Python sympy.Add方法代碼示例

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def sympy_to_grim(expr, **kwargs):
    import sympy
    assert isinstance(expr, sympy.Expr)
    if expr.is_Integer:
        return Expr(int(expr))
    if expr.is_Symbol:
        return Expr(symbol_name=expr.name)
    if expr is sympy.pi:
        return Pi
    if expr is sympy.E:
        return ConstE
    if expr is sympy.I:
        return ConstI
    if expr.is_Add:
        args = [sympy_to_grim(x, **kwargs) for x in expr.args]
        return Add(*args)
    if expr.is_Mul:
        args = [sympy_to_grim(x, **kwargs) for x in expr.args]
        return Mul(*args)
    if expr.is_Pow:
        args = [sympy_to_grim(x, **kwargs) for x in expr.args]
        b, e = args
        return Pow(b, e)
    raise NotImplementedError("converting %s to Grim", type(expr)) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def _print_Sum(self, expr):
        if len(expr.limits) == 1:
            tex = r"\sum_{%s=%s}^{%s} " % \
                tuple([ self._print(i) for i in expr.limits[0] ])
        else:
            def _format_ineq(l):
                return r"%s \leq %s \leq %s" % \
                    tuple([self._print(s) for s in (l[1], l[0], l[2])])

            tex = r"\sum_{\substack{%s}} " % \
                str.join('\\\\', [ _format_ineq(l) for l in expr.limits ])

        if isinstance(expr.function, Add):
            tex += r"\left(%s\right)" % self._print(expr.function)
        else:
            tex += self._print(expr.function)

        return tex 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def _print_Product(self, expr):
        if len(expr.limits) == 1:
            tex = r"\prod_{%s=%s}^{%s} " % \
                tuple([ self._print(i) for i in expr.limits[0] ])
        else:
            def _format_ineq(l):
                return r"%s \leq %s \leq %s" % \
                    tuple([self._print(s) for s in (l[1], l[0], l[2])])

            tex = r"\prod_{\substack{%s}} " % \
                str.join('\\\\', [ _format_ineq(l) for l in expr.limits ])

        if isinstance(expr.function, Add):
            tex += r"\left(%s\right)" % self._print(expr.function)
        else:
            tex += self._print(expr.function)

        return tex 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def _sympystr(self, print_obj):
        if len(self.terms) == 0:
            return ZERO_STR

        self = self._with_sorted_terms()
        s = ''
        for coef, pdop in self.terms:
            coef_str = print_obj.doprint(coef)
            pd_str = print_obj.doprint(pdop)

            if coef == S(1):
                s += pd_str
            elif coef == S(-1):
                s += '-' + pd_str
            else:
                if isinstance(coef, Add):
                    s += '(' + coef_str + ')*' + pd_str
                else:
                    s += coef_str + '*' + pd_str
            s += ' + '

        s = s.replace('+ -', '- ')
        s = s[:-3]
        return s 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def _replace_op_func(e, variable):

    if isinstance(e, Operator):
        return OperatorFunction(e, variable)
    
    if e.is_Number:
        return e
    
    if isinstance(e, Pow):
        return Pow(_replace_op_func(e.base, variable), e.exp)
    
    new_args = [_replace_op_func(arg, variable) for arg in e.args]
    
    if isinstance(e, Add):
        return Add(*new_args)
    
    elif isinstance(e, Mul):
        return Mul(*new_args)
    
    else:
        return e 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def _eval_expand_expectation(self, **hints):
        A = self.args[0]
        if isinstance(A, Add):
            # <A + B> = <A> + <B>
            return Add(*(Expectation(a, self.is_normal_order).expand(expectation=True) for a in A.args))

        if isinstance(A, Mul):
            # <c A> = c<A> where c is a commutative term
            A = A.expand()
            cA, ncA = A.args_cnc()
            return Mul(Mul(*cA), Expectation(Mul._from_args(ncA), self.is_normal_order).expand())
        
        if isinstance(A, Integral):
            # <∫adx> ->  ∫<a>dx
            func, lims = A.function, A.limits
            new_args = [Expectation(func, self.is_normal_order).expand()]
            for lim in lims:
                new_args.append(lim)
            return Integral(*new_args)
        
        return self 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def _eval_expand_tensorproduct(self, **hints):
        """Distribute TensorProducts across addition."""
        args = self.args
        add_args = []
        stop = False
        for i in range(len(args)):
            if isinstance(args[i], Add):
                for aa in args[i].args:
                    tp = TensorProduct(*args[:i] + (aa,) + args[i + 1:])
                    if isinstance(tp, TensorProduct):
                        tp = tp._eval_expand_tensorproduct()
                    add_args.append(tp)
                break

        if add_args:
            return Add(*add_args)
        else:
            return self 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def _normal_ordered_form_terms(expr, independent=False, recursive_limit=10,
                               _recursive_depth=0):
    """
    Helper function for normal_ordered_form: loop through each term in an
    addition expression and call _normal_ordered_form_factor to perform the
    factor to an normally ordered expression.
    """

    new_terms = []
    for term in expr.args:
        if isinstance(term, Mul):
            new_term = _normal_ordered_form_factor(
                term, recursive_limit=recursive_limit,
                _recursive_depth=_recursive_depth, independent=independent)
            new_terms.append(new_term)
        elif isinstance(term, Expectation):
            term = Expectation(normal_ordered_form(term.args[0]), term.is_normal_order)
            new_terms.append(term)
        else:
            new_terms.append(term)

    return Add(*new_terms) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def test_differentiable():
    a = Function(name="a", grid=Grid((10, 10)))
    e = Function(name="e", grid=Grid((10, 10)))

    assert isinstance(1.2 * a.dx, Mul)
    assert isinstance(e + a, Add)
    assert isinstance(e * a, Mul)
    assert isinstance(a * a, Pow)
    assert isinstance(1 / (a * a), Pow)

    addition = a + 1.2 * a.dx
    assert isinstance(addition, Add)
    assert all(isinstance(a, Differentiable) for a in addition.args)

    addition2 = a + e * a.dx
    assert isinstance(addition2, Add)
    assert all(isinstance(a, Differentiable) for a in addition2.args) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def test_diffify():
    a = Function(name="a", grid=Grid((10, 10)))
    e = Function(name="e", grid=Grid((10, 10)))

    assert isinstance(diffify(sympy.Mul(*[1.2, a.dx])), Mul)
    assert isinstance(diffify(sympy.Add(*[a, e])), Add)
    assert isinstance(diffify(sympy.Mul(*[e, a])), Mul)
    assert isinstance(diffify(sympy.Mul(*[a, a])), Pow)
    assert isinstance(diffify(sympy.Pow(*[a*a, -1])), Pow)

    addition = diffify(sympy.Add(*[a, sympy.Mul(*[1.2, a.dx])]))
    assert isinstance(addition, Add)
    assert all(isinstance(a, Differentiable) for a in addition.args)

    addition2 = diffify(sympy.Add(*[a, sympy.Mul(*[e, a.dx])]))
    assert isinstance(addition2, Add)
    assert all(isinstance(a, Differentiable) for a in addition2.args) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def indexify(self, indices=None, lshift=False, subs=None):
        """Create a types.Indexed from the current object."""
        if indices is not None:
            return Indexed(self.indexed, *indices)

        # Substitution for each index (spacing only used in own dimension)
        subs = subs or {}
        subs = [{**{d.spacing: 1, -d.spacing: -1}, **subs} for d in self.dimensions]

        # Add halo shift
        shift = self._size_nodomain.left if lshift else tuple([0]*len(self.dimensions))
        # Indices after substitutions
        indices = [sympy.sympify((a - o + f).xreplace(s)) for a, o, f, s in
                   zip(self.args, self.origin, shift, subs)]
        indices = [i.xreplace({k: sympy.Integer(k) for k in i.atoms(sympy.Float)})
                   for i in indices]
        return self.indexed[indices] 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def _add_question_or_entity(context, p, q, is_question):
  """Generates entity or question for adding p + q."""
  value = p.value + q.value

  if is_question:
    template = random.choice([
        '{p} + {q}',
        '{p}+{q}',
        'Work out {p} + {q}.',
        'Add {p} and {q}.',
        'Put together {p} and {q}.',
        'Sum {p} and {q}.',
        'Total of {p} and {q}.',
        'Add together {p} and {q}.',
        'What is {p} plus {q}?',
        'Calculate {p} + {q}.',
        'What is {p} + {q}?',
    ])
    return example.Problem(
        question=example.question(context, template, p=p, q=q),
        answer=value)
  else:
    return composition.Entity(
        context=context,
        value=value,
        description='Let {self} = {p} + {q}.',
        p=p, q=q) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def _surd_coefficients(sympy_exp):
  """Extracts coefficients a, b, where sympy_exp = a + b * sqrt(base)."""
  sympy_exp = sympy.simplify(sympy.expand(sympy_exp))

  def extract_b(b_sqrt_base):
    """Returns b from expression of form b * sqrt(base)."""
    if isinstance(b_sqrt_base, sympy.Pow):
      # Just form sqrt(base)
      return 1
    else:
      assert isinstance(b_sqrt_base, sympy.Mul)
      assert len(b_sqrt_base.args) == 2
      assert b_sqrt_base.args[0].is_rational
      assert isinstance(b_sqrt_base.args[1], sympy.Pow)  # should be sqrt.
      return b_sqrt_base.args[0]

  if sympy_exp.is_rational:
    # Form: a.
    return sympy_exp, 0
  elif isinstance(sympy_exp, sympy.Add):
    # Form: a + b * sqrt(base)
    assert len(sympy_exp.args) == 2
    assert sympy_exp.args[0].is_rational
    a = sympy_exp.args[0]
    b = extract_b(sympy_exp.args[1])
    return a, b
  else:
    # Form: b * sqrt(base).
    return 0, extract_b(sympy_exp) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def expanded_signs_and_terms(self):
    """Returns a list of arguments, plus any sub-arguments from sub-adds.

    E.g., if this op is `Add(Add(2, Neg(3)), Mul(4, 5), 1)`, then will return
    `[(True, 2), (False, 3), (True, Mul(4, 5)), (True, 1)]` (the arguments of
    the inner add have been extracted).
    """ 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Add [as 別名]
def __init__(self, *args):
    super(Add, self).__init__(args)