For lack of knowlege of a better place to report these things, here is a bug appearing in Maple versions 3, 4, 5, 5.1 and 6.
> algsubs(x=y, 1/x ); 1/x The correct output should be 1/y.
The bug affects expressions containing operands of the form x^k for negative integers
k.
I have traced it to the following line in ‘algsubs/expanded‘, which causes it to falsely assert
that x^k (k<0) is already in "expanded form":
> `algsubs/expanded`(1/x,[x]); true > print(`algsubs/expanded`); proc(f, vars) ... elif type(f, `^`) then evalb(not (has(op(1, f), vars) and type(op(1, f), `+`))) ...
It is easy but annoying to fix this problem. Does WaterlooMaple make available a patch file of elementary bug fixes such as this? ("elementary" = bugs not associated with the kernel). One could then simply tack it into the .mapleinit file and, VOILA, no need to wait until the next release version... I found not even a report of known bugs at www.maplesoft.com! Could someone please advise me of existing repositories?
But the online documentation for algsubs (in Maple 5 at least) states specifically:
Note that the requirement for monomials in a to divide monomials in f means that the negative powers of u in the following example are not substituted, and must be handled separately as shown.
> f := a/u^4+b/u^2+c+d*u^2+e*u^4; a b 2 4 f := ---- + ---- + c + d u + e u 4 2 u u > algsubs(u^2=v,f); 2 b a d v + c + e v + ---- + ---- 2 4 u u > algsubs(1/u^2=1/v,f); 2 4 2 a + v b + c v e u + d u + -------------- 2 v
Hence, to substitute for both positive and negative powers
> algsubs(u^2=v,algsubs(1/u^2=1/v,f)); 4 3 2 e v + d v + a + v b + c v ---------------------------- 2 v
Well, you may do the following:
> restart; > seq(algsubs(1/x=1/y,1/x^k),k=1..10); 1 1 1 1 1 1 1 1 1 1/y, ----, ----, ----, ----, ----, ----, ----, ----, --- 2 3 4 5 6 7 8 9 10 y y y y y y y y y > seq(algsubs(1/x=1/y,x^(-k)),k=1..10); 1 1 1 1 1 1 1 1 1 1/y, ----, ----, ----, ----, ----, ----, ----, ----, --- 2 3 4 5 6 7 8 9 10 y y y y y y y y y