@@ -261,12 +261,12 @@ def plot(self, chart=None, ambient_coords=None, mapping=None,
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Plot of the vector alone (arrow + label)::
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- sage: v.plot()
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+ sage: v.plot() # needs sage.plot
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Graphics object consisting of 2 graphics primitives
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Plot atop of the chart grid::
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- sage: X.plot() + v.plot()
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+ sage: X.plot() + v.plot() # needs sage.plot
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Graphics object consisting of 20 graphics primitives
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.. PLOT::
@@ -280,7 +280,7 @@ def plot(self, chart=None, ambient_coords=None, mapping=None,
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Plots with various options::
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- sage: X.plot() + v.plot(color='green', scale=2, label='V')
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+ sage: X.plot() + v.plot(color='green', scale=2, label='V') # needs sage.plot
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Graphics object consisting of 20 graphics primitives
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.. PLOT::
@@ -294,7 +294,7 @@ def plot(self, chart=None, ambient_coords=None, mapping=None,
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::
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- sage: X.plot() + v.plot(print_label=False)
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+ sage: X.plot() + v.plot(print_label=False) # needs sage.plot
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Graphics object consisting of 19 graphics primitives
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.. PLOT::
@@ -308,7 +308,7 @@ def plot(self, chart=None, ambient_coords=None, mapping=None,
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::
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- sage: X.plot() + v.plot(color='green', label_color='black',
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+ sage: X.plot() + v.plot(color='green', label_color='black', # needs sage.plot
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....: fontsize=20, label_offset=0.2)
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Graphics object consisting of 20 graphics primitives
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@@ -323,7 +323,7 @@ def plot(self, chart=None, ambient_coords=None, mapping=None,
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::
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- sage: X.plot() + v.plot(linestyle=':', width=4, arrowsize=8,
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+ sage: X.plot() + v.plot(linestyle=':', width=4, arrowsize=8, # needs sage.plot
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....: fontsize=20)
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Graphics object consisting of 20 graphics primitives
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@@ -342,15 +342,15 @@ def plot(self, chart=None, ambient_coords=None, mapping=None,
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(a, b)
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sage: v = Tp((1+a, -b^2), name='v') ; v.display()
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v = (a + 1) ∂/∂x - b^2 ∂/∂y
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- sage: X.plot() + v.plot(parameters={a: -2, b: 3})
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+ sage: X.plot() + v.plot(parameters={a: -2, b: 3}) # needs sage.plot
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Graphics object consisting of 20 graphics primitives
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Special case of the zero vector::
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sage: v = Tp.zero() ; v
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Tangent vector zero at Point p on the 2-dimensional differentiable
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manifold M
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- sage: X.plot() + v.plot()
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+ sage: X.plot() + v.plot() # needs sage.plot
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Graphics object consisting of 19 graphics primitives
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Vector tangent to a 4-dimensional manifold::
@@ -365,7 +365,7 @@ def plot(self, chart=None, ambient_coords=None, mapping=None,
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We cannot make a 4D plot directly::
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- sage: v.plot()
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+ sage: v.plot() # needs sage.plot
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Traceback (most recent call last):
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...
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ValueError: the number of coordinates involved in the plot must
@@ -375,7 +375,7 @@ def plot(self, chart=None, ambient_coords=None, mapping=None,
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the argument ``ambient_coords``. For instance, for a 2-dimensional
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plot in terms of the coordinates `(x, y)`::
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- sage: v.plot(ambient_coords=(x,y))
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+ sage: v.plot(ambient_coords=(x,y)) # needs sage.plot
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Graphics object consisting of 2 graphics primitives
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.. PLOT::
@@ -391,14 +391,14 @@ def plot(self, chart=None, ambient_coords=None, mapping=None,
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Similarly, for a 3-dimensional plot in terms of the coordinates
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`(t, x, y)`::
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- sage: g = v.plot(ambient_coords=(t,x,z))
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- sage: print(g)
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+ sage: g = v.plot(ambient_coords=(t,x,z)) # needs sage.plot
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+ sage: print(g) # needs sage.plot
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Graphics3d Object
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This plot involves only the components `v^t`, `v^x` and `v^z` of `v`.
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A nice 3D view atop the coordinate grid is obtained via::
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- sage: (X.plot(ambient_coords=(t,x,z)) # long time
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+ sage: (X.plot(ambient_coords=(t,x,z)) # long time # needs sage.plot
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....: + v.plot(ambient_coords=(t,x,z),
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....: label_offset=0.5, width=6))
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Graphics3d Object
@@ -431,8 +431,8 @@ def plot(self, chart=None, ambient_coords=None, mapping=None,
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sage: v = XS.frame()[1].at(p) ; v # the coordinate vector ∂/∂phi at p
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Tangent vector ∂/∂ph at Point p on the 2-dimensional differentiable
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manifold S^2
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- sage: graph_v = v.plot(mapping=F)
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- sage: graph_S2 = XS.plot(chart=X3, mapping=F, number_values=9) # long time
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+ sage: graph_v = v.plot(mapping=F) # needs sage.plot
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+ sage: graph_S2 = XS.plot(chart=X3, mapping=F, number_values=9) # long time, needs sage.plot
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sage: graph_v + graph_S2 # long time
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Graphics3d Object
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