Re: How do I eliminate premultipliers of "1." ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg31189] Re: How do I eliminate premultipliers of "1." ?*From*: Mirek Gruszkiewicz <gruszkiewicz at ornl.gov>*Date*: Tue, 16 Oct 2001 01:19:20 -0400 (EDT)*Organization*: Oak Ridge National Lab, Oak Ridge, TN*References*: <9q8oeb$co$1@smc.vnet.net> <9qbi0g$2d4$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

How about this: b = 1.; c = 1.00000000000001; In[24]:= c == 1 Out[24]= True In[22]:= b - c == 0 Out[22]= False In[21]:= b - c Out[21]= -9.992007221626409`*^-15 In[27]:= b == c Out[27]= True Not only 1 and 1. will test equal but even 1 and 1.<13 zeros>1 will test equal. Numbers which give a nonzero difference when subtracted may test Equal ! It is not an outright error, not a bug, shouldn't even be surprising, since in this case it works as advertised in the Book. Equal is not the same as , say, .EQ. in Fortran. Equal is what WR, Inc. says it is. SameQ gives exact comparisons, c === 1., or 1.===1, even 0. === 0 False Still not the same as .EQ. in Fortran. Mirek Gruszkiewicz Alan Mason wrote: > Hello Brett. > You can get rid of them by applying a rule. > > In[9]:= > expr = 1.0 a > > Out[9]= > 1. a > > In[10]:= > expr2 = expr /. 1.0 u_:> u > > Out[10]= > a > > .. I agree with you, though. Mathematica 4.1 even claims that 1.0 == 1 is > True. > In[5]:= > 1.0 \[Equal] 1 > > Out[5]= > True > > I consider this an outright error. 1.0 means a floating-point approximation > to 1, whereas 1 is exactly 1 > > The correct way to treat 1.0/1.0 is somewhat ambiguous. Does 1.0 stand for > the same approximation at each appearance? If so, the ratio should be 1; > otherwise, it should be 1.0. > > Alan > > "Brett Patterson" <bap at roe.ac.uk> wrote in message > news:9q8oeb$co$1 at smc.vnet.net... > > Consider the following: > > > > In[1] := 1 a / 1 > > Out[1] := a > > > > In[2] := 1.0 a / 1.0 > > Out[2] := 1. a > > > > Now consider these identities: > > > > In[3] := (1 / 1) == 1 > > Out[3] := True > > > > In[4] := (1.0 / 1.0) == 1.0 > > Out[4] := True > > > > In[5] := (1 / 1) == 1.0 > > Out[5] := True > > > > In[6] := (1.0 / 1.0) == 1 > > Out[6] := True > > > > Given that it is clear mathematically that I want the > > answer to In[2] to evaluate to just "a", and given that > > Mathematica is clearly recognizing that 1.0 / 1.0 is the > > same as 1 / 1, can someone please tell me why Out[2] contains > > the premultiplier "1." and how to eliminate it in expressions > > that might contain this superfluous unit multiplier in various places. > > > > Thanks! > > > > Brett Patterson > > > > UK Astronomy Technology Centre > > The Royal Observatory > > Blackford Hill > > Edinburgh EH9 3HJ > > Scotland > >