Indeed, factoring saves time only when almost all of the factors can be canceled. Otherwise, the factors will just be multiplied back together – at great cost – to arrive back at nearly the original terms (magnitude wise), which then must be multiplied with each other to yield the final product.
For example, if we start with 12 and factor it into 2x2x3, do we win or lose if we can cancel only one term? Two BigInt multiplications (e.g., 2x3xN, where N is large) is probably more costly than the original single multiplication (12xN), which makes our factoring a net loss, even though 2x3=6 is smaller than 12. Simply put, when it comes to run time the number of multiplications is what matters most.
We probably win only when we can cancel all or all but one of the factors. Given that our numerators and denominators are often greatly unbalanced, how often will that happen? Our emprical results suggest not enough to be worthwhile. More likely, we will end up with one side of the dividing line plagued with little factors, like aphids on a rosebud, each sucking up an expensive multiplication.
Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
Read Where should I post X? if you're not absolutely sure you're posting in the right place.
Please read these before you post! —
Posts may use any of the Perl Monks Approved HTML tags:
You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
- a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
Link using PerlMonks shortcuts! What shortcuts can I use for linking?
See Writeup Formatting Tips and other pages linked from there for more info.
| & || & |
| < || < |
| > || > |
| [ || [ |
| ] || ] ||