9.8: Discussion
Yolanda took a sip of coffee “I'm glad I paid attention when we were studying vector spaces, bases, and dimension. All this stuff about solutions for recurrence equations made complete sense. And I can really understand why the professor was making a big deal out of factoring. We saw it our first semester when we were learning about partial fractions in calculus. And we saw it again with the differential equations stuff. Isn't it really neat to see how it all fits together?” All this enthusiasm was too much for Alice who was not having a good day. Bob was more sympathetic, saying “Except for the detail about zero as a root of an advancement operator polynomial, I was ok with this chapter.” Xing said “Here we learned a precise approach that depended only on factoring. I've been reading on the web and I see that there have been some recent breakthroughs on factoring.” Bob jumped back in “But even if you can factor like crazy, if you have a large degree polynomial in the advancement operator equation, then you will have lots of initial conditions. This might be a second major hurdle.” Dave mumbled “Just do the factoring. The rest is easy.” Carlos again was quiet but he knew that Dave was right. Solving big systems of linear equations is relatively easy. The challenge is in the factoring stage.