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\input macro.tex
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\line{\sevenrm a104.tex[106,phy] \today\hfill}

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{\rmn
{\narrower\smallskip\noindent
{\bf Exercise.} 

\noindent
Write a program that reads two polynomials
$a(x)=a↓0+a↓1x+a↓2x↑2+\cdots +a↓mx↑m$, 
$b(x)=b↓0+b↓1x+b↓2x↑2+\cdots +b↓mx↑m$, 
and prints the quotient $q(x)$ and remainder $r(x)$ when $a(x)$
is divided by $b(x)$. For example, if 
$$\eqalignno{a(x)&=4+6x+10x↑2+10x↑3+5x↑4+2x↑5\,,\cr
b(x)&=1+2x+1x↑2\,,\cr
\noalign{\hbox{\hskip20pt{then}}}
q(x)&=1+3x+3x↑2+1x↑3\,,\cr
r(x)&=3+1x\,.\cr}$$
Assume $b↓n≠0$. Use {\tt REAL} arithmetic. 

Input convention: $a↓0a↓1a↓2\ldots$ sentinel $b↓0b↓1b↓2\ldots b↓n$ sentinel
where any number larger than $10↑6$ will work as a sentinel.
\smallskip}
}

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\line{\copyright 1984 Robert W. Floyd; \hfil}
%First draft (not published) ??\hfil}
%revised: Date; subsequently revised.\hfill}

\bye