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Changed order of multiplication in Times[a, b, c] in version 6?!
*To*: mathgroup at smc.vnet.net
*Subject*: [mg77568] Changed order of multiplication in Times[a, b, c] in version 6?!
*From*: Andrew Moylan <andrew.j.moylan at gmail.com>
*Date*: Wed, 13 Jun 2007 07:27:20 -0400 (EDT)
I think the order in which the pairwise multiplication in Times[a, b,
c] has changed between version 5.2 and version 6! Can anyone comment
on this?
Example:
Here are three exact numbers whose product is Sqrt[-1]:
Times[(1 + I)*10^2000, (1 + I)*1/2*10^-2000, 1]
Here are those numbers in approximate form, labelled a, b, and c:
{a, b, c} =
{
1.`15.954589770191005*^2000*(1 + I),
5.`15.954589770191005*^-2001*(1 + I),
1. + 0.*I
};
Here are their various pairwise products:
Inputting:
{
a*b,
b*c,
a*c
}
yields the output:
{
0``15.653559774527023 + 1.`15.653559774527023*I,
0. + 0.*I,
1.`15.954589770191005*^2000 + 1.`15.954589770191005*^2000*I
}
So far, all these results are identical between versions 5.2 and 6.
Now consider a*b*c. Here is what is given version 5.2:
0``15.653559774526984 + 1.`15.653559774526984*I
This happens to be the right answer, because it has done the
multiplication in the order (a*b)*c.
Here is what is given for a*b*c in version 6:
0. + 0.*I
This happens to be the wrong answer, because it has done the
multiplication in the order a*(b*c).
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