 2)
         >>> MOMonomial(4, x)
         <MOMonomial 4x^2>
-        >>> m = MOMonomial(4, 'x')
+        >>> m = MOMonomial(-1, 'x')
         >>> m
-        <MOMonomial 4x>
-        >>> print(m)
-        4x
-        >>> print(m.__txt__)
-        4x
-        >>> print(m.__tex__)
-        4x
+        <MOMonomial - x>
+        >>> print(m.tree)
+        -
+         > None
+         > x
         >>> MOMonomial(4, 'x', 1)
         <MOMonomial 4x>
         >>> MOMonomial(4, 'x', 2)
@@ -154,6 +170,13 @@ class MOMonomial(Molecule):
         >>> x2 = MOstrPower('x', 2)
         >>> MOMonomial(4, x2, 3)
         <MOMonomial 4x^6>
+        >>> m = MOMonomial(-1, 'x', 2)
+        >>> m
+        <MOMonomial - x^2>
+        >>> print(m.tree)
+        -
+         > None
+         > x^2
         >>> MOMonomial(0, x)
         Traceback (most recent call last):
             ...
@@ -183,34 +206,21 @@ class MOMonomial(Molecule):
         self._power = _power
 
         try:
-            if self._coefficient.value != 1:
-                _tree = Tree("*", self._coefficient, self.strpower)
-            else:
+            if self.coefficient.value == 1:
                 _tree = self.strpower
+            else:
+                _tree = Tree("*", self.coefficient, self.strpower)
         except AttributeError:
-            _tree = Tree("*", self._coefficient, self.strpower)
+            _tree = Tree("*", self.coefficient, self.strpower)
 
         Molecule.__init__(self, _tree)
 
-    def __str__(self):
-        if self._coefficient != -1:
-            return super(MOMonomial, self).__str__()
-        else:
-            return "- " + self.strpower.__str__()
-
     @property
-    def __txt__(self):
-        if self._coefficient != -1:
-            return super(MOMonomial, self).__txt__
-        else:
-            return "- " + self.strpower.__txt__
+    def tree(self):
+        if self._coefficient == -1:
+            return Tree("-", None, self.strpower)
 
-    @property
-    def __tex__(self):
-        if self._coefficient != -1:
-            return super(MOMonomial, self).__tex__
-        else:
-            return "- " + self.strpower.__tex__
+        return Tree("*", self.coefficient, self.strpower)
 
     @property
     def coefficient(self):
@@ -258,6 +268,31 @@ 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/compute/__init__.py

@@ -70,7 +70,8 @@ def compute_capacities(node):
     op = OPERATIONS[node]
     lines = [[node] + [mo.__name__ for mo in MOS]]
     for left_mo in MOS:
-        lines.append([left_mo.__name__] + [(left_mo, i) in op.funcs for i in MOS])
+        lines.append([left_mo.__name__] +
+                     [(left_mo, i) in op.funcs for i in MOS])
     return lines
 
 

