Built-in Mathematica Symbol

IntegerPart

IntegerPart[x]
gives the integer part of x.

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

IntegerPart[x] in effect takes all digits to the left of the decimal point and drops the others.

IntegerPart[x]+FractionalPart[x] is always exactly x.

IntegerPart[x] returns an integer when x is any numeric quantity, whether or not it is an explicit number.

For exact numeric quantities, IntegerPart internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable $MaxExtraPrecision.

IntegerPart applies separately to real and imaginary parts of complex numbers.

IntegerPart automatically threads over lists.

EXAMPLES

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Basic Examples (1)

Find the integer part of a real number:

In[1]:=

Out[1]=

Scope (4)

Use exact numeric quantities:

IntegerPart threads element-wise over lists:

Manipulate IntegerPart symbolically:

Evaluate an integral:

Generalizations & Extensions (4)

Use with negative arguments:

Use with complex-number arguments:

IntegerPart can deal with real-valued intervals:

Infinite arguments give symbolic results:

Series expansion:

Applications (8)

Iso-curves become full-dimensional regions for piecewise constant functions:

Fibonacci numbers:

Implement a divide-and-conquer-type recursion relation:

Find the 1000000

digit of the fraction 1/99^2 in base 10:

Compare with RealDigits functionality:

Find the day of the week in the Gregorian calendar:

Birthday of Leonard Euler:

Compare with DateString:

Implement the Frisch continuous-but-nowhere-differentiable function:

Properties & Relations (5)

Simplify expressions containing IntegerPart:

Symbolically expand for complex arguments:

IntegerPart is idempotent:

Use PiecewiseExpand to canonicalize:

Reduce equations containing IntegerPart:

Possible Issues (3)

Numerical decision procedures with default settings cannot simplify this expression:

Use Simplify to resolve:

Machine-precision numericalization of IntegerPart can give wrong results:

Use arbitrary-precision evaluation instead:

Because the answer is exact, raising the internal precision does not remove the message:

Symbolic preprocessing of functions containing IntegerPart can be time-consuming:

As a discontinuous function, IntegerPart can cause numerical algorithms to converge slowly:

Neat Examples (1)

Build a nondecreasing sequence of integers where each number n occurs n times [more info]:

Generate the sequence up to 5:

Group the same numbers: