Chop

Replaces a real number very close to 0 with exact 0.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageChop!↗

Chop(x)0 if $|x|$ is smaller than about $10^{-10}$, else x unchanged.

Chop(x, tolerance)0 if $|x|$ is smaller than tolerance, else x unchanged.

Typed signatures

Type	Package	Applies
(T) -> T where T: number	compute-engine	always
(any, number?) -> any	combinatoricsreplaces compute-engine	always

Domain: Arithmetic

Details

• Replaces a value smaller in magnitude than about $10^{-10}$ with exact 0 -- cleanup for the floating-point noise left over from a numeric computation.
• Chops the real and imaginary parts of a complex number independently.
• Only the value's own magnitude matters -- $\mathrm{Chop}(1.000000000001)$ stays as is, since it isn't close to 0, even though it's close to the integer 1.
• A second argument overrides the default $10^{-10}$ threshold.

Examples

3 more kept as data, checked against the oracles

Basic #

Values not near zero pass through unchanged

live ↗

In$\mathrm{chop}(1.2)$Out$1.2$

Values smaller than about $10^{-10}$ collapse to exactly 0

live ↗

In$\mathrm{chop}(1.0\cdot10^{-11})$Out$0.0$

Negative values chop the same way

live ↗

In$\mathrm{chop}(-1.0\cdot10^{-11})$Out$0.0$

Chops the real and imaginary parts independently

live ↗

In$\mathrm{chop}(1.0\cdot10^{-12}+3i)$Out$3.0i$

Scope #

Threads element-wise over a list

live ↗

In$\mathrm{chop}(\bigl\lbrack1.2, 1.0\cdot10^{-11}, 3.5\bigr\rbrack)$Out$\bigl\lbrack1.2, 0.0, 3.5\bigr\rbrack$

A negligible imaginary part is dropped, leaving a real number

live ↗

In$\mathrm{chop}(1+1.0\cdot10^{-14}i)$Out$1.0$

Stays symbolic

live ↗

In$\mathrm{chop}(x)$Out$\mathrm{chop}(x)$

Exact numbers not near zero pass through

live ↗

In$\mathrm{chop}(\frac{1}{3})$Out$\frac{1}{3}$

A second argument sets the tolerance, here chopping anything below 0.01

live ↗

In$\mathrm{chop}(0.001, 0.01)$Out$0$

...and a tighter tolerance keeps a value the default would chop

live ↗

In$\mathrm{chop}(1.0\cdot10^{-15}, 1.0\cdot10^{-20})$Out$1.0\cdot10^{-15}$

Applications #

Cleans up the floating-point residue from computing $3\times(1/3)-1$ numerically

live ↗

In$\mathrm{chop}(3N(\frac{1}{3})-1)$Out$0.0$

Possible issues #

Only the value's own magnitude matters -- this stays as is since it isn't close to 0, even though it's close to the integer 1

live ↗

In$\mathrm{chop}(1+1.0\cdot10^{-12})$Out$1.000\,000\,000\,001$

A hard cutoff at about $10^{-10}$: a value just above the threshold survives untouched

live ↗

In$\mathrm{chop}(1.000\,000\,000\,1\cdot10^{-10})$Out$1.000\,000\,000\,1\cdot10^{-10}$

An exact small number is chopped too

live ↗

In$\mathrm{chop}(10^{-20})$Out$0$

A negligible imaginary part is dropped

live ↗

In$\mathrm{chop}(2+i×10^{-12})$Out$2$

About

Examples	18
Checked against	Wolfram Language 17 agree1 differ
Crosswalk	Wolfram Language

See also: Round