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

@@ -1,246 +0,0 @@
-#! /usr/bin/env python
-# -*- coding: utf-8 -*-
-# vim:fenc=utf-8
-#
-# Copyright © 2017 lafrite <lafrite@Poivre>
-#
-# Distributed under terms of the MIT license.
-
-"""
-Tools to extract random leafs, random variables, generate random values and
-fill new trees
-
-Flow
-----
-
-Tree with RdLeaf
-|
-| Extract rdLeaf
-|
-List of leafs to generate
-|
-| extract_rv
-|
-List random variables to generate
-|
-| Generate
-|
-Dictionnary of generated random variables
-|
-| Compute leafs
-|
-Dictionnary of computed leafs
-|
-| Replace
-|
-Tree with RdLeaf replaced by generated values
-
-:example:
-
->>> from ..tree import Tree
->>> rd_t = Tree("/", RdLeaf("a"), RdLeaf("a*k"))
->>> print(rd_t)
-/
- > {a}
- > {a*k}
->>> leafs = extract_rdleaf(rd_t)
->>> leafs
-['a', 'a*k']
->>> rd_varia = extract_rv(leafs)
->>> rd_varia # doctest: +SKIP
-{'a', 'k'}
->>> generated = random_generator(rd_varia, conditions=['a%2+1'])
->>> generated # doctest: +SKIP
-{'a': 7, 'k': 4}
->>> computed = compute_leafs(leafs, generated)
->>> computed # doctest: +SKIP
-{'a': 7, 'a*k': 28}
->>> replaced = replace_rdleaf(rd_t, computed)
->>> print(replaced) # doctest: +SKIP
-/
- > 7
- > 28
-
-"""
-
-from random import choice
-from functools import reduce
-from .leaf import RdLeaf
-
-
-def extract_rdleaf(tree):
-    """ Extract rdLeaf in a Tree
-
-    :example:
-    >>> from ..tree import Tree
-    >>> rd_t = Tree("+", RdLeaf("a"), RdLeaf("a*k"))
-    >>> extract_rdleaf(rd_t)
-    ['a', 'a*k']
-    >>> rd_t = Tree("+", RdLeaf("a"), 2)
-    >>> extract_rdleaf(rd_t)
-    ['a']
-    """
-    rd_leafs = []
-    for leaf in tree.get_leafs():
-        try:
-            leaf.rdleaf
-        except AttributeError:
-            pass
-        else:
-            rd_leafs.append(leaf.name)
-    return rd_leafs
-
-
-def extract_rv(leafs):
-    """ Extract the set of random values from the leaf list
-
-    :param leafs: list of leafs
-    :return: set of random values
-
-    :example:
-    >>> leafs = ["a", "a*k"]
-    >>> extract_rv(leafs) == {'a', 'k'}
-    True
-    """
-    rd_values = set()
-    for leaf in leafs:
-        for c in leaf:
-            if c.isalpha():
-                rd_values.add(c)
-    return rd_values
-
-
-def compute_leafs(leafs, generated_values):
-    """ Compute leafs from generated random values
-
-    :param generated_values: Dictionnary of name:generated value
-    :param leafs: list of leafs
-    :return: Dictionnary of evaluated leafs from generated values
-
-    :example:
-    >>> leafs = ["a", "a*k"]
-    >>> generated_values = {"a":2, "k":3}
-    >>> compute_leafs(leafs, generated_values)
-    {'a': 2, 'a*k': 6}
-    """
-    return {leaf: eval(leaf, generated_values) for leaf in leafs}
-
-
-def replace_rdleaf(tree, computed_leafs):
-    """ Replace RdLeaf by the corresponding computed value
-
-    >>> from ..tree import Tree
-    >>> rd_t = Tree("+", RdLeaf("a"), RdLeaf("a*k"))
-    >>> computed_leafs = {'a': 2, 'a*k': 6}
-    >>> print(replace_rdleaf(rd_t, computed_leafs))
-    +
-     > 2
-     > 6
-    """
-
-    def replace(leaf):
-        try:
-            return leaf.replace(computed_leafs)
-        except AttributeError:
-            return leaf
-
-    return tree.map_on_leaf(replace)
-
-
-def random_generator(
-    rd_variables, conditions=[], rejected=[0], min_max=(-10, 10), variables_scope={}
-):
-    """ Generate random variables
-
-    :param rd_variables: list of random variables to generate
-    :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
-    :return: dictionnary of generated variables
-
-    :example:
-    >>> gene = random_generator(["a", "b"], 
-    ...                  ["a > 0"],
-    ...                  [0], (-10, 10),
-    ...                  {"a": {"rejected": [0, 1]},
-    ...                   "b": {"min_max": (-5, 0)}})
-    >>> gene["a"] > 0
-    True
-    >>> gene["a"] != 0
-    True
-    >>> gene["b"] < 0
-    True
-    >>> gene = random_generator(["a", "b"], 
-    ...                  ["a % b == 0"],
-    ...                  [0, 1], (-10, 10))
-    >>> gene["a"] not in [0, 1]
-    True
-    >>> gene["b"] in list(range(-10, 11))
-    True
-    >>> gene["a"] % gene["b"]
-    0
-    """
-    complete_scope = build_variable_scope(
-        rd_variables, rejected, min_max, variables_scope
-    )
-    choices_list = {
-        v: list(
-            set(
-                range(
-                    complete_scope[v]["min_max"][0], complete_scope[v]["min_max"][1] + 1
-                )
-            ).difference(complete_scope[v]["rejected"])
-        )
-        for v in rd_variables
-    }
-
-    # quantity_choices = reduce(lambda x,y : x*y,
-    #                           [len(choices_list[v]) for v in choices_list])
-    # TODO: améliorer la méthode de rejet avec un cache |dim. mai 12 17:04:11 CEST 2019
-
-    generate_variable = {v: choice(choices_list[v]) for v in rd_variables}
-
-    while not all([eval(c, __builtins__, generate_variable) for c in conditions]):
-        generate_variable = {v: choice(choices_list[v]) for v in rd_variables}
-
-    return generate_variable
-
-
-def build_variable_scope(rd_variables, rejected, min_max, variables_scope):
-    """ Build variables scope from incomplete one
-
-    :param rd_variables: list of random variables to generate
-    :param rejected: Rejected values for the generator 
-    :param min_max: (min, max) limits in between variables will be generated
-    :param variables_scope: rejected and min_max define for individual variables
-    :return: complete variable scope
-
-    :example:
-    >>> completed = build_variable_scope(["a", "b", "c", "d"], [0], (-10, 10),
-    ...                      {"a": {"rejected": [0, 1]},
-    ...                       "b": {"min_max": (-5, 0)},
-    ...                       "c": {"rejected": [2], "min_max": (0, 5)}})
-    >>> complete = {'a': {'rejected': [0, 1], 'min_max': (-10, 10)}, 
-    ...             'b': {'rejected': [0], 'min_max': (-5, 0)},
-    ...             'c': {'rejected': [2], 'min_max': (0, 5)},
-    ...             'd': {'rejected': [0], 'min_max': (-10, 10)}}
-    >>> completed == complete
-    True
-    """
-    complete_scope = variables_scope.copy()
-    for v in rd_variables:
-        try:
-            complete_scope[v]
-        except KeyError:
-            complete_scope[v] = {"rejected": rejected, "min_max": min_max}
-        else:
-            try:
-                complete_scope[v]["rejected"]
-            except KeyError:
-                complete_scope[v]["rejected"] = rejected
-            try:
-                complete_scope[v]["min_max"]
-            except KeyError:
-                complete_scope[v]["min_max"] = min_max
-    return complete_scope

