1 - Combining plots

Let’s understand what happens when a plot command is executed:

from sympy import *
from spb import *
var("x")
p = plot(sin(x), cos(x), log(x), backend=MB)

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The plot function is going to loop over the provided arguments: it will create and store one data series for each expression. So, in the previous example p contains 3 data series. Once the data series are created, they will be used by the backend (the wrapper to the plotting library) to generate numerical data.

Effectively, p is a container of data series. We can quickly visualize them by printing the plot object:

>>> print(p)
Plot object containing:
[0]: cartesian line: sin(x) for x over (-10.0, 10.0)
[1]: cartesian line: cos(x) for x over (-10.0, 10.0)
[2]: cartesian line: log(x) for x over (-10.0, 10.0)

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We can retrieve a list containing all data series from a plot object by calling the series attribute:

p.series

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Alternatively, we can retrieve a single data series by indexing the plot object:

>>> print(p[0])
cartesian line: sin(x) for x over (-10.0, 10.0)

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We can combine multiple plots together in three ways:

summing them up: this will create a new plot containing all data series from all initial plots. For example:
```
c = S(2) / 10
p1 = plot(cos(x) * exp(-c * x), (x, 0, 10), "f(x)", title="plot 1")
p2 = plot(
    (exp(-c * x), "upper limit"),
    (-exp(-c * x), "lower limit"), (x, 0, 10), {"linestyle": "--"},
    title="plot 2", xlabel="xx", ylabel="yy")
```
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And then:
```
p3 = p1 + p2
p3.show()
# or more quickly: (p1 + p2).show()
```
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Note that the final plot uses the keyword arguments of the left-most plot in the summation. In the previous example, the resulting plot has the title of p1. Now, let’s sum them up in a different order:
```
(p2 + p1).show()
```
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Here, the resulting plot is using the title and axis labels of p2.
We can use the extend method to achieve the same goal as before:
```
p1.extend(p2)
p1.show()
```
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using the append method to append one specific data series from one plot object to another. For example:

>>> p1 = plot(cos(x) * exp(-c * x), (x, 0, 10), "f(x)",
...     title="plot 1", show=False)
>>> p2 = plot(
...     (exp(-c * x), "upper limit"),
...     (-exp(-c * x), "lower limit"), (x, 0, 10), {"linestyle": "--"},
...     title="plot 2", xlabel="xx", ylabel="yy", show=False)
>>> p1.append(p2[0])
>>> print(p1)
Plot object containing:
[0]: cartesian line: exp(-x/5)*cos(x) for x over (0.0, 10.0)
[1]: cartesian line: exp(-x/5) for x over (0.0, 10.0)
>>> p1.show()

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