I understand that I can use Chop to force a very small number to be treated as 0 and can use PossibleZeroQ to as a way to test whether such a number might effectively be 0, but applying Chop every time a small number is close to zero in order to "make it be" zero is tedious and error prone; while PossibleZeroQ seems to have its own ideas about what constitutes 0.
Are there global settings that will let me
- treat every number smaller than some specified value as
0, effectively applyingChopautomatically to all results; and - specify how large a number
PossibleZeroQshould recognize as0?
Answer
As was pointed out in the comments, $Post is a way to go here. Take as an example:
FourierDCT[FourierDCT[{0, 0, 1, 0, 0}, 2], 3]
(*{0., -5.55112*10^-17, 1., 1.38778*10^-17, 1.38778*10^-17}*)
Now lets set $Post to Chop with tolerance 10^-13.
$Post = Chop[#, 10^-13] &;
This will apply the Chop function to every output thereafter.
FourierDCT[FourierDCT[{0, 0, 1, 0, 0}, 2], 3]
(*{0, 0, 1., 0, 0}*)
If you want to make this behavior semi-permanent, you can set $Post in any one of your init.m files. A good choice might be the one located at
$InstallationDirectory <> "\\SystemFiles\\Kernel\\Packages\\init.m"
If you do this and want to not Chop for a particular output you can always clear $Post or remove this from init.m and restart the kernel.
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