Regarding pre-defined variables and rings for using SAGE to teach calculus, I'd like us to keep one thing in mind. Busy students, at all levels of intelligence, are extremely good at doing one type of calculation: how long with it take to do a given task. The average student is not computer-savvy and so we must be sensitive to these easily-frustrated students.
There are two sides: (1) those for predefining variables and rings (2) those against predefining variables and rings. I've presented a compomise (in order to predefine variables and rings, you have to enter a command such as "load_calculus"). (1) is probably the simplest solution but whatever works easily for the student user is fine with me. William Stein wrote: > On Mon, 04 Dec 2006 04:52:02 -0800, Joel B. Mohler > <[EMAIL PROTECTED]> wrote: > > >> On Sunday 03 December 2006 10:23, William Stein wrote: >> >>>> If the predefined indeterminate belongs to a ring, which ring is it? >>>> >>> Very likely it would just be ZZ[a,b,c,d...,z, A,B,C,...,Z]. >>> Alternatively, >>> they could be "formal indeterminates" that don't belong to some "formal >>> >>> ring", >>> but that's less easy to think about. >>> >> What if you want to differentiate f(x)=x^x. This is senseless in a >> polynomial >> ring. >> > > > This is the same as saying that "1/2" is senseless if 1 and 2 > are integers. > > This is not a problem. That the expression x^x does not define an element > of the polynomial ring, is not a problem. > Exponentiation of an element of the polynomial ring to the power > of a non-integer would be a constructor for some other sort of object, > namely a function in some general function space. > > > William > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
