示例#1
0
def test__sort_gens():
    assert _sort_gens([]) == ()

    assert _sort_gens([x]) == (x,)
    assert _sort_gens([p]) == (p,)
    assert _sort_gens([q]) == (q,)

    assert _sort_gens([x, p]) == (x, p)
    assert _sort_gens([p, x]) == (x, p)
    assert _sort_gens([q, p]) == (p, q)

    assert _sort_gens([q, p, x]) == (x, p, q)

    assert _sort_gens([x, p, q], wrt=x) == (x, p, q)
    assert _sort_gens([x, p, q], wrt=p) == (p, x, q)
    assert _sort_gens([x, p, q], wrt=q) == (q, x, p)

    assert _sort_gens([x, p, q], wrt='x') == (x, p, q)
    assert _sort_gens([x, p, q], wrt='p') == (p, x, q)
    assert _sort_gens([x, p, q], wrt='q') == (q, x, p)

    assert _sort_gens([x, p, q], wrt='x,q') == (x, q, p)
    assert _sort_gens([x, p, q], wrt='q,x') == (q, x, p)
    assert _sort_gens([x, p, q], wrt='p,q') == (p, q, x)
    assert _sort_gens([x, p, q], wrt='q,p') == (q, p, x)

    assert _sort_gens([x, p, q], wrt='x, q') == (x, q, p)
    assert _sort_gens([x, p, q], wrt='q, x') == (q, x, p)
    assert _sort_gens([x, p, q], wrt='p, q') == (p, q, x)
    assert _sort_gens([x, p, q], wrt='q, p') == (q, p, x)

    assert _sort_gens([x, p, q], wrt=[x, 'q']) == (x, q, p)
    assert _sort_gens([x, p, q], wrt=[q, 'x']) == (q, x, p)
    assert _sort_gens([x, p, q], wrt=[p, 'q']) == (p, q, x)
    assert _sort_gens([x, p, q], wrt=[q, 'p']) == (q, p, x)

    assert _sort_gens([x, p, q], wrt=['x', 'q']) == (x, q, p)
    assert _sort_gens([x, p, q], wrt=['q', 'x']) == (q, x, p)
    assert _sort_gens([x, p, q], wrt=['p', 'q']) == (p, q, x)
    assert _sort_gens([x, p, q], wrt=['q', 'p']) == (q, p, x)

    assert _sort_gens([x, p, q], sort='x > p > q') == (x, p, q)
    assert _sort_gens([x, p, q], sort='p > x > q') == (p, x, q)
    assert _sort_gens([x, p, q], sort='p > q > x') == (p, q, x)

    assert _sort_gens([x, p, q], wrt='x', sort='q > p') == (x, q, p)
    assert _sort_gens([x, p, q], wrt='p', sort='q > x') == (p, q, x)
    assert _sort_gens([x, p, q], wrt='q', sort='p > x') == (q, p, x)

    X = symbols('x0,x1,x2,x10,x11,x12,x20,x21,x22')

    assert _sort_gens(X) == X
示例#2
0
def plot_implicit(expr, x_var=None, y_var=None, **kwargs):
    """A plot function to plot implicit equations / inequalities.

    Arguments
    =========

    - ``expr`` : The equation / inequality that is to be plotted.
    - ``x_var`` (optional) : symbol to plot on x-axis or tuple giving symbol
      and range as ``(symbol, xmin, xmax)``
    - ``y_var`` (optional) : symbol to plot on y-axis or tuple giving symbol
      and range as ``(symbol, ymin, ymax)``

    If neither ``x_var`` nor ``y_var`` are given then the free symbols in the
    expression will be assigned in the order they are sorted.

    The following keyword arguments can also be used:

    - ``adaptive``. Boolean. The default value is set to True. It has to be
        set to False if you want to use a mesh grid.

    - ``depth`` integer. The depth of recursion for adaptive mesh grid.
        Default value is 0. Takes value in the range (0, 4).

    - ``points`` integer. The number of points if adaptive mesh grid is not
        used. Default value is 200.

    - ``title`` string .The title for the plot.

    - ``xlabel`` string. The label for the x-axis

    - ``ylabel`` string. The label for the y-axis

    plot_implicit, by default, uses interval arithmetic to plot functions. If
    the expression cannot be plotted using interval arithmetic, it defaults to
    a generating a contour using a mesh grid of fixed number of points. By
    setting adaptive to False, you can force plot_implicit to use the mesh
    grid. The mesh grid method can be effective when adaptive plotting using
    interval arithmetic, fails to plot with small line width.

    Examples:
    =========

    Plot expressions:

    >>> from sympy import plot_implicit, cos, sin, symbols, Eq, And
    >>> x, y = symbols('x y')

    Without any ranges for the symbols in the expression

    >>> p1 = plot_implicit(Eq(x**2 + y**2, 5))

    With the range for the symbols

    >>> p2 = plot_implicit(Eq(x**2 + y**2, 3),
    ...         (x, -3, 3), (y, -3, 3))

    With depth of recursion as argument.

