Hm, since we wanted to get away from implicit functions, the consistent think to do would be to always require the base when a user wants to use the log function. I think that this could avoid some confusion. In every CAS, I have to check in the documentation what the program means by log(x). In sage I had to read through the whole doc string and get to the examples before I was able to deduce that log(x) is the natural log of x:
Type: function Base Class: <type 'function'> String Form: <function log at 0xf5f4df0> Namespace: Interactive Definition: log(x, base=None) Docstring: Return the logarithm of x to the given base. Calls the ``log`` method of the object x when computing the logarithm, thus allowing use of logarithm on any object containing a ``log`` method. In other words, log works on more than just real numbers. TODO: Add p-adic log example. EXAMPLES:: sage: log(e^2) 2 sage: log(1024, 2); RDF(log(1024, 2)) 10 I think that the doc string should say that log(x) = log(x,e) right at the beginning. Stan William Stein wrote: > On Sun, Aug 23, 2009 at 2:54 PM, William Stein<wst...@gmail.com> wrote: > >> On Sun, Aug 23, 2009 at 2:35 PM, Tim Lahey <tim.la...@gmail.com> wrote: >> >>> On Aug 23, 2009, at 5:25 PM, William Stein wrote: >>> >>> >>>> So since Tim's from Waterloo that might explain his preference for ln. >>>> >>> I preferred ln(x) well before I learned Maple. Plus, all my textbooks >>> used >>> ln(x). >>> > > OK, Wikipedia has a pretty useful discussion. It mentions 'As > recently as 1984, Paul Halmos in his "automathography" I Want to Be a > Mathematician heaped contempt on what he considered the childish "ln" > notation, which he said no mathematician had ever used.' I read that > book, so maybe that is one reason I don't like "ln". The Wikipedia > page also says: > > "If, as in "log(x)", the base is not given explicitly, it may be > understood implicitly by discipline: > > * Mathematicians understand "log(x)" to mean log_e(x). Calculus > textbooks will occasionally write "log(x)" to represent "log_10(x)". > > * Many engineers, biologists, astronomers, and some others write > only "ln(x)" or "log_e(x)" when they mean the natural logarithm of x, > and take "log(x)" to mean log_10(x) or, in computer science, log2(x). > > * In most commonly used computer programming languages, including C, > C++, Java, Haskell, Fortran, Python, Ruby, and BASIC, the "log" > function returns the natural logarithm. The base-10 function, if it is > available, is generally "log10." > > This chaos, historically, originates from the fact that the natural > logarithm has nice mathematical properties (such as its derivative > being 1/x, and having a simple definition), while the base 10 > logarithms, or decimal logarithms, were more convenient for speeding > calculations (back when they were used for that purpose)." > > > > > --- > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---