Editing Polynomial long division (section)

==Pseudocode==

The algorithm can be represented in [[pseudocode]] as follows, where +, −, and × represent polynomial arithmetic, and lead(r) / lead(d) represents the polynomial obtained by dividing the two leading terms:

 '''function''' n / d '''is'''
     require d ≠ 0
     q ← 0
     r ← n             // At each step n = d × q + r
 
     '''while''' r ≠ 0 '''and''' degree(r) ≥ degree(d) '''do'''
         t ← lead(r) / lead(d)       // Divide the leading terms
         q ← q + t
         r ← r − t × d
 
     '''return''' (q, r)

This works equally well when degree(''n'') < degree(''d''); in that case the result is just the trivial (0, ''n'').

This algorithm describes exactly the above paper and pencil method: {{var|d}} is written on the left of the ")"; {{var|q}} is written, term after term, above the horizontal line, the last term being the value of {{var|t}}; the region under the horizontal line is used to compute and write down the successive values of {{var|r}}.