    >>> p3 = plot_implicit(Eq(x**2 + y**2, 5),
    ...         (x, -4, 4), (y, -4, 4), depth = 2)

    Using mesh grid and not using adaptive meshing.

    >>> p4 = plot_implicit(Eq(x**2 + y**2, 5),
    ...         (x, -5, 5), (y, -2, 2), adaptive=False)

    Using mesh grid with number of points as input.

    >>> p5 = plot_implicit(Eq(x**2 + y**2, 5),
    ...         (x, -5, 5), (y, -2, 2),
    ...         adaptive=False, points=400)

    Plotting regions.

    >>> p6 = plot_implicit(y > x**2)

    Plotting Using boolean conjunctions.

    >>> p7 = plot_implicit(And(y > x, y > -x))
    """
    has_equality = False  # Represents whether the expression contains an Equality,
    # GreaterThan or LessThan

    def arg_expand(bool_expr):
        """
        Recursively expands the arguments of an Boolean Function
        """
        for arg in bool_expr.args:
            if isinstance(arg, BooleanFunction):
                arg_expand(arg)
            elif isinstance(arg, Relational):
                arg_list.append(arg)

    arg_list = []
    if isinstance(expr, BooleanFunction):
        arg_expand(expr)

        # Check whether there is an equality in the expression provided.
        if any(isinstance(e, (Equality, GreaterThan, LessThan)) for e in arg_list):
            has_equality = True

    elif not isinstance(expr, Relational):
        expr = Eq(expr, 0)
        has_equality = True
    elif isinstance(expr, (Equality, GreaterThan, LessThan)):
        has_equality = True

    xyvar = [i for i in (x_var, y_var) if i is not None]
    free_symbols = expr.free_symbols
    range_symbols = Tuple(*flatten(xyvar)).free_symbols
    undeclared = free_symbols - range_symbols
    if len(free_symbols & range_symbols) > 2:
        raise NotImplementedError("Implicit plotting is not implemented for " "more than 2 variables")

    # Create default ranges if the range is not provided.
    default_range = Tuple(-5, 5)

    def _range_tuple(s):
        if isinstance(s, Symbol):
            return Tuple(s) + default_range
        if len(s) == 3:
            return Tuple(*s)
        raise ValueError("symbol or `(symbol, min, max)` expected but got %s" % s)

    if len(xyvar) == 0:
        xyvar = list(_sort_gens(free_symbols))
    var_start_end_x = _range_tuple(xyvar[0])
    x = var_start_end_x[0]
    if len(xyvar) != 2:
        if x in undeclared or not undeclared:
            xyvar.append(Dummy("f(%s)" % x.name))
        else:
            xyvar.append(undeclared.pop())
    var_start_end_y = _range_tuple(xyvar[1])

    use_interval = kwargs.pop("adaptive", True)
    nb_of_points = kwargs.pop("points", 300)
    depth = kwargs.pop("depth", 0)
    # Check whether the depth is greater than 4 or less than 0.
    if depth > 4:
        depth = 4
    elif depth < 0:
        depth = 0

    series_argument = ImplicitSeries(
        expr, var_start_end_x, var_start_end_y, has_equality, use_interval, depth, nb_of_points
    )
    show = kwargs.pop("show", True)

    # set the x and y limits
    kwargs["xlim"] = tuple(float(x) for x in var_start_end_x[1:])
    kwargs["ylim"] = tuple(float(y) for y in var_start_end_y[1:])
    # set the x and y labels
    kwargs.setdefault("xlabel", var_start_end_x[0].name)
    kwargs.setdefault("ylabel", var_start_end_y[0].name)
    p = Plot(series_argument, **kwargs)
    if show:
        p.show()
    return p
示例#3
0
def test__sort_gens():
    assert _sort_gens([]) == ()

    assert _sort_gens([x]) == (x,)
    assert _sort_gens([p]) == (p,)
    assert _sort_gens([q]) == (q,)

    assert _sort_gens([x,p]) == (x,p)
    assert _sort_gens([p,x]) == (x,p)
    assert _sort_gens([q,p]) == (p,q)

    assert _sort_gens([q,p,x]) == (x,p,q)

    assert _sort_gens([x,p,q], wrt='x') == (x,p,q)
    assert _sort_gens([x,p,q], wrt='p') == (p,x,q)
    assert _sort_gens([x,p,q], wrt='q') == (q,x,p)

    assert _sort_gens([x,p,q], sort='x < p < q') == (x, p, q)
    assert _sort_gens([x,p,q], sort='p < x < q') == (p, x, q)
    assert _sort_gens([x,p,q], sort='p < q < x') == (p, q, x)

    assert _sort_gens([x,p,q], wrt='x', sort='q < p') == (x, q, p)
    assert _sort_gens([x,p,q], wrt='p', sort='q < x') == (p, q, x)
    assert _sort_gens([x,p,q], wrt='q', sort='p < x') == (q, p, x)