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.

Asked By: Rajesh Swarnkar

||

Source

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.

Answered By: Khaled DELLAL

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

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