> < ^ Date: Tue, 23 Feb 1993 14:32:26 +0100
> < ^ From: Frank Celler <frank.celler@math.rwth-aachen.de >
> < ^ Subject: Re: First impressions of 3.2

I found a routine for the Gcd, but not for
the division. Did I miss something?

no, you are not missing anything, the routine 'EuclideanQuotient' was not

The following routine should work for polynomials over fields:

```-----------------------------------------------------------------------------
EuclideanQuotient := function ( f, g )
local   m,  n,  i,  k,  c,  q,  R,  val;
```
```# <f> and <g> must have the same field
if f.baseRing <> g.baseRing  then
Error( "<f> and <g> must have the same base ring" );
fi;
```

# and they must be ordinary polynomials
if f.valuation < 0 then
Error( "<f> must not be a laurent polynomial" );
fi;
if g.valuation < 0 then
Error( "<g> must not be a laurent polynomial" );
fi;
R := f.baseRing;

```# if <g> is zero signal an error
if 0 = Length(g.coefficients)  then
Error( "<g> must not be zero" );
fi;
```

# if <f> is zero return it
if 0 = Length(f.coefficients) then
return f;
fi;

# remove the valuation of <f> and <g>
f := ShiftedCoeffs( f.coefficients, f.valuation );
g := ShiftedCoeffs( g.coefficients, g.valuation );

```# Try to divide <f> by <g>
q := [];
n := Length(g);
m := Length(f) - n;
for i  in [ 0 .. m ]  do
c := f[m-i+n] / g[n];
for k  in [ 1 .. n ]  do
f[m-i+k] := f[m-i+k] - c * g[k];
od;
q[m-i+1] := c;
od;
```

# return the polynomial
return Polynomial( R, q, 0 );

```end;
-----------------------------------------------------------------------------
```

best wishes
Frank Celler

> < [top]