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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="InftyQuotRem"></a>
InftyQuotRem
</h2>

Computes quotient and remainder with respect to the degree
valuation.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := InftyQuotRem(a, b);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>of q and r</td>
</tr>
<tr>
<td>quotient field elements</td>
<td><pre>  a,b  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#InftyVal">InftyVal</a>, <a href="kashref.html#InftyGcd">InftyGcd</a>, <a href="kashref.html#InftyLcm">InftyLcm</a>

<p>

<h3>
Description:
</h3>
Let a, b \in FF_q(x). The function computes q, r \in FF_q(x)
such that a = qb + r and \nu_\infty(q)  &gt;=  0.
The rest r is chosen such that
r = \sum_{i=\nu_\infty(a)}^{\nu_\infty(b)-1} c_i x^{-i}
and c_i \in FF_q. By these conditions q, r are
uniquely determined.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>

<pre>

kash> k := FF(5, 2);
Finite field of size 5^2
kash> kx := PolyAlg(k);
Univariate Polynomial Ring in x over GF(5^2)

kash> x := Poly(kx, [1,0]);
x
kash> a := x + 2 + 3/x + 4/x^2;
(x^3 + 2*x^2 + 3*x + 4)/x^2
kash> InftyQuotRem(a, x);
[ (x^3 + 2*x^2 + 3*x + 4)/x^3, 0 ]
kash> InftyQuotRem(a, x/x);
[ (2*x^2 + 3*x + 4)/x^2, x ]
kash> InftyQuotRem(a, 1/x);
[ (3*x + 4)/x, x + 2 ]
kash> InftyQuotRem(a, 1/x^2);
[ 4, (x^2 + 2*x + 3)/x ]
kash> InftyQuotRem(a, 1/x^3);
[ 0, (x^3 + 2*x^2 + 3*x + 4)/x^2 ]

</pre>

<p>


<hr>

<p>
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