On Thursday, January 16, 2014 10:45:31 AM UTC-8, John H Palmieri wrote: > > > > On Wednesday, January 15, 2014 2:17:10 PM UTC-8, rjf wrote: >> >> If the polynomial is multivariate, you need to specify the >> quotient/remainder "main variable". >> I don't see it in the syntax you give below. >> consider x+y divided by x-y. can give 1 with remainder 2y. >> It can also give -1 with remainder 2x. >> RJF >> >> PS, I think it is unfortunate if a user of Sage must know what is meant >> by a polynomial ring in order to >> do something from high school algebra. Just saying. >> > > Even if it's a univariate polynomial, the lcm, or the quotient and > remainder for that matter, depend on the ring in which you're working: is > it Z[x], Q[x], Q(x), etc.? So is it really unfortunate that someone has to > be mathematically precise to get a valid mathematical answer? I think that > some people may be taught in high school that a quadratic like x^2+1 has no > roots. > That would be sad.
> Is it unfortunate that someone has to know the difference between R and C > to "do something from high school algebra"? > lcm in early school grades is probably discussed only in the context of integers. Can we discuss lcm without mathematical precision? Not entirely. It depends on knowing that "least" has a meaning, and "common multiple" which has to do with factors. If you don't have unique factors and an ordering, you should not be asking for an lcm. What are the factors of 10? 2*5 . 10*1, how about 100 * (1/10)? how about x* (10/x) ? I think it is a mistake to require inessential math sophistication from users ( a mistake made by Axiom and perhaps Sage), but it is also a mistake to go too far in the other direction assuming the user is totally naive by default. There is a role for software for elementary mathematics education, showing "steps" etc. Such software could be built using computer algebra systems "under the covers" but would be largely distinct. See the web site calc101.com which does calculus homework showing steps. There are also programs for drilling and testing. > -- > John > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
