IntegerPart
IntegerPart[x]
gives the integer part of x.
Details
- 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
open all close allBasic Examples (3)
Scope (28)
Numerical Evaluation (6)
Evaluate efficiently at high precision:
IntegerPart threads elementwise over lists:
IntegerPart can deal with real‐valued intervals:
Compute average-case statistical intervals using Around:
Specific Values (6)
Values of IntegerPart at fixed points:
Value at Infinity:
Manipulate IntegerPart symbolically:
Find a value of x for which the IntegerPart[x]=1:
Visualization (4)
Plot the IntegerPart function:
Plot scaled IntegerPart functions:
Plot IntegerPart in three dimensions:
Visualize IntegerPart in the complex plane:
Function Properties (9)
IntegerPart is defined for all real and complex inputs:
IntegerPart can produce infinitely large and small results:
IntegerPart is an odd function:
IntegerPart is not an analytic function:
It has both singularities and discontinuities:
IntegerPart is nondecreasing:
IntegerPart is not injective:
IntegerPart is not surjective:
IntegerPart is neither non-negative nor non-positive:
IntegerPart is neither convex nor concave:
Differentiation and Integration (3)
Applications (9)
Iso-curves become full‐dimensional regions for piecewise constant functions:
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:
Compare with DateString:
Implement the Frisch continuous-but-nowhere-differentiable function:
Consider the IntegerPart of the earthquake magnitudes recorded in the US from 1935 to 1989:
The integer parts of the magnitudes recorded on a Richter scale can be modeled with a ParetoDistribution:
Compare the histogram of the magnitudes with the fitted distribution:
Find the probability of an earthquake with magnitude at least 6 on the Richter scale:
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 
occurs 
times [more info]:
Text
Wolfram Research (1996), IntegerPart, Wolfram Language function, https://reference.wolfram.com/language/ref/IntegerPart.html.
CMS
Wolfram Language. 1996. "IntegerPart." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/IntegerPart.html.
APA
Wolfram Language. (1996). IntegerPart. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/IntegerPart.html