Recursively generate LaTeX expression for continued fractions for a given python list

Question

I am trying to generate LaTeX string expression for continued fractions in Jupyter Notebook. for example, a given Python list x=[1,2,3,4,5] can be written as continued fraction:

Structure expression to generate this LaTeX fraction is \\frac{Numerator}{Denominator}

With Non-recursive code :

from IPython.display import display, Markdown

# Non-recursive: 
def nest_frac(previous_expr, numerator_expr1, denominator_expr2):
    return previous_expr + " + \\frac{"+ numerator_expr1 + "}{" + denominator_expr2 + "}"

# Cumbersome, error-prone
display(Markdown("$"+ \
                 nest_frac("1","1", \
                           nest_frac("2","1", \
                                     nest_frac("3","1", \
                                              nest_frac("4","1", "5") \
                                              )  \
                                     ) \
                          ) \
            + "$") \
       )

x = [1,2,3,4,5]

How to recursively generate expression provided a python list.

Answer 1

We can define the function nest_frac_N taking x as an additional argument:

def nest_frac_N(previous_expr, numerator_expr1, denominator_expr2, x):
    
    temp_frac=str(x[len(x)-1]-1) +"+  \\frac{"+str(numerator_expr1)+"}{"+str(x[len(x)-1])+"}"
    
    for i in reversed(x[:len(x)-2]):
        
        temp_frac = str(i) +"+  \\frac{1}{"+temp_frac+"}"
    
    return temp_frac

If we need an output for x=[1,2,3,4,5] we do:

>>> x = [1,2,3,4,5]
>>> nest_frac_N(1, 1, 1, x)
... '1+  \\frac{1}{2+  \\frac{1}{3+  \\frac{1}{4+  \\frac{1}{5}}}}'

To get the markdown format we use :

display(Markdown("$"+nest_frac_N(1, 1, 1, x)+"$"))

Let's the x size to 10 to ensure that function is flexible :

Output

>>> x = [1,2,3,4,5,6,7,8,9,10]
>>> nest_frac_N(1, 1, 1, x)
... '1+  \\frac{1}{2+  \\frac{1}{3+  \\frac{1}{4+  \\frac{1}{5+  \\frac{1}{6+  \\frac{1}{7+  \\frac{1}{8+  \\frac{1}{9+  \\frac{1}{10}}}}}}}}}'

And to get the markdown :

display(Markdown("$"+nest_frac_N(1, 1, 1, x)+"$"))

And we can easily re-set the function in a way to display directly the markdown format.