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

@@ -91,9 +91,11 @@ def mul2tex(left, right):
     '- 3x'
     >>> mul2tex(a, a)
     'x \\times x'
+    >>> mul2tex(a, MO.factory(-3))
+    'x(- 3)'
     """
     left_ = render_with_parenthesis(left, "*")
-    right_ = render_with_parenthesis(right, "*")
+    right_ = render_with_parenthesis(right, "*", is_at_right=True)
 
     display_time = True
     # if (right_[0].isalpha() and (left_.isnumeric() or left_.isdecimal())) or right_[
@@ -117,17 +119,17 @@ 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 +140,7 @@ def div2tex(left, right):
     except (AttributeError, ValueError):
         right_ = right.__tex__
 
-    return "\\frac{" + left_ + "}{" + right_ + "}"
+    return "\\dfrac{" + left_ + "}{" + right_ + "}"
 
 
 def pow2tex(left, right):
@@ -183,20 +185,17 @@ def pow2tex(left, right):
     return f"{left_}^{{{right_}}}"
 
 
-def render_with_parenthesis(subtree, operator):
+def render_with_parenthesis(subtree, operator, is_at_right=False):
     subtree_need_parenthesis = False
     try:
         subtree.node
     except AttributeError:
         try:
-            if (
-                OPERATORS[subtree.MAINOP]["precedence"]
-                < OPERATORS[operator]["precedence"]
-            ):
-                subtree_need_parenthesis = True
-        except (AttributeError, KeyError):
-            pass
             subtree_ = subtree.__tex__
+        except AttributeError:
+            subtree_ = str(subtree)
+        if subtree_.startswith("-") and OPERATORS["-"]["precedence"] < OPERATORS[operator]["precedence"] and is_at_right:
+            subtree_need_parenthesis = True
     else:
         if OPERATORS[subtree.node]["precedence"] < OPERATORS[operator]["precedence"]:
             subtree_need_parenthesis = True
@@ -207,7 +206,8 @@ def render_with_parenthesis(subtree, operator):
     return subtree_
 
 
-OPERATOR2TEX = {"+": plus2tex, "-": minus2tex, "*": mul2tex, "/": div2tex, "^": pow2tex}
+OPERATOR2TEX = {"+": plus2tex, "-": minus2tex,
+                "*": mul2tex, "/": div2tex, "^": pow2tex}
 
 
 def tree2tex(tree):
@@ -227,8 +227,17 @@ def tree2tex(tree):
     from ..tree import Tree
 
     if not isinstance(tree, Tree):
-        raise ValueError(f"Can only render a Tree (got {type(tree).__name__}: {tree})")
-    return OPERATOR2TEX[tree.node](tree.left_value, tree.right_value)
+        raise ValueError(
+            f"Can only render a Tree (got {type(tree).__name__}: {tree})")
+
+    def expand(leaf):
+        try:
+            return leaf.tree
+        except AttributeError:
+            return leaf
+    expanded_tree = tree.map_on_leaf(expand)
+
+    return OPERATOR2TEX[expanded_tree.node](expanded_tree.left_value, expanded_tree.right_value)
 
 
 # -----------------------------

mapytex/calculus/core/renders/tree2txt.py

@@ -91,11 +91,13 @@ def mul2txt(left, right):
     '- 3x'
     >>> mul2txt(a, a)
     'x * x'
+    >>> mul2txt(a, MO.factory(-3))
+    'x(- 3)'
     """
     display_time = True
 
     left_ = render_with_parenthesis(left, "*")
-    right_ = render_with_parenthesis(right, "*")
+    right_ = render_with_parenthesis(right, "*", is_at_right=True)
 
     if right_[0].isalpha():
         # TODO: C'est bien beurk en dessous... |ven. déc. 21 12:03:07 CET 2018
@@ -187,20 +189,22 @@ def pow2txt(left, right):
     return f"{left_}^{right_}"
 
 
-def render_with_parenthesis(subtree, operator):
+def tree_with_parenthesis(subtree, operator):
+    """ Assuming the subtree is a tree, then have .node """
+    pass
+
+
+def render_with_parenthesis(subtree, operator, is_at_right=False):
     subtree_need_parenthesis = False
     try:
         subtree.node
     except AttributeError:
         try:
-            if (
-                OPERATORS[subtree.MAINOP]["precedence"]
-                < OPERATORS[operator]["precedence"]
-            ):
-                subtree_need_parenthesis = True
-        except (AttributeError, KeyError):
-            pass
             subtree_ = subtree.__txt__
+        except AttributeError:
+            subtree_ = str(subtree)
+        if subtree_.startswith("-") and OPERATORS["-"]["precedence"] < OPERATORS[operator]["precedence"] and is_at_right:
+            subtree_need_parenthesis = True
     else:
         if OPERATORS[subtree.node]["precedence"] < OPERATORS[operator]["precedence"]:
             subtree_need_parenthesis = True
@@ -211,7 +215,8 @@ def render_with_parenthesis(subtree, operator):
     return subtree_
 
