numerics - Is there a way to globally set when to treat a very small number as zero?

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 applying Chop automatically to all results; and

specify how large a number PossibleZeroQ should recognize as 0?

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.

Comments

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