On Tue, May 13, 2008 at 3:51 PM, Zach wrote: > Please excuse me, I am really quite new to Axiom and much of > abstract algebra terminology.
Welcome. > I hope this is the right place for these questions. If not, > could someone point me in the right direction. Yes, it is a good place to ask such questions. > I am currently reading the Axiom tome, er.. book, but it is good > to have a human to bounce ideas off of. Another useful place might be: http://axiom-wiki.newsynthesis.org > > Here is a really simple example, we have real number `a' and > vectors `v1' and `v2'. Given: > > a*v1=v2 > > solve(a*v1=v2) > ==> [a = v2/v1] > > I would like to solve for a. If I put this in, Axiom assumes v1 and v2 to > be things that have a defined division (a field I guess). But really we > have no division by a vector (a ring, perhaps?), You have the right general idea. > so what I would like is for axiom to solve this by > > a * v1 . v1 = v2 . v1 > a = (v2 . v1) / (v1 . v1) > ??? This is not a solution to the original equation! > I assume that I do this by giving Axiom some type information, > like specifying v1 and v2 as Vector (or Matrix) Fraction Integer > or something. Well no, not really. Currently Axiom has no domain for symbolic computations with vectors. Specifying v1:Vector Fraction Integer does not allow symbolic computations with the symbol 'v1', instead it declares that the *type* of the variable 'v1' is 'Vector Fraction Integer'. From this declaration Axiom expects 'v1' to eventually be given a value, e.g. v1::= [1/2, 1/3, 1/4] Axiom does have other domains like Polynomial which includes symbolic variables. > What is the best way of tackling these types of problems? > It would be possible (and quite interesting) to create a new domain in Axiom for symbolic vector calculations. Regards, Bill Page. _______________________________________________ Axiom-math mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-math
