I am done

rl/Lib/site-packages/sympy/plotting/tests/test_experimental_lambdify.py

@@ -0,0 +1,77 @@
+from sympy.core.symbol import symbols, Symbol
+from sympy.functions import Max
+from sympy.plotting.experimental_lambdify import experimental_lambdify
+from sympy.plotting.intervalmath.interval_arithmetic import \
+    interval, intervalMembership
+
+
+# Tests for exception handling in experimental_lambdify
+def test_experimental_lambify():
+    x = Symbol('x')
+    f = experimental_lambdify([x], Max(x, 5))
+    # XXX should f be tested? If f(2) is attempted, an
+    # error is raised because a complex produced during wrapping of the arg
+    # is being compared with an int.
+    assert Max(2, 5) == 5
+    assert Max(5, 7) == 7
+
+    x = Symbol('x-3')
+    f = experimental_lambdify([x], x + 1)
+    assert f(1) == 2
+
+
+def test_composite_boolean_region():
+    x, y = symbols('x y')
+
+    r1 = (x - 1)**2 + y**2 < 2
+    r2 = (x + 1)**2 + y**2 < 2
+
+    f = experimental_lambdify((x, y), r1 & r2)
+    a = (interval(-0.1, 0.1), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(True, True)
+    a = (interval(-1.1, -0.9), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(False, True)
+    a = (interval(0.9, 1.1), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(False, True)
+    a = (interval(-0.1, 0.1), interval(1.9, 2.1))
+    assert f(*a) == intervalMembership(False, True)
+
+    f = experimental_lambdify((x, y), r1 | r2)
+    a = (interval(-0.1, 0.1), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(True, True)
+    a = (interval(-1.1, -0.9), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(True, True)
+    a = (interval(0.9, 1.1), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(True, True)
+    a = (interval(-0.1, 0.1), interval(1.9, 2.1))
+    assert f(*a) == intervalMembership(False, True)
+
+    f = experimental_lambdify((x, y), r1 & ~r2)
+    a = (interval(-0.1, 0.1), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(False, True)
+    a = (interval(-1.1, -0.9), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(False, True)
+    a = (interval(0.9, 1.1), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(True, True)
+    a = (interval(-0.1, 0.1), interval(1.9, 2.1))
+    assert f(*a) == intervalMembership(False, True)
+
+    f = experimental_lambdify((x, y), ~r1 & r2)
+    a = (interval(-0.1, 0.1), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(False, True)
+    a = (interval(-1.1, -0.9), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(True, True)
+    a = (interval(0.9, 1.1), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(False, True)
+    a = (interval(-0.1, 0.1), interval(1.9, 2.1))
+    assert f(*a) == intervalMembership(False, True)
+
+    f = experimental_lambdify((x, y), ~r1 & ~r2)
+    a = (interval(-0.1, 0.1), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(False, True)
+    a = (interval(-1.1, -0.9), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(False, True)
+    a = (interval(0.9, 1.1), interval(-0.1, 0.1))
+    assert f(*a) == intervalMembership(False, True)
+    a = (interval(-0.1, 0.1), interval(1.9, 2.1))
+    assert f(*a) == intervalMembership(True, True)