 
-OPERATOR2TXT = {"+": plus2txt, "-": minus2txt, "*": mul2txt, "/": div2txt, "^": pow2txt}
+OPERATOR2TXT = {"+": plus2txt, "-": minus2txt,
+                "*": mul2txt, "/": div2txt, "^": pow2txt}
 
 
 def tree2txt(tree):
@@ -231,8 +236,17 @@ def tree2txt(tree):
     from ..tree import Tree
 
     if not isinstance(tree, Tree):
-        raise ValueError(f"Can only render a Tree (got {type(tree).__name__}: {tree})")
-    return OPERATOR2TXT[tree.node](tree.left_value, tree.right_value)
+        raise ValueError(
+            f"Can only render a Tree (got {type(tree).__name__}: {tree})")
+
+    def expand(leaf):
+        try:
+            return leaf.tree
+        except AttributeError:
+            return leaf
+    expanded_tree = tree.map_on_leaf(expand)
+
+    return OPERATOR2TXT[expanded_tree.node](expanded_tree.left_value, expanded_tree.right_value)
 
 
 # -----------------------------

mapytex/calculus/core/str2.py

@@ -15,7 +15,6 @@ 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
 
 __all__ = ["str2"]
 
@@ -395,9 +394,7 @@ 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 not ( is_operator(tok)  or tok =="(" ):
                 previous = tok
 
             target_.send(tok)
@@ -482,7 +479,8 @@ def lookforNumbers(target):
                         if current.replace("-", "", 1).isdigit():
                             current += tok
                         else:
-                            raise ParsingError(f"Can't build decimal with '{current}'")
+                            raise ParsingError(
+                                f"Can't build decimal with '{current}'")
                     elif tok == "-":
                         if current == "":
                             current = tok
@@ -800,7 +798,8 @@ def str2(sink, convert_to_mo=True):
                 operator_corout(missing_times(moify_cor(pparser(sink))))
             )
         else:
-            str2_corout = lookforNumbers(operator_corout(missing_times(pparser(sink))))
+            str2_corout = lookforNumbers(
+                operator_corout(missing_times(pparser(sink))))
 
         for i in expression.replace(" ", ""):
             str2_corout.send(i)
@@ -810,60 +809,7 @@ def str2(sink, convert_to_mo=True):
 
     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>]
-    """
-    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>]
-    """
-    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
-
-
 str2nestedlist = str2(list_sink)
-
-
 # -----------------------------
 # Reglages pour 'vim'
 # vim:set autoindent expandtab tabstop=4 shiftwidth=4:

mapytex/calculus/core/tree.py

@@ -11,7 +11,7 @@ Tree class
 
 from .tree_tools import to_nested_parenthesis, postfix_concatenate, show_tree
 from .coroutine import coroutine, STOOOP
-from .str2 import str2, rdstr2
+from .str2 import str2
 from .operator import OPERATORS, is_operator
 
 __all__ = ["Tree", "MutableTree"]
@@ -51,7 +51,7 @@ class Tree:
         self.right_value = right_value
 
     @classmethod
-    def from_str(cls, expression, convert_to_mo=True, random=False):
+    def from_str(cls, expression, convert_to_mo=True):
         """ Initiate a tree from an string expression
 
         :example:
@@ -77,17 +77,8 @@ class Tree:
          > *
          | > 3
          | > n
-        >>> t = Tree.from_str("2+{n}*x", random=True)
-        >>> print(t)
-        +
-         > 2
-         > *
-         | > {n}
-         | > x
-
-
         """
-        t = MutableTree.from_str(expression, convert_to_mo, random)
+        t = MutableTree.from_str(expression, convert_to_mo)
         return cls.from_any_tree(t)
 
     @classmethod
@@ -898,7 +889,7 @@ class MutableTree(Tree):
         self.right_value = right_value
 
     @classmethod
-    def from_str(cls, expression, convert_to_mo=True, random=False):
+    def from_str(cls, expression, convert_to_mo=True):
         """ Initiate the MutableTree
 
         :example:
@@ -954,12 +945,7 @@ class MutableTree(Tree):
          | | > 8
          | | > 3
          | > x
-
         """
-        if random:
-            str_2_mut_tree = rdstr2(cls.sink)
-            return str_2_mut_tree(expression)
-        else:
         str_2_mut_tree = str2(cls.sink, convert_to_mo)
         return str_2_mut_tree(expression)
 

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/calculus/random/__init__.py

@@ -0,0 +1,19 @@
+from .list import list_generator as list
+from .expression import expression_generator as expression
+
+__all__ = ["list", "expression"]
+
+"""
+Generate random stuffs
+======================
+
+list_generator
+==============
+
+Generate random lists
+
+expression_generator
+====================
+
+Generate random Expression
+"""

