roman_pearce

Mr. Roman Pearce

1688 Reputation

19 Badges

20 years, 75 days
CECM/SFU
Research Associate
Abbotsford, British Columbia, Canada

I am a research associate at Simon Fraser University and a member of the Computer Algebra Group at the CECM.

MaplePrimes Activity


These are replies submitted by roman_pearce

Maple doesn't have the algorithms to cope with this type of system. It is positive dimensional (HilbertDimension=3) and not easy to factor or eliminate variables. You can compute a graded reverse lex Groebner basis using FGb, but little else. I suggest you try the Singular computer algebra system.
Sorry I missed that. Yeah, you need a new computer. Let us know how it goes.
The CPU will run Maple twice as fast, but I'm not sure if that's a good reason to upgrade. It sounds like your current machine has decent specs, and what you're describing sounds like software problems. I would try backing up files and reinstalling Windows from scratch before replacing the whole machine. Then be careful about what software you install. You might be surprised at how fast it becomes. If you want a new machine, the Core i7 is the best thing out there for the foreseeable future.
The Core i7 is definitely a very fast cpu for running Maple. We have one in our lab. It could easily be twice as fast as the older AMD chip. However Maple 13 doesn't use parallel algorithms, so you're not going to see much of a boost from quad cores currently. I would stick with the older machine just because it has plenty of RAM, but the i7's are really nice.
I don't like using heuristics to solve problems, I think we put far too much effort into them. They made sense when computers were 10000 times slower, when computer algebra was in its infancy. Now I think it needs to be a technology, where the time required to solve something is predictable and the methods are robust. i.e. the user should be able to hit enter and have complete confidence that the fastest possible methods are being used, with the time required proportional to some number of bits.
It's also not a good idea to waste the user's cpu time, or likewise to assume that cpu cores will be sitting idle even if they currently often are. The reality is that only one method wins the race so the time spent running the other methods is wasted. Parallelism should not be taken as an excuse to make a program n times less efficient. In fact, doing so could be tragic if we are facing a future with more but slower cores.
It depends on the implementation, but theoretically F5 is the better algorithm.
It depends on the implementation, but theoretically F5 is the better algorithm.
You can choose any subset of the syzygies. For graded orders Faugere suggests choosing all the syzygies of lowest total degree. For general orders you should choose syzygies with the smallest monomials. However, you don't have to take all those syzygies. If you have a really fast C routine mod p then it makes sense. But if you're working over a coefficient domain with blowup then it may be better to choose only a subset of those syzygies that are small, and hope that the biggest ones can be eliminated by criteria later or reduced more efficiently with a more complete basis.
You can choose any subset of the syzygies. For graded orders Faugere suggests choosing all the syzygies of lowest total degree. For general orders you should choose syzygies with the smallest monomials. However, you don't have to take all those syzygies. If you have a really fast C routine mod p then it makes sense. But if you're working over a coefficient domain with blowup then it may be better to choose only a subset of those syzygies that are small, and hope that the biggest ones can be eliminated by criteria later or reduced more efficiently with a more complete basis.
Here are slides from an old talk I gave. This is how I implemented it in Maple. http://www.cecm.sfu.ca/~rpearcea/maplef4.pdf I find it helps immensely to write out the steps of the algorithm by hand, and consider that a computer must do the same things that you do. It will start you down the road to optimizing and ultimately designing your own methods. Good luck.
Here are slides from an old talk I gave. This is how I implemented it in Maple. http://www.cecm.sfu.ca/~rpearcea/maplef4.pdf I find it helps immensely to write out the steps of the algorithm by hand, and consider that a computer must do the same things that you do. It will start you down the road to optimizing and ultimately designing your own methods. Good luck.
It does indeed return the integer gcd.
It does indeed return the integer gcd.
You should be able to edit the post to fix it. There's an edit button at the bottom.
First 11 12 13 14 15 16 17 Last Page 13 of 39