rl/Lib/site-packages/sympy/plotting/tests/test_plot_implicit.py

@@ -0,0 +1,146 @@
+from sympy.core.numbers import (I, pi)
+from sympy.core.relational import Eq
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.functions.elementary.complexes import re
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.trigonometric import (cos, sin, tan)
+from sympy.logic.boolalg import (And, Or)
+from sympy.plotting.plot_implicit import plot_implicit
+from sympy.plotting.plot import unset_show
+from tempfile import NamedTemporaryFile, mkdtemp
+from sympy.testing.pytest import skip, warns, XFAIL
+from sympy.external import import_module
+from sympy.testing.tmpfiles import TmpFileManager
+
+import os
+
+#Set plots not to show
+unset_show()
+
+def tmp_file(dir=None, name=''):
+    return NamedTemporaryFile(
+    suffix='.png', dir=dir, delete=False).name
+
+def plot_and_save(expr, *args, name='', dir=None, **kwargs):
+    p = plot_implicit(expr, *args, **kwargs)
+    p.save(tmp_file(dir=dir, name=name))
+    # Close the plot to avoid a warning from matplotlib
+    p._backend.close()
+
+def plot_implicit_tests(name):
+    temp_dir = mkdtemp()
+    TmpFileManager.tmp_folder(temp_dir)
+    x = Symbol('x')
+    y = Symbol('y')
+    #implicit plot tests
+    plot_and_save(Eq(y, cos(x)), (x, -5, 5), (y, -2, 2), name=name, dir=temp_dir)
+    plot_and_save(Eq(y**2, x**3 - x), (x, -5, 5),
+            (y, -4, 4), name=name, dir=temp_dir)
+    plot_and_save(y > 1 / x, (x, -5, 5),
+            (y, -2, 2), name=name, dir=temp_dir)
+    plot_and_save(y < 1 / tan(x), (x, -5, 5),
+            (y, -2, 2), name=name, dir=temp_dir)
+    plot_and_save(y >= 2 * sin(x) * cos(x), (x, -5, 5),
+            (y, -2, 2), name=name, dir=temp_dir)
+    plot_and_save(y <= x**2, (x, -3, 3),
+            (y, -1, 5), name=name, dir=temp_dir)
+
+    #Test all input args for plot_implicit
+    plot_and_save(Eq(y**2, x**3 - x), dir=temp_dir)
+    plot_and_save(Eq(y**2, x**3 - x), adaptive=False, dir=temp_dir)
+    plot_and_save(Eq(y**2, x**3 - x), adaptive=False, n=500, dir=temp_dir)
+    plot_and_save(y > x, (x, -5, 5), dir=temp_dir)
+    plot_and_save(And(y > exp(x), y > x + 2), dir=temp_dir)
+    plot_and_save(Or(y > x, y > -x), dir=temp_dir)
+    plot_and_save(x**2 - 1, (x, -5, 5), dir=temp_dir)
+    plot_and_save(x**2 - 1, dir=temp_dir)
+    plot_and_save(y > x, depth=-5, dir=temp_dir)
+    plot_and_save(y > x, depth=5, dir=temp_dir)
+    plot_and_save(y > cos(x), adaptive=False, dir=temp_dir)
+    plot_and_save(y < cos(x), adaptive=False, dir=temp_dir)
+    plot_and_save(And(y > cos(x), Or(y > x, Eq(y, x))), dir=temp_dir)
+    plot_and_save(y - cos(pi / x), dir=temp_dir)
+
+    plot_and_save(x**2 - 1, title='An implicit plot', dir=temp_dir)
+
+@XFAIL
+def test_no_adaptive_meshing():
+    matplotlib = import_module('matplotlib', min_module_version='1.1.0', catch=(RuntimeError,))
+    if matplotlib:
+        try:
+            temp_dir = mkdtemp()
+            TmpFileManager.tmp_folder(temp_dir)
+            x = Symbol('x')
+            y = Symbol('y')
+            # Test plots which cannot be rendered using the adaptive algorithm
+
+            # This works, but it triggers a deprecation warning from sympify(). The
+            # code needs to be updated to detect if interval math is supported without
+            # relying on random AttributeErrors.
+            with warns(UserWarning, match="Adaptive meshing could not be applied"):
+                plot_and_save(Eq(y, re(cos(x) + I*sin(x))), name='test', dir=temp_dir)
+        finally:
+            TmpFileManager.cleanup()
+    else:
+        skip("Matplotlib not the default backend")
+def test_line_color():
+    x, y = symbols('x, y')
+    p = plot_implicit(x**2 + y**2 - 1, line_color="green", show=False)
+    assert p._series[0].line_color == "green"
+    p = plot_implicit(x**2 + y**2 - 1, line_color='r', show=False)
+    assert p._series[0].line_color == "r"
+
+def test_matplotlib():
+    matplotlib = import_module('matplotlib', min_module_version='1.1.0', catch=(RuntimeError,))
+    if matplotlib:
+        try:
+            plot_implicit_tests('test')
+            test_line_color()
+        finally:
+            TmpFileManager.cleanup()
+    else:
+        skip("Matplotlib not the default backend")
+
+
+def test_region_and():
+    matplotlib = import_module('matplotlib', min_module_version='1.1.0', catch=(RuntimeError,))
+    if not matplotlib:
+        skip("Matplotlib not the default backend")
+
+    from matplotlib.testing.compare import compare_images
+    test_directory = os.path.dirname(os.path.abspath(__file__))
+
+    try:
+        temp_dir = mkdtemp()
+        TmpFileManager.tmp_folder(temp_dir)
+
+        x, y = symbols('x y')
+
+        r1 = (x - 1)**2 + y**2 < 2
+        r2 = (x + 1)**2 + y**2 < 2
+
+        test_filename = tmp_file(dir=temp_dir, name="test_region_and")
+        cmp_filename = os.path.join(test_directory, "test_region_and.png")
+        p = plot_implicit(r1 & r2, x, y)
+        p.save(test_filename)
+        compare_images(cmp_filename, test_filename, 0.005)
+
+        test_filename = tmp_file(dir=temp_dir, name="test_region_or")
+        cmp_filename = os.path.join(test_directory, "test_region_or.png")
+        p = plot_implicit(r1 | r2, x, y)
+        p.save(test_filename)
+        compare_images(cmp_filename, test_filename, 0.005)
+
+        test_filename = tmp_file(dir=temp_dir, name="test_region_not")
+        cmp_filename = os.path.join(test_directory, "test_region_not.png")
+        p = plot_implicit(~r1, x, y)
+        p.save(test_filename)
+        compare_images(cmp_filename, test_filename, 0.005)
+
+        test_filename = tmp_file(dir=temp_dir, name="test_region_xor")
+        cmp_filename = os.path.join(test_directory, "test_region_xor.png")
+        p = plot_implicit(r1 ^ r2, x, y)
+        p.save(test_filename)
+        compare_images(cmp_filename, test_filename, 0.005)
+    finally:
+        TmpFileManager.cleanup()

