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Mathematica > Mathematics and Algorithms > Mathematical Functions > Numerical Functions > Chop >

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Chop

Chop[expr]
replaces approximate real numbers in expr that are close to zero by the exact integer

Zero out elements that are very close to 0:

Out[1]=

Out[2]=

Drop small imaginary parts:

Convert from approximate zeros to exact zeros:

Test if two numbers are the same to a certain tolerance:

They are the same to the default tolerance of

They are not the same to the tolerance of

Eliminate very small terms before comparing with Equal:

They are not equal because a small number is not equal to zero:

Once the small terms are eliminated, equality holds:

A functional implementation of Chop:

Chop is much faster for large expressions:

Machine complex numbers have machine reals for both real and imaginary parts:

Consequently, Chop does not make the real part of machine complex numbers an exact zero:

Small imaginary parts from machine complex numbers are eliminated to make a machine real: