Python Add.fromiter方法代码示例

# 需要导入模块: from sympy import Add [as 别名]
# 或者: from sympy.Add import fromiter [as 别名]
def cancel_terms(sym, x_term, coef):
    if coef.is_Add:
        for arg_c in coef.args:
            sym = cancel_terms(sym, x_term, arg_c)
    else:
        terms = Add.make_args(sym)
        return Add.fromiter(t for t in terms if t != x_term*coef)

# 需要导入模块: from sympy import Add [as 别名]
# 或者: from sympy.Add import fromiter [as 别名]
 def _print_Add(self, expr):
     if len(expr.args) != 2:
         return "add({}, {})".format(
             self._print(expr.args[0]),
             self._print(Add.fromiter(expr.args[1:]))
         )
     return "add({}, {})".format(
         self._print(expr.args[0]),
         self._print(expr.args[1]),
     )

# 需要导入模块: from sympy import Add [as 别名]
# 或者: from sympy.Add import fromiter [as 别名]
def dot(vect1, vect2):
    """
    Returns dot product of two vectors.

    Examples
    ========

    >>> from sympy.vector import CoordSys3D
    >>> from sympy.vector.vector import dot
    >>> R = CoordSys3D('R')
    >>> v1 = R.i + R.j + R.k
    >>> v2 = R.x * R.i + R.y * R.j + R.z * R.k
    >>> dot(v1, v2)
    R.x + R.y + R.z

    """
    if isinstance(vect1, Add):
        return Add.fromiter(dot(i, vect2) for i in vect1.args)
    if isinstance(vect2, Add):
        return Add.fromiter(dot(vect1, i) for i in vect2.args)
    if isinstance(vect1, BaseVector) and isinstance(vect2, BaseVector):
        if vect1._sys == vect2._sys:
            return S.One if vect1 == vect2 else S.Zero
        try:
            from .functions import express
            return dot(vect1, express(vect2, vect1._sys))
        except:
            return Dot(vect1, vect2)
    if isinstance(vect1, VectorZero) or isinstance(vect2, VectorZero):
        return S.Zero
    if isinstance(vect1, VectorMul):
        v1, m1 = next(iter(vect1.components.items()))
        return m1*dot(v1, vect2)
    if isinstance(vect2, VectorMul):
        v2, m2 = next(iter(vect2.components.items()))
        return m2*dot(vect1, v2)

    return Dot(vect1, vect2)

# 需要导入模块: from sympy import Add [as 别名]
# 或者: from sympy.Add import fromiter [as 别名]
 def recurse_expr(expr, index_ranges={}):
     if expr.is_Mul:
         nonmatargs = []
         pos_arg = []
         pos_ind = []
         dlinks = {}
         link_ind = []
         counter = 0
         args_ind = []
         for arg in expr.args:
             retvals = recurse_expr(arg, index_ranges)
             assert isinstance(retvals, list)
             if isinstance(retvals, list):
                 for i in retvals:
                     args_ind.append(i)
             else:
                 args_ind.append(retvals)
         for arg_symbol, arg_indices in args_ind:
             if arg_indices is None:
                 nonmatargs.append(arg_symbol)
                 continue
             if isinstance(arg_symbol, MatrixElement):
                 arg_symbol = arg_symbol.args[0]
             pos_arg.append(arg_symbol)
             pos_ind.append(arg_indices)
             link_ind.append([None]*len(arg_indices))
             for i, ind in enumerate(arg_indices):
                 if ind in dlinks:
                     other_i = dlinks[ind]
                     link_ind[counter][i] = other_i
                     link_ind[other_i[0]][other_i[1]] = (counter, i)
                 dlinks[ind] = (counter, i)
             counter += 1
         counter2 = 0
         lines = {}
         while counter2 < len(link_ind):
             for i, e in enumerate(link_ind):
                 if None in e:
                     line_start_index = (i, e.index(None))
                     break
             cur_ind_pos = line_start_index
             cur_line = []
             index1 = pos_ind[cur_ind_pos[0]][cur_ind_pos[1]]
             while True:
                 d, r = cur_ind_pos
                 if pos_arg[d] != 1:
                     if r % 2 == 1:
                         cur_line.append(transpose(pos_arg[d]))
                     else:
                         cur_line.append(pos_arg[d])
                 next_ind_pos = link_ind[d][1-r]
                 counter2 += 1
                 # Mark as visited, there will be no `None` anymore:
                 link_ind[d] = (-1, -1)
                 if next_ind_pos is None:
                     index2 = pos_ind[d][1-r]
                     lines[(index1, index2)] = cur_line
                     break
                 cur_ind_pos = next_ind_pos
         ret_indices = list(j for i in lines for j in i)
         lines = {k: MatMul.fromiter(v) if len(v) != 1 else v[0] for k, v in lines.items()}
         return [(Mul.fromiter(nonmatargs), None)] + [
             (MatrixElement(a, i, j), (i, j)) for (i, j), a in lines.items()
         ]
     elif expr.is_Add:
         res = [recurse_expr(i) for i in expr.args]
         d = collections.defaultdict(list)
         for res_addend in res:
             scalar = 1
             for elem, indices in res_addend:
                 if indices is None:
                     scalar = elem
                     continue
                 indices = tuple(sorted(indices, key=default_sort_key))
                 d[indices].append(scalar*remove_matelement(elem, *indices))
                 scalar = 1
         return [(MatrixElement(Add.fromiter(v), *k), k) for k, v in d.items()]
     elif isinstance(expr, KroneckerDelta):
         i1, i2 = expr.args
         if dimensions is not None:
             identity = Identity(dimensions[0])
         else:
             identity = S.One
         return [(MatrixElement(identity, i1, i2), (i1, i2))]
     elif isinstance(expr, MatrixElement):
         matrix_symbol, i1, i2 = expr.args
         if i1 in index_ranges:
             r1, r2 = index_ranges[i1]
             if r1 != 0 or matrix_symbol.shape[0] != r2+1:
                 raise ValueError("index range mismatch: {0} vs. (0, {1})".format(
                     (r1, r2), matrix_symbol.shape[0]))
         if i2 in index_ranges:
             r1, r2 = index_ranges[i2]
             if r1 != 0 or matrix_symbol.shape[1] != r2+1:
                 raise ValueError("index range mismatch: {0} vs. (0, {1})".format(
                     (r1, r2), matrix_symbol.shape[1]))
         if (i1 == i2) and (i1 in index_ranges):
             return [(trace(matrix_symbol), None)]
         return [(MatrixElement(matrix_symbol, i1, i2), (i1, i2))]
     elif isinstance(expr, Sum):
#.........这里部分代码省略.........

# 需要导入模块: from sympy import Add [as 别名]
# 或者: from sympy.Add import fromiter [as 别名]
def convert_to(expr, target_units):
    """
    Convert ``expr`` to the same expression with all of its units and quantities
    represented as factors of ``target_units``, whenever the dimension is compatible.

    ``target_units`` may be a single unit/quantity, or a collection of
    units/quantities.

    Examples
    ========

    >>> from sympy.physics.units import speed_of_light, meter, gram, second, day
    >>> from sympy.physics.units import mile, newton, kilogram, atomic_mass_constant
    >>> from sympy.physics.units import kilometer, centimeter
    >>> from sympy.physics.units import convert_to
    >>> convert_to(mile, kilometer)
    25146*kilometer/15625
    >>> convert_to(mile, kilometer).n()
    1.609344*kilometer
    >>> convert_to(speed_of_light, meter/second)
    299792458*meter/second
    >>> convert_to(day, second)
    86400*second
    >>> 3*newton
    3*newton
    >>> convert_to(3*newton, kilogram*meter/second**2)
    3*kilogram*meter/second**2
    >>> convert_to(atomic_mass_constant, gram)
    1.66053904e-24*gram

    Conversion to multiple units:

    >>> convert_to(speed_of_light, [meter, second])
    299792458*meter/second
    >>> convert_to(3*newton, [centimeter, gram, second])
    300000*centimeter*gram/second**2

    Conversion to Planck units:

    >>> from sympy.physics.units import gravitational_constant, hbar
    >>> convert_to(atomic_mass_constant, [gravitational_constant, speed_of_light, hbar]).n()
    7.62950196312651e-20*gravitational_constant**(-0.5)*hbar**0.5*speed_of_light**0.5