mapytex/calculus/random/core/__init__.py

@@ -0,0 +1,65 @@
+#! /usr/bin/env python
+# -*- coding: utf-8 -*-
+# vim:fenc=utf-8
+#
+# Copyright © 2017 lafrite <lafrite@Poivre>
+#
+# Distributed under terms of the MIT license.
+
+"""
+Tools to extract random leaves, random variables, generate random values and
+fill new trees
+
+Flow
+----
+
+Tree with RdLeaf
+|
+| Extract rdLeaf
+|
+List of leaves to generate
+|
+| extract_rv
+|
+List random variables to generate
+|
+| Generate
+|
+Dictionnary of generated random variables
+|
+| Compute leaves
+|
+Dictionnary of computed leaves
+|
+| Replace
+|
+Tree with RdLeaf replaced by generated values
+
+:example:
+
+>>> from .random_tree import RandomTree
+>>> from .leaf import RdLeaf
+>>> from .generate import random_generator
+>>> from .grammar import extract_letters, eval_words
+>>> rd_t = RandomTree("/", RdLeaf("a"), RdLeaf("a*k"))
+>>> print(rd_t)
+/
+ > {a}
+ > {a*k}
+>>> leaves = rd_t.random_leaves
+>>> leaves = ['a', 'a*k']
+>>> rd_varia = extract_letters(leaves)
+>>> sorted(list(rd_varia))
+['a', 'k']
+>>> generated = random_generator(rd_varia, conditions=['a%2+1'], global_config={"min_max": (-10, 10), "rejected":[0, 1]})
+>>> generated # doctest: +SKIP
+{'a': 7, 'k': 4}
+>>> computed = eval_words(leaves, generated)
+>>> computed # doctest: +SKIP
+{'a': 7, 'a*k': 28}
+>>> replaced = rd_t.eval_random_leaves(computed)
+>>> print(replaced) # doctest: +SKIP
+/
+ > 7
+ > 28
+"""

mapytex/calculus/random/core/generate.py

@@ -0,0 +1,116 @@
+#! /usr/bin/env python
+# -*- coding: utf-8 -*-
+# vim:fenc=utf-8
+#
+# Copyright © 2017 lafrite <lafrite@Poivre>
+#
+# Distributed under terms of the MIT license.
+
+
+from random import choice
+import math
+
+EVAL_FUN = {**math.__dict__}
+
+
+
+def complete_variable_configs(
+    variables, global_config: dict = {}, configs: dict = {}
+) -> dict:
+    """Completes variables configurations with the global configuration
+
+    :param variables: list of random variables to generate
+    :param global_config: global parameters
+    :param configs: global parameters
+    :return: complete variable scope
+
+    :example:
+    >>> completed = complete_variable_configs(["a", "b", "c", "d"],
+    ...                      global_config={"rejected": [], "min_max": (-10, 10)},
+    ...                      configs={
+    ...                       "a": {"rejected": [0, 1]},
+    ...                       "b": {"min_max": (-5, 0)},
+    ...                       "c": {"rejected": [2], "min_max": (0, 5)}
+    ...                       })
+    >>> completed["a"] == {'rejected': [0, 1], 'min_max': (-10, 10)}
+    True
+    >>> completed["b"] == {'rejected': [], 'min_max': (-5, 0)}
+    True
+    >>> completed['c'] == {'rejected': [2], 'min_max': (0, 5)}
+    True
+    >>> completed['d'] == {'rejected': [], 'min_max': (-10, 10)}
+    True
+    """
+    complete_configs = configs.copy()
+    for variable in variables:
+        try:
+            complete_configs[variable]
+        except KeyError:
+            complete_configs[variable] = global_config
+        else:
+            complete_configs[variable] = dict(global_config, **configs[variable])
+    return complete_configs
+
+
+def random_generator(
+    variables: list[str],
+    conditions: list[str] = [],
+    global_config: dict = {},
+    configs: dict = {},
+) -> dict[str, int]:
+    """Generate random variables
+
+    :param variables: list of random variables to generate
+    :param conditions: condition over variables
+    :param global_config: global parameters
+    :param configs: global parameters
+    :return: dictionnary of generated variables
+
+    In variables and configurations, you have access to all math module functions
+
+    :example:
+    >>> gene = random_generator(["a", "b"],
+    ...                  ["a > 0"],
+    ...                  {"rejected": [0], "min_max":(-10, 10)},
+    ...                  {"a": {"rejected": [0, 1]},
+    ...                   "b": {"min_max": (-5, 0)},
+    ...                  })
+    >>> gene["a"] > 0
+    True
+    >>> gene["a"] != 0
+    True
+    >>> gene["b"] < 0
+    True
+    >>> gene = random_generator(["a", "b"],
+    ...                  ["a % b == 0"],
+    ...                  {"rejected": [0, 1], "min_max":(-10, 10)}
+    ...                  )
+    >>> gene["a"] not in [0, 1]
+    True
+    >>> gene["b"] in list(range(-10, 11))
+    True
+    >>> gene["a"] % gene["b"]
+    0
+    """
+    complete_scope = complete_variable_configs(variables, global_config, configs)
+    choices_list = {
+        v: list(
+            set(
+                range(
+                    complete_scope[v]["min_max"][0], complete_scope[v]["min_max"][1] + 1
+                )
+            ).difference(complete_scope[v]["rejected"])
+        )
+        for v in variables
+    }
+
+    # quantity_choices = reduce(lambda x,y : x*y,
+    #                           [len(choices_list[v]) for v in choices_list])
+    # TODO: améliorer la méthode de rejet avec un cache |dim. mai 12 17:04:11 CEST 2019
+
+    generate_variable = {v: choice(choices_list[v]) for v in variables}
+
+    while not all([eval(c, EVAL_FUN, generate_variable) for c in conditions]):
+        generate_variable = {v: choice(choices_list[v]) for v in variables}
+
+    return generate_variable