rl/Lib/site-packages/sympy/plotting/tests/test_region_and.png.import

@@ -0,0 +1,34 @@
+[remap]
+
+importer="texture"
+type="CompressedTexture2D"
+uid="uid://ccgrfp1kviy0t"
+path="res://.godot/imported/test_region_and.png-c1d9a0695d86ddf4348962c5b17879ff.ctex"
+metadata={
+"vram_texture": false
+}
+
+[deps]
+
+source_file="res://rl/Lib/site-packages/sympy/plotting/tests/test_region_and.png"
+dest_files=["res://.godot/imported/test_region_and.png-c1d9a0695d86ddf4348962c5b17879ff.ctex"]
+
+[params]
+
+compress/mode=0
+compress/high_quality=false
+compress/lossy_quality=0.7
+compress/hdr_compression=1
+compress/normal_map=0
+compress/channel_pack=0
+mipmaps/generate=false
+mipmaps/limit=-1
+roughness/mode=0
+roughness/src_normal=""
+process/fix_alpha_border=true
+process/premult_alpha=false
+process/normal_map_invert_y=false
+process/hdr_as_srgb=false
+process/hdr_clamp_exposure=false
+process/size_limit=0
+detect_3d/compress_to=1

rl/Lib/site-packages/sympy/plotting/tests/test_region_not.png.import

@@ -0,0 +1,34 @@
+[remap]
+
+importer="texture"
+type="CompressedTexture2D"
+uid="uid://bwcwpn78v6jsw"
+path="res://.godot/imported/test_region_not.png-f3250ebd2c1022cb029e786ee370fd83.ctex"
+metadata={
+"vram_texture": false
+}
+
+[deps]
+
+source_file="res://rl/Lib/site-packages/sympy/plotting/tests/test_region_not.png"
+dest_files=["res://.godot/imported/test_region_not.png-f3250ebd2c1022cb029e786ee370fd83.ctex"]
+
+[params]
+
+compress/mode=0
+compress/high_quality=false
+compress/lossy_quality=0.7
+compress/hdr_compression=1
+compress/normal_map=0
+compress/channel_pack=0
+mipmaps/generate=false
+mipmaps/limit=-1
+roughness/mode=0
+roughness/src_normal=""
+process/fix_alpha_border=true
+process/premult_alpha=false
+process/normal_map_invert_y=false
+process/hdr_as_srgb=false
+process/hdr_clamp_exposure=false
+process/size_limit=0
+detect_3d/compress_to=1

rl/Lib/site-packages/sympy/plotting/tests/test_region_or.png.import

@@ -0,0 +1,34 @@
+[remap]
+
+importer="texture"
+type="CompressedTexture2D"
+uid="uid://ptn7si3a6w3e"
+path="res://.godot/imported/test_region_or.png-fcd19de9f7f9d11aa222486f596ec33d.ctex"
+metadata={
+"vram_texture": false
+}
+
+[deps]
+
+source_file="res://rl/Lib/site-packages/sympy/plotting/tests/test_region_or.png"
+dest_files=["res://.godot/imported/test_region_or.png-fcd19de9f7f9d11aa222486f596ec33d.ctex"]
+
+[params]
+
+compress/mode=0
+compress/high_quality=false
+compress/lossy_quality=0.7
+compress/hdr_compression=1
+compress/normal_map=0
+compress/channel_pack=0
+mipmaps/generate=false
+mipmaps/limit=-1
+roughness/mode=0
+roughness/src_normal=""
+process/fix_alpha_border=true
+process/premult_alpha=false
+process/normal_map_invert_y=false
+process/hdr_as_srgb=false
+process/hdr_clamp_exposure=false
+process/size_limit=0
+detect_3d/compress_to=1

rl/Lib/site-packages/sympy/plotting/tests/test_region_xor.png.import

@@ -0,0 +1,34 @@
+[remap]
+
+importer="texture"
+type="CompressedTexture2D"
+uid="uid://dp0upq1njbej6"
+path="res://.godot/imported/test_region_xor.png-b5f7c27e2fb8694466c39ee95db567dc.ctex"
+metadata={
+"vram_texture": false
+}
+
+[deps]
+
+source_file="res://rl/Lib/site-packages/sympy/plotting/tests/test_region_xor.png"
+dest_files=["res://.godot/imported/test_region_xor.png-b5f7c27e2fb8694466c39ee95db567dc.ctex"]
+
+[params]
+
+compress/mode=0
+compress/high_quality=false
+compress/lossy_quality=0.7
+compress/hdr_compression=1
+compress/normal_map=0
+compress/channel_pack=0
+mipmaps/generate=false
+mipmaps/limit=-1
+roughness/mode=0
+roughness/src_normal=""
+process/fix_alpha_border=true
+process/premult_alpha=false
+process/normal_map_invert_y=false
+process/hdr_as_srgb=false
+process/hdr_clamp_exposure=false
+process/size_limit=0
+detect_3d/compress_to=1

