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Re: [mg5061] Solve results
Posted:
Oct 30, 1996 12:14 AM


>At 02:48 AM 10/26/96 +0000, you wrote: >>I recently came upon this and was wondering if it's a Solve bug, some >>notation I'm not familiar with, or just an unfortunate happenstance. >> >>When I give Mathematica the equation x^38==0, this is what it returns: >> >>In[1]:= >>Out[1]= >> >>But if I first factor the polynomial instead: >> >>In[2]:= >>Out[2]= >> >>if I use reduce instead of solve >> >>In[3]:= >>Out[3]= >> >> >>My question is: why the different behaviors, and how can I tell in advance >>which to use? >> >>++ >>  I understand mine's a risky plan, >> Greg Anderson  and your system can't miss >> dwarf@wam.umd.edu  but is security, after all a cause >> timbwolf@eng.umd.edu  or symptom of happiness. >>  >>++ Dream Theater  A Matter of Time >> >> >Somehow the Mma input and output did not make it into your message. > >When I input Solve[x^3==8,x], I get the following answer > >{{x>2}, {x>2(1)^1/3},{x>2(1)^2/3} which is correct. > >Most people do not recognize the solution process when > >imaginary solutions are present. The 8 on the rhs of the > >equation is really 8*Exp[I*2*Pi]. The cube root of this > >expression is 2*Exp[I*0], 2*Exp[I*(2/3)*Pi], and 2*Exp[I*(4/3)*Pi]. > >Note that the 3rd power of each is 8*Exp[I*2*Pi]. Applying Euler's > >Formula (Exp[I*theta]=Cos[theta]+I*Sin[theta]) will give > >you the more conventional solution, which I suspect is the > >second example. The third example, is I believe just the > >rectangular version of the Solve solution. > >Very few Algebra courses cover the use of Euler's formula, > >which is a bridge between polar and rectangular, > >which is commonly used in Electrical Engineering for AC circuit > >theory problems and I suspect many other places. > >I have not seen Solve make a mistake, so I would place my > >trust on the initial results. Incidentally, one can always > >check the results from all three cases, with ease. > >Hope this helps. > >Sherman C. Reed > >