mapytex/calculus/random/core/grammar.py

@@ -0,0 +1,43 @@
+import math
+
+EVAL_FUN = {**math.__dict__}
+
+def extract_letters(words: list[str]) -> set[str]:
+    """Extracts unique letters from a list of words
+
+    :param words: list of leafs
+    :return: set of letters
+
+    :example:
+    >>> leafs = ["a", "a*k"]
+    >>> extract_letters(leafs) == {'a', 'k'}
+    True
+    """
+    letters = set()
+    for word in words:
+        for c in word:
+            if c.isalpha():
+                letters.add(c)
+    return letters
+
+
+def eval_words(words: list[str], values: dict[str, int]) -> dict[str, int]:
+    """Evaluate words replacing letters with values
+
+    :param words: list of words
+    :param values: Dictionary of letters:value
+    :return: Dictionary of evaluated words from generated values
+
+    In words, you have access to all math module functions
+
+    :example:
+    >>> leafs = ["a", "a*k"]
+    >>> generated_values = {"a":2, "k":3}
+    >>> eval_words(leafs, generated_values)
+    {'a': 2, 'a*k': 6}
+    >>> leafs = ["exp(a)", "gcd(a, k)"]
+    >>> generated_values = {"a":2, "k":3}
+    >>> eval_words(leafs, generated_values)
+    {'exp(a)': 7.38905609893065, 'gcd(a, k)': 1}
+    """
+    return {word: eval(word, EVAL_FUN, values) for word in words}

mapytex/calculus/random/core/int_gene.py

@@ -111,8 +111,7 @@ def filter_random(min_value=-10, max_value=10, rejected=[0, 1], accept_callbacks
 
 class FilterRandom(object):
 
-    """ Integer random generator which filter then choose candidate
-    """
+    """Integer random generator which filter then choose candidate"""
 
     # TODO: Faire un cache pour éviter de reconstruire les listes à chaque fois |ven. déc. 21 19:07:42 CET 2018
 

mapytex/calculus/random/core/leaf.py

@@ -9,7 +9,7 @@
 """
 
 """
-from ..coroutine import *
+from ...core.coroutine import coroutine, STOOOP
 
 
 @coroutine
@@ -17,7 +17,7 @@ def look_for_rdleaf(target):
     """Coroutine which look to "{...}" which are RdLeaf
 
     :example:
-    >>> from ..str2 import list_sink
+    >>> from ...core.str2 import list_sink
     >>> str2list = look_for_rdleaf(list_sink)
     >>> for i in "{a}+{a*b}-2":
     ...    str2list.send(i)
@@ -53,9 +53,7 @@ def look_for_rdleaf(target):
 
 
 class RdLeaf:
-    """ Random leaf
-
-    """
+    """Random leaf"""
 
     def __init__(self, name):
         self._name = name

mapytex/calculus/random/core/random_tree.py

@@ -0,0 +1,118 @@
+from ...core.tree import MutableTree, Tree
+from ...core.MO import moify
+from .grammar import extract_letters, eval_words
+from .generate import random_generator
+from .str2 import rdstr2
+
+
+class RandomTree(MutableTree):
+    """MutableTree that accept {a} syntax for random generation
+
+    :example:
+    >>> t = RandomTree()
+    >>> type(t)
+    <class 'mapytex.calculus.random.core.random_tree.RandomTree'>
+    """
+
+    @classmethod
+    def from_str(cls, expression):
+        """Initiate a random tree from a string that need to be parsed
+
+        :exemple:
+        >>> t = RandomTree.from_str("{b}*x+{c}")
+        >>> print(t)
+        +
+         > *
+         | > {b}
+         | > x
+         > {c}
+        >>> t = RandomTree.from_str("{a}*({b}*x+{c})")
+        >>> print(t)
+        *
+         > {a}
+         > +
+         | > *
+         | | > {b}
+         | | > x
+         | > {c}
+        """
+        str_2_mut_tree = rdstr2(cls.sink)
+        return str_2_mut_tree(expression)
+
+    @property
+    def random_leaves(self) -> list[str]:
+        """Get list of random leaves
+
+        :example:
+        >>> from .leaf import RdLeaf
+        >>> random_tree = RandomTree("+", RdLeaf("a"), RdLeaf("a*k"))
+        >>> random_tree.random_leaves
+        ['a', 'a*k']
+        >>> random_tree = RandomTree("+", RdLeaf("a"), 2)
+        >>> random_tree.random_leaves
+        ['a']
+        """
+        rd_leafs = []
+        for leaf in self.get_leafs():
+            try:
+                leaf.rdleaf
+            except AttributeError:
+                pass
+            else:
+                rd_leafs.append(leaf.name)
+        return rd_leafs
+
+    @property
+    def random_value(self) -> set[str]:
+        """Get set of random values to generate
+
+        :example:
+        >>> from .leaf import RdLeaf
+        >>> random_tree = RandomTree("+", RdLeaf("a"), RdLeaf("a*k"))
+        >>> random_tree.random_value == {'a', 'k'}
+        True
+        >>> random_tree = RandomTree("+", RdLeaf("a"), 2)
+        >>> random_tree.random_value
+        {'a'}
+        """
+        return extract_letters(self.random_leaves)
+
+    def eval_random_leaves(self, leaves_value: dict[str, int]):
+        """Given random leaves value get the tree
+
+        :example:
+        >>> from .leaf import RdLeaf
+        >>> rd_t = RandomTree("+", RdLeaf("a"), RdLeaf("a*k"))
+        >>> leaves_values = {'a': 2, 'a*k': 6}
+        >>> t = rd_t.eval_random_leaves(leaves_values)
+        >>> type(t)
+        <class 'mapytex.calculus.core.tree.Tree'>
+        >>> print(t)
+        +
+         > 2
+         > 6
+        """
+
+        def replace(leaf):
+            try:
+                return leaf.replace(leaves_value)
+            except AttributeError:
+                return leaf
+
+        return self.map_on_leaf(replace).map_on_leaf(moify)
+
+    def generate(
+        self, conditions: list[str] = [], global_config: dict = {}, configs: dict = {}
+    ) -> Tree:
+        """Generate a random version of self
+
+        :param conditions: list of conditions
+        :param config: global configuration for generated values
+        :param configs: specific configuration for each generated values
+
+        """
+        generated_values = random_generator(
+            self.random_value, conditions, global_config, configs
+        )
+        leaves = eval_words(self.random_leaves, generated_values)
+        return self.eval_random_leaves(leaves)