rl/Lib/site-packages/sympy/plotting/tests/test_textplot.py

@@ -0,0 +1,203 @@
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.exponential import log
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import sin
+from sympy.plotting.textplot import textplot_str
+
+from sympy.utilities.exceptions import ignore_warnings
+
+
+def test_axes_alignment():
+    x = Symbol('x')
+    lines = [
+        '      1 |                                                     ..',
+        '        |                                                  ...  ',
+        '        |                                                ..     ',
+        '        |                                             ...       ',
+        '        |                                          ...          ',
+        '        |                                        ..             ',
+        '        |                                     ...               ',
+        '        |                                  ...                  ',
+        '        |                                ..                     ',
+        '        |                             ...                       ',
+        '      0 |--------------------------...--------------------------',
+        '        |                       ...                             ',
+        '        |                     ..                                ',
+        '        |                  ...                                  ',
+        '        |               ...                                     ',
+        '        |             ..                                        ',
+        '        |          ...                                          ',
+        '        |       ...                                             ',
+        '        |     ..                                                ',
+        '        |  ...                                                  ',
+        '     -1 |_______________________________________________________',
+        '         -1                         0                          1'
+    ]
+    assert lines == list(textplot_str(x, -1, 1))
+
+    lines = [
+        '      1 |                                                     ..',
+        '        |                                                 ....  ',
+        '        |                                              ...      ',
+        '        |                                           ...         ',
+        '        |                                       ....            ',
+        '        |                                    ...                ',
+        '        |                                 ...                   ',
+        '        |                             ....                      ',
+        '      0 |--------------------------...--------------------------',
+        '        |                      ....                             ',
+        '        |                   ...                                 ',
+        '        |                ...                                    ',
+        '        |            ....                                       ',
+        '        |         ...                                           ',
+        '        |      ...                                              ',
+        '        |  ....                                                 ',
+        '     -1 |_______________________________________________________',
+        '         -1                         0                          1'
+    ]
+    assert lines == list(textplot_str(x, -1, 1, H=17))
+
+
+def test_singularity():
+    x = Symbol('x')
+    lines = [
+        '     54 | .                                                     ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ','        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '   27.5 |--.----------------------------------------------------',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |   .                                                   ',
+        '        |    \\                                                  ',
+        '        |     \\                                                 ',
+        '        |      ..                                               ',
+        '        |        ...                                            ',
+        '        |           .............                               ',
+        '      1 |_______________________________________________________',
+        '         0                          0.5                        1'
+    ]
+    assert lines == list(textplot_str(1/x, 0, 1))
+
+    lines = [
+        '      0 |                                                 ......',
+        '        |                                         ........      ',
+        '        |                                 ........              ',
+        '        |                           ......                      ',
+        '        |                      .....                            ',
+        '        |                  ....                                 ',
+        '        |               ...                                     ',
+        '        |             ..                                        ',
+        '        |          ...                                          ',
+        '        |         /                                             ',
+        '     -2 |-------..----------------------------------------------',
+        '        |      /                                                ',
+        '        |     /                                                 ',
+        '        |    /                                                  ',
+        '        |   .                                                   ',
+        '        |                                                       ',
+        '        |  .                                                    ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '     -4 |_______________________________________________________',
+        '         0                          0.5                        1'
+    ]
+    # RuntimeWarning: divide by zero encountered in log
+    with ignore_warnings(RuntimeWarning):
+        assert lines == list(textplot_str(log(x), 0, 1))
+
+
+def test_sinc():
+    x = Symbol('x')
+    lines = [
+        '      1 |                          . .                          ',
+        '        |                         .   .                         ',
+        '        |                                                       ',
+        '        |                        .     .                        ',
+        '        |                                                       ',
+        '        |                       .       .                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                      .         .                      ',
+        '        |                                                       ',
+        '    0.4 |-------------------------------------------------------',
+        '        |                     .           .                     ',
+        '        |                                                       ',
+        '        |                    .             .                    ',
+        '        |                                                       ',
+        '        |    .....                                     .....    ',
+        '        |  ..     \\         .               .         /     ..  ',
+        '        | /        \\                                 /        \\ ',
+        '        |/          \\      .                 .      /          \\',
+        '        |            \\    /                   \\    /            ',
+        '   -0.2 |_______________________________________________________',
+        '         -10                        0                          10'
+    ]
+    # RuntimeWarning: invalid value encountered in double_scalars
+    with ignore_warnings(RuntimeWarning):
+        assert lines == list(textplot_str(sin(x)/x, -10, 10))
+
+
+def test_imaginary():
+    x = Symbol('x')
+    lines = [
+        '      1 |                                                     ..',
+        '        |                                                   ..  ',
+        '        |                                                ...    ',
+        '        |                                              ..       ',
+        '        |                                            ..         ',
+        '        |                                          ..           ',
+        '        |                                        ..             ',
+        '        |                                      ..               ',
+        '        |                                    ..                 ',
+        '        |                                   /                   ',
+        '    0.5 |----------------------------------/--------------------',
+        '        |                                ..                     ',
+        '        |                               /                       ',
+        '        |                              .                        ',
+        '        |                                                       ',
+        '        |                             .                         ',
+        '        |                            .                          ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '      0 |_______________________________________________________',
+        '         -1                         0                          1'
+    ]
+    # RuntimeWarning: invalid value encountered in sqrt
+    with ignore_warnings(RuntimeWarning):
+        assert list(textplot_str(sqrt(x), -1, 1)) == lines
+
+    lines = [
+        '      1 |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '      0 |-------------------------------------------------------',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '        |                                                       ',
+        '     -1 |_______________________________________________________',
+        '         -1                         0                          1'
+    ]
+    assert list(textplot_str(S.ImaginaryUnit, -1, 1)) == lines

