Section 1.1: Creating an Integral Table

Let’s consider the task of constructing a simple integral table. The first column will represent the integrand ( f(x) ), while the second column will show the indefinite integral.

Using the sympy library, one might typically initiate the following code, which would display the results vertically—definitely not our desired outcome:

from sympy import *

from sympy.abc import x, n

fs = [x**n, sin(x), cos(x), exp(x)]

for f in fs:

display(f)

integ = integrate(f, x)

display(integ)

To present multiple items in a horizontal format, the ipywidgets package can be utilized. First, install it via pip:

pip install ipywidgets

The ipywidgets library includes a variety of standard widgets, such as input fields, buttons, sliders, and color selectors. For our purpose, we will use the Output widget, which is particularly useful as it can display any rich output from IPython. The layout of our table will be managed by another class from ipywidgets: GridspecLayout. Its interface is quite user-friendly, and it is beneficial to encapsulate it within a function:

from ipywidgets import GridspecLayout, Output

def display_table(table_data):

"""Display data in a table layout in Jupyter."""

nrows = len(table_data)

ncols = len(table_data[0])

grid = GridspecLayout(nrows, ncols)

for row_idx, row_data in enumerate(table_data):

for col_idx, col in enumerate(row_data):

out = Output()

with out:

display(col)

grid[row_idx, col_idx] = out

display(grid)

By utilizing this function, we can systematically compile the items we wish to exhibit, row by row, and then invoke our helper function:

from sympy import *

from sympy.abc import x, n

fs = [x**n, sin(x), cos(x), exp(x)]

rows = []

for f in fs:

integ = Integral(f, x)

result = integrate(f, x)

rows.append([integ, result])

display_table(rows)

And there you have it! The GridspecLayout allows for extensive customization, enabling you to modify its appearance using the full capabilities of CSS. However, this brief guide is designed to help you get started and point you in the right direction for further exploration.