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Question: Do I have this right then?

Question:Do I have this right then?

william budd 268 Maple
integer
June 02 2007
0
Using _EnvAllSolutions:=true; with solve(sin(x)=1,x)the answer returned is 1/2Pi+2Pi_Z1~. The Maple User Manual on page 82 says that Maple uses variables of the form _ZN~ to represent arbitrary integers thus my understanding is that the answer returned can be interpreted as 1/2Pi+2nPi where n is any integer. Correct? Now for the more difficult situation where I an not sure my understanding is correct. Using _EnvAllSolutions:=true; with solve(sin^2(x)/x,x)the answer returned is Pi(2_Z1~+_B1~). In this case, the -Z1~ is again any arbitrary integer but _B1~ is quite different. Using about(_B1~) the return tells me that _B1~ is assumed to be : OrProp(0,1). If I understand OrProp(0,1)correctly it is simply saying that _B1~ is 0 or 1 or both in which case, the solution (where n is any integer) is 2nPi or (2n+1)Pi or both, which is an even or odd number of Pi or both. Am I interpreting _B1~ correctly? If not, what is the correct meaning of _B1~? If I am correctly interpreting _B1~ Maple is not giving me a firm answer but an either or both situation which seems strange and is why I would like some feed back here. Thanks a lot.
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