rl/Lib/site-packages/sympy/plotting/tests/test_utils.py

@@ -0,0 +1,110 @@
+from pytest import raises
+from sympy import (
+    symbols, Expr, Tuple, Integer, cos, solveset, FiniteSet, ImageSet)
+from sympy.plotting.utils import (
+    _create_ranges, _plot_sympify, extract_solution)
+from sympy.physics.mechanics import ReferenceFrame, Vector as MechVector
+from sympy.vector import CoordSys3D, Vector
+
+
+def test_plot_sympify():
+    x, y = symbols("x, y")
+
+    # argument is already sympified
+    args = x + y
+    r = _plot_sympify(args)
+    assert r == args
+
+    # one argument needs to be sympified
+    args = (x + y, 1)
+    r = _plot_sympify(args)
+    assert isinstance(r, (list, tuple, Tuple)) and len(r) == 2
+    assert isinstance(r[0], Expr)
+    assert isinstance(r[1], Integer)
+
+    # string and dict should not be sympified
+    args = (x + y, (x, 0, 1), "str", 1, {1: 1, 2: 2.0})
+    r = _plot_sympify(args)
+    assert isinstance(r, (list, tuple, Tuple)) and len(r) == 5
+    assert isinstance(r[0], Expr)
+    assert isinstance(r[1], Tuple)
+    assert isinstance(r[2], str)
+    assert isinstance(r[3], Integer)
+    assert isinstance(r[4], dict) and isinstance(r[4][1], int) and isinstance(r[4][2], float)
+
+    # nested arguments containing strings
+    args = ((x + y, (y, 0, 1), "a"), (x + 1, (x, 0, 1), "$f_{1}$"))
+    r = _plot_sympify(args)
+    assert isinstance(r, (list, tuple, Tuple)) and len(r) == 2
+    assert isinstance(r[0], Tuple)
+    assert isinstance(r[0][1], Tuple)
+    assert isinstance(r[0][1][1], Integer)
+    assert isinstance(r[0][2], str)
+    assert isinstance(r[1], Tuple)
+    assert isinstance(r[1][1], Tuple)
+    assert isinstance(r[1][1][1], Integer)
+    assert isinstance(r[1][2], str)
+
+    # vectors from sympy.physics.vectors module are not sympified
+    # vectors from sympy.vectors are sympified
+    # in both cases, no error should be raised
+    R = ReferenceFrame("R")
+    v1 = 2 * R.x + R.y
+    C = CoordSys3D("C")
+    v2 = 2 * C.i + C.j
+    args = (v1, v2)
+    r = _plot_sympify(args)
+    assert isinstance(r, (list, tuple, Tuple)) and len(r) == 2
+    assert isinstance(v1, MechVector)
+    assert isinstance(v2, Vector)
+
+
+def test_create_ranges():
+    x, y = symbols("x, y")
+
+    # user don't provide any range -> return a default range
+    r = _create_ranges({x}, [], 1)
+    assert isinstance(r, (list, tuple, Tuple)) and len(r) == 1
+    assert isinstance(r[0], (Tuple, tuple))
+    assert r[0] == (x, -10, 10)
+
+    r = _create_ranges({x, y}, [], 2)
+    assert isinstance(r, (list, tuple, Tuple)) and len(r) == 2
+    assert isinstance(r[0], (Tuple, tuple))
+    assert isinstance(r[1], (Tuple, tuple))
+    assert r[0] == (x, -10, 10) or (y, -10, 10)
+    assert r[1] == (y, -10, 10) or (x, -10, 10)
+    assert r[0] != r[1]
+
+    # not enough ranges provided by the user -> create default ranges
+    r = _create_ranges(
+        {x, y},
+        [
+            (x, 0, 1),
+        ],
+        2,
+    )
+    assert isinstance(r, (list, tuple, Tuple)) and len(r) == 2
+    assert isinstance(r[0], (Tuple, tuple))
+    assert isinstance(r[1], (Tuple, tuple))
+    assert r[0] == (x, 0, 1) or (y, -10, 10)
+    assert r[1] == (y, -10, 10) or (x, 0, 1)
+    assert r[0] != r[1]
+
+    # too many free symbols
+    raises(ValueError, lambda: _create_ranges({x, y}, [], 1))
+    raises(ValueError, lambda: _create_ranges({x, y}, [(x, 0, 5), (y, 0, 1)], 1))
+
+
+def test_extract_solution():
+    x = symbols("x")
+
+    sol = solveset(cos(10 * x))
+    assert sol.has(ImageSet)
+    res = extract_solution(sol)
+    assert len(res) == 20
+    assert isinstance(res, FiniteSet)
+
+    res = extract_solution(sol, 20)
+    assert len(res) == 40
+    assert isinstance(res, FiniteSet)