    """
    if not isinstance(target_units, (collections.Iterable, Tuple)):
        target_units = [target_units]

    if isinstance(expr, Add):
        return Add.fromiter(convert_to(i, target_units) for i in expr.args)

    expr = sympify(expr)

    if not isinstance(expr, Quantity) and expr.has(Quantity):
        expr = expr.replace(lambda x: isinstance(x, Quantity), lambda x: x.convert_to(target_units))

    def get_total_scale_factor(expr):
        if isinstance(expr, Mul):
            return reduce(lambda x, y: x * y, [get_total_scale_factor(i) for i in expr.args])
        elif isinstance(expr, Pow):
            return get_total_scale_factor(expr.base) ** expr.exp
        elif isinstance(expr, Quantity):
            return expr.scale_factor
        return expr

    depmat = _get_conversion_matrix_for_expr(expr, target_units)
    if depmat is None:
        return expr

    expr_scale_factor = get_total_scale_factor(expr)
    return expr_scale_factor * Mul.fromiter((1/get_total_scale_factor(u) * u) ** p for u, p in zip(target_units, depmat))

# 需要导入模块: from sympy import Add [as 别名]
# 或者: from sympy.Add import fromiter [as 别名]
def get_max_coef(sym, x_term):
    return Add.fromiter(
        get_max_coef_mul(s, x_term) for s in Add.make_args(sym)
    )

# 需要导入模块: from sympy import Add [as 别名]
# 或者: from sympy.Add import fromiter [as 别名]
def divergence(vect, coord_sys=None, doit=True):
    """
    Returns the divergence of a vector field computed wrt the base
    scalars of the given coordinate system.

    Parameters
    ==========

    vector : Vector
        The vector operand

    coord_sys : CoordSys3D
        The coordinate system to calculate the gradient in
        Deprecated since version 1.1

    doit : bool
        If True, the result is returned after calling .doit() on
        each component. Else, the returned expression contains
        Derivative instances

    Examples
    ========

    >>> from sympy.vector import CoordSys3D, divergence
    >>> R = CoordSys3D('R')
    >>> v1 = R.x*R.y*R.z * (R.i+R.j+R.k)

    >>> divergence(v1)
    R.x*R.y + R.x*R.z + R.y*R.z
    >>> v2 = 2*R.y*R.z*R.j
    >>> divergence(v2)
    2*R.z

    """
    coord_sys = _get_coord_sys_from_expr(vect, coord_sys)
    if len(coord_sys) == 0:
        return S.Zero
    elif len(coord_sys) == 1:
        if isinstance(vect, (Cross, Curl, Gradient)):
            return Divergence(vect)
        # TODO: is case of many coord systems, this gets a random one:
        coord_sys = next(iter(coord_sys))
        i, j, k = coord_sys.base_vectors()
        x, y, z = coord_sys.base_scalars()
        h1, h2, h3 = coord_sys.lame_coefficients()
        vx = _diff_conditional(vect.dot(i), x, h2, h3) \
             / (h1 * h2 * h3)
        vy = _diff_conditional(vect.dot(j), y, h3, h1) \
             / (h1 * h2 * h3)
        vz = _diff_conditional(vect.dot(k), z, h1, h2) \
             / (h1 * h2 * h3)
        res = vx + vy + vz
        if doit:
            return res.doit()
        return res
    else:
        if isinstance(vect, (Add, VectorAdd)):
            return Add.fromiter(divergence(i, doit=doit) for i in vect.args)
        elif isinstance(vect, (Mul, VectorMul)):
            vector = [i for i in vect.args if isinstance(i, (Vector, Cross, Gradient))][0]
            scalar = Mul.fromiter(i for i in vect.args if not isinstance(i, (Vector, Cross, Gradient)))
            res = Dot(vector, gradient(scalar)) + scalar*divergence(vector, doit=doit)
            if doit:
                return res.doit()
            return res
        elif isinstance(vect, (Cross, Curl, Gradient)):
            return Divergence(vect)
        else:
            raise Divergence(vect)