mapytex/calculus/random/core/str2.py

@@ -0,0 +1,40 @@
+from ...core.operator import is_operator
+from functools import partial
+from ...core.str2 import (
+    concurent_broadcast,
+    lookforNumbers,
+    pparser,
+    missing_times,
+    lookfor,
+)
+from ...core.coroutine import STOOOP
+from ...core.MO import moify_cor
+from .leaf import look_for_rdleaf
+
+
+def rdstr2(sink):
+    """Return a pipeline which parse random expression and with sink as endpoint
+
+    :example:
+    >>> from ...core.str2 import list_sink
+    >>> 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])
+
+    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

mapytex/calculus/random/expression.py

@@ -0,0 +1,43 @@
+from ..API.expression import Expression
+from .core.random_tree import RandomTree
+
+DEFAUTL_CONFIG = {
+    "rejected": [0, 1],
+    "min_max": (-10, 10),
+}
+
+
+def expression_generator(
+    template: str,
+    conditions: list[str] = [],
+    global_config: dict = {},
+    configs: dict = {},
+):
+    """Generate a random expression
+
+    :param template: the template of the expression
+    :param conditions: conditions on randomly generate variable
+    :param global_config: configuration for all variables
+    :param configs: configuration for each variables
+    :return: Expression or Token generated
+
+    :example:
+    >>> e = expression_generator("{a}/{a*k}")
+    >>> e # doctest: +SKIP
+    <Exp: -3 / -15>
+    >>> e = expression_generator("{a}/{a*k} - 3*{b}", configs={'a':{'min_max':(10, 30)}})
+    >>> e # doctest: +SKIP
+    <Exp: 18 / 108 - 3 * 9>
+    >>> e = expression_generator("{a}*x + {b}*x + 3", conditions=["a>b"], global_config={"rejected":[0, 1]})
+    >>> print(e) # doctest: +SKIP
+    10x - 6x + 3
+    >>> ee = e.simplify()
+    >>> print(ee) # doctest: +SKIP
+    4x + 3
+
+    """
+    rd_tree = RandomTree.from_str(template)
+    generated_tree = rd_tree.generate(
+        conditions, dict(DEFAUTL_CONFIG, **global_config), configs
+    )
+    return Expression._post_processing(generated_tree)

mapytex/calculus/random/list.py

@@ -0,0 +1,64 @@
+"""
+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}
+"""
+
+from .core.generate import random_generator
+from .core.grammar import extract_letters, eval_words
+
+DEFAUTL_CONFIG = {
+    "rejected": [0],
+    "min_max": (-10, 10),
+}
+
+
+def list_generator(
+    template: list[str],
+    conditions: list[str] = [],
+    global_config: dict = {},
+    configs: dict = {},
+) -> list[int]:
+    """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 global_config: configuration for all variables
+    :param configs: configuration for each variables
+    :return: list 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
+    >>> a, ab, b, c = list_generator(["a", "a*b", "b", "c"], conditions=["a-b==0"])
+    >>> a - b == 0
+    True
+    >>> a, ab, b, c = list_generator(["a", "a*b", "b", "c"], global_config={"rejected": [2, 3, 5, 7]})
+    >>> a not in [2, 3, 5, 7]
+    True
+    >>> b not in [2, 3, 5, 7]
+    True
+    >>> c not in [2, 3, 5, 7]
+    True
+    >>> a, ab, b, c = list_generator(["a", "a*b", "b", "c"], configs={"a": {"rejected": [2, 3, 5, 7]}})
+    >>> a not in [2, 3, 5, 7]
+    True
+    """
+    rv = extract_letters(template)
+    rv_gen = random_generator(
+        rv, conditions, dict(DEFAUTL_CONFIG, **global_config), configs
+    )
+    generated = eval_words(template, rv_gen)
+    return [generated[v] for v in template]

mapytex/geometry/pythagore.py

@@ -18,6 +18,7 @@ def random_pythagore(v_min = 1, v_max = 10, nbr_format = lambda x : x) :
     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

@@ -32,11 +32,17 @@ class Dataset(list):
     """
 
