
Re: An independent integration test suite
Posted:
Jul 24, 2013 3:14 AM


On 7/24/2013 1:25 AM, daly@axiomdeveloper.org wrote: > On Wednesday, July 24, 2013 1:21:51 AM UTC4, Albert Rich wrote: >> On Tuesday, July 23, 2013 2:32:20 PM UTC10, da...@axiomdeveloper.org wrote: >> >> >> >>> We differ on some results because Rubi (or whatever program you are using >> >>> to create the optimal results) assumes that square roots have only a single >> >>> positive value. Axiom does not want to make this simplification so given >> >>> sqrt(3)*sqrt(7)*sqrt(21)  21 >> >>> Axiom will not simplify this to zero but the Rubi test suite does. >> >> >> >> Surly there must be a way to tell Axiom to choose the principal branch so sqrt(4)2 will simplify to zero? >> >> >> >> Albert > > Actually, as you can guess, the real results are more complicated. > Given > > (sqrt(b^2*x^24)sqrt(b*x2)*sqrt(b*x+2))/ > (sqrt(b*x2)*sqrt(b*x+2)*sqrt(b^2*x^24)) > > under what conditions is this identically zero? > > If I extract the numerator and ask if it zero? > Axiom replies false. Is there an algorithm to show > that this is identically zero? I'd be happy to > implement it. I reread a paper on the subject and > now I'm more confused than when I started. > > Tim >
hello Tim;
This is in M 9.01: For domain Reals, Mathematica gives conditions for zero
 Clear[x, b]; num = (Sqrt[b^2*x^2  4]  Sqrt[b*x  2]*Sqrt[b*x + 2]); den = Sqrt[b*x  2]*Sqrt[b*x + 2]*Sqrt[b^2*x^2  4]; Reduce[(num/den) == 0, {x, b}, Reals] 
(x < 0 && b < 2/x)  (x > 0 && b > 2/x)
But in Complex domain, it gives warnings due to branch cuts, so not possible to decide on conditions for sure in this case:
 Clear[x, b]; num = (Sqrt[b^2*x^2  4]  Sqrt[b*x  2]*Sqrt[b*x + 2]); den = Sqrt[b*x  2]*Sqrt[b*x + 2]*Sqrt[b^2*x^2  4]; Reduce[(num/den) == 0, {x, b}, Complexes] 
 During evaluation of In[29]:= Reduce::useq: The answer found by Reduce contains unsolved equation(s) {0==(Sqrt[2+Times[<<2>>]] Sqrt[2+Times[<<2>>]]+Sqrt[4+Power[<<2>>] Power[<<2>>]])/Sqrt[2+b x]}. A likely reason for this is that the solution set depends on branch cuts of Mathematica functions. >>
Out[32]= Sqrt[2 + b x] != 0 && 0 == (Sqrt[2 + b x] Sqrt[2 + b x] + Sqrt[4 + b^2 x^2])/Sqrt[2 + b x] && 2 + b x != 0 
But if one wants one instance which makes num/den = 0, then there is a command for that:
FindInstance[(num/den) == 0, {x, b}, Complexes] {{x > 0, b > 0}}
Nasser

