On Tue, Dec 05, 2006 at 09:29:06AM -0800, William Stein wrote: > You know, honestly, the problem of how to express do Calculus with > a computer algebra system is not exactly a new one. It's been > to some degree completely and totally solved by Mathematica. > Maybe the real discussion we should be having is how can we > make a basic interface to SAGE for doing calculus that is very similar > to mathematica's? Only if there is a strong technical reason why > something is not possible in Python, should we even be having these > discussions. Basically, before we continue going along the route > suggested by you and Robert, I would like a very good justification > for why Mathematica/Maple got it wrong (despite millions of users > and two decades of polishing and work). Otherwise, I don't understand > why we don't just do something similar to Mathematica. This reduces > the learning curve for some people a lot, and means we spend time > solving problems instead of coming up with a new design that is probably > wrong anyways, then spending a lot of time testing it, only to find > that it really doesn't work for various reasons.
William, thanks for your kind hint for me to be quiet a bit. I believe you are right that I should be so. After this e-mail and a few additions to the wiki, I will be quiet on this topic. However, I don't agree that the suggestion of using variables from the polynomial ring is doing what mathematica does. Some Examples: Exhibit 1: My understanding is that you want f(1) to be 1 in sage, but mathematica is not so. In[1]:= f=x Out[1]= x In[2]:= f(1) Out[2]= x Exhibit 2: Mathematica has a dummy variable. In[12]:= f[x_]:=Sin[x] In[13]:= f'[x] Out[13]= Cos[x] In[14]:= f'[y] Out[14]= Cos[y] Exhibit 3: Part of the expected second variable is the name of the independent variable. In[6]:= Plot[Sin[x]] Plot::argmu: Plot called with 1 argument; 2 or more arguments are expected. I apologize if I've made too much noise about all this, but I think that a clear concept of a dummy variable needs to be introduced. I have thought of no easy way to do that with-out a rather painful bit of preparsing. I definitely agree that the preparser should be avoided if possible. Currently, I see no evidence that we can have a real idea of dummy variables with-out pre-parser work. -- Joel --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