     @classmethod
-    def random(cls, length, data_name="Valeurs",
-               distrib="gauss", rd_args=(0, 1),
+    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):
+        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)
 
@@ -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

@@ -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

@@ -4,11 +4,15 @@
 from random import randint, uniform, gauss, choice
 
 
-def random_generator(length,
-                     distrib=gauss, rd_args=(0, 1),
+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):
+    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

@@ -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
         """
@@ -109,11 +108,13 @@ class WeightedDataset(dict):
         (1, 3, 4, 5, 5)
 
         """
-        return (min(self.keys()),
+        return (
+            min(self.keys()),
             self.quartile(1),
             self.quartile(2),
             self.quartile(3),
-                max(self.keys()))
+            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)

requirements.txt

@@ -21,6 +21,6 @@ pyparsing==2.3.0
 pytest==3.10.1
 simplegeneric==0.8.1
 six==1.11.0
-tabulate==0.8.2
+tabulate==0.8.7
 traitlets==4.3.2
 wcwidth==0.1.7

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',
+    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',
-    ],
+    install_requires=["multipledispatch", "tabulate"],
 )

test/calculus/core/test_render.py

@@ -0,0 +1,31 @@
+import mapytex
+
+def test_default_render():
+    assert mapytex.render.render_name == "txt"
+
+def test_default_rending():
+    e = mapytex.Expression("2*3")
+    assert str(e) == "2*3"
+
+def test_changing_render():
+    assert mapytex.render.render_name == "txt"
+    mapytex.render.set_render("tex")
+    assert mapytex.render.render_name == "tex"
+    mapytex.render.set_render("txt")
+    assert mapytex.render.render_name == "txt"
+
+
+def test_changing_rending():
+    e = mapytex.Expression.from_str("2*3")
+    f = mapytex.Expression.from_str("2/3")
+    assert str(e) == "2 * 3"
+    assert str(f) == "2 / 3"
+    mapytex.render.set_render("tex")
+    assert str(e) == "2 \\times 3"
+    assert str(f) == "\\dfrac{2}{3}"
+    mapytex.render.set_render("txt")
+    assert str(e) == "2 * 3"
+    assert str(f) == "2 / 3"
+
+
+

test/calculus/random/test_expression_generator.py

@@ -0,0 +1,15 @@
+import mapytex
+
+def test_generate_expression():
+    random_expression = mapytex.random.expression("{a}+{b}")
+    assert type(random_expression).__name__ == "Expression"
+    random_expression = mapytex.random.expression("{a}/{b}")
+    assert type(random_expression).__name__ == "Fraction"
+
+def test_generate_expression_calculus():
+    random_expression = mapytex.random.expression("{a}+{a*b}")
+    assert type(random_expression).__name__ == "Expression"
+    random_expression = mapytex.random.expression("{a}/{a*b}", global_config={"min_max": (2, 10)})
+    assert type(random_expression).__name__ == "Fraction"
+    assert random_expression.numerator / random_expression.denominator <= 1
+

test/calculus/random/test_list_generator.py

@@ -0,0 +1,55 @@
+import mapytex
+
+def test_generate_list():
+    random_list = mapytex.random.list(["a", "b"])
+    assert len(random_list) == 2
+    random_list = mapytex.random.list(["a", "b", "c"])
+    assert len(random_list) == 3
+    random_list = mapytex.random.list(["a", "b", "a", "b"])
+    assert random_list[0] == random_list[2]
+    assert random_list[1] == random_list[3]
+
+def test_generate_list_calculus():
+    random_list = mapytex.random.list(["a", "b", "a+b"])
+    assert random_list[0] + random_list[1] == random_list[2]
+
+    random_list = mapytex.random.list(["a", "b", "a-b"])
+    assert random_list[0] - random_list[1] == random_list[2]
+
+    random_list = mapytex.random.list(["a", "b", "a*b"])
+    assert random_list[0] * random_list[1] == random_list[2]
+
+    random_list = mapytex.random.list(["a", "b", "a/b"])
+    assert random_list[0] / random_list[1] == random_list[2]
+
+def test_generate_list_calculus_math():
+    import math
+    a, b, gcd = mapytex.random.list(["a", "b", "gcd(a, b)"])
+    assert math.gcd(a, b) == gcd
+    a, b, exp, cos = mapytex.random.list(["a", "b", "exp(a)", "cos(b)"])
+    assert math.exp(a) == exp
+    assert math.cos(b) == cos
+
+
+def test_generate_list_conditions():
+    a, b = mapytex.random.list(["a", "b"], conditions=["a + b == 10"])
+    assert a + b == 10
+    a, b = mapytex.random.list(["a", "b"], conditions=["a * b > 0", "a + b == 10"])
+    assert a + b == 10
+    assert a * b > 0
+
+def test_generate_list_conditions_math():
+    import math
+    a, b = mapytex.random.list(["a", "b"], conditions=["gcd(a, b) == 3"])
+    assert math.gcd(a, b) == 3
+
+def test_generate_list_global_config():
+    global_config = {"rejected": [0, 1, 2, 3]}
+    a, = mapytex.random.list(["a"], global_config=global_config)
+    assert a not in global_config["rejected"]
+
+    global_config = {"min_max": (20, 30)}
+    a, = mapytex.random.list(["a"], global_config=global_config)
+    assert a >= 20
+    assert a <= 30
+