<div dir="ltr"><div class="markdown-here-wrapper" style="font-size:1em;font-family:Helvetica,arial,freesans,clean,sans-serif;color:rgb(34,34,34);background-color:rgb(255,255,255);border:none;line-height:1.2"><blockquote style="margin:1em 0px;border-left:4px solid rgb(221,221,221);padding:0px 1em;color:rgb(119,119,119);quotes:none">
<p style="margin:1em 0px"> “the intuitive way” is the decreasing powers.</p>
</blockquote>
<p style="margin:1em 0px">An argument against this is that accessing the ith power of x is spelt:</p>
<ul style="padding-left:2em;margin:1em 0px">
<li style="margin:1em 0px"><code style="font-size:0.85em;font-family:Consolas,Inconsolata,Courier,monospace;margin:0px 0.15em;padding:0px 0.3em;white-space:nowrap;border:1px solid rgb(234,234,234);background-color:rgb(248,248,248);border-radius:3px;display:inline">x.coeffs[i]</code> for increasing powers</li>
<li style="margin:1em 0px"><code style="font-size:0.85em;font-family:Consolas,Inconsolata,Courier,monospace;margin:0px 0.15em;padding:0px 0.3em;white-space:nowrap;border:1px solid rgb(234,234,234);background-color:rgb(248,248,248);border-radius:3px;display:inline">x.coeffs[-i-1]</code> for decreasing powers</li>
</ul>
<p style="margin:1em 0px">The former is far more natural than the latter, and avoids a potential off-by-one error</p>
<blockquote style="margin:1em 0px;border-left:4px solid rgb(221,221,221);padding:0px 1em;color:rgb(119,119,119);quotes:none">
<p style="margin:1em 0px"> If I ask someone to write down the coefficients of a polynomial I don’t think anyone would start from c[2]</p>
</blockquote>
<p style="margin:1em 0px">You wouldn’t? I’d expect to see</p>
<p style="margin:1em 0px"><img src="https://latex.codecogs.com/svg.latex?f(x)%20%3D%20a_3x%5E3%20%2B%20a_2x%5E2%20%2B%20a_1x%20%2B%20a_0" alt="f(x) = a_3x^3 + a_2x^2 + a_1x + a_0"></p>
<p style="margin:1em 0px">rather than</p>
<p style="margin:1em 0px"><img src="https://latex.codecogs.com/svg.latex?f(x)%20%3D%20a_0x%5E3%20%2B%20a_1x%5E2%20%2B%20a_2x%20%2B%20a_3" alt="f(x) = a_0x^3 + a_1x^2 + a_2x + a_3"></p>
<p style="margin:1em 0px">Sure, I’d write it starting with the highest power, but I’d still number my coefficients to match the powers.</p><p style="margin:1em 0px"><br></p><p style="margin:1em 0px">Eric</p>
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