IntegerQ¶

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description¶

IntegerQ[expr]

gives True if expr is an Integer or BigInt, False otherwise.

Notes

Returns False on rationals with denominator \> 1, reals, and symbolic expressions (even those that are integer-valued, e.g. 2 Pi / Pi).

Examples (14)¶

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (4)¶

In[1]:= StringQ["AbC"]
Out[1]= True

In[2]:= StringQ[""]
Out[2]= True

In[3]:= StringQ[123]
Out[3]= False

In[4]:= StringQ[] StringQ::argx: StringQ called with 0 arguments; 1 argument is expected.

Scope (6)¶

In[5]:= MachineNumberQ[Sin[1000.]]
Out[5]= True

Overflows to +inf

In[6]:= MachineNumberQ[Exp[1000.]]
Out[6]= False

In[7]:= MachineNumberQ[-29037945.290347]
Out[7]= True

MPFR, not machine

In[8]:= MachineNumberQ[N[Pi, 30]]
Out[8]= False

In[9]:= MachineNumberQ[1.0 + 2.0 I]
Out[9]= True

Exact Gaussian integer

In[10]:= MachineNumberQ[1 + 2 I]
Out[10]= False

Applications (4)¶

An exact integer

In[11]:= IntegerQ[5]
Out[11]= True

A Real is not an integer, even at an integral value

In[12]:= IntegerQ[5.0]
Out[12]= False

A Rational is not an integer

In[13]:= IntegerQ[1/2]
Out[13]= False

A symbol is not known to be one, so False

In[14]:= IntegerQ[x]
Out[14]= False

Implementation notes¶

builtin_integerq (src/core.c) returns True exactly when expr_is_integer_like(arg) holds (an EXPR_INTEGER or EXPR_BIGINT), and False otherwise.

Attributes: Protected.

References¶

See also: AtomQ, NumberQ, StringQ, MachineNumberQ, Complex, ExactNumberQ

Source: src/core.c
Specification: docs/spec/builtins/expression-information.md
Tests: tests/test_bigint.c
Tests: tests/test_core.c
Tests: tests/test_divisible.c
Tests: tests/test_meminfo.c

Notes & additional examples¶

Notes¶

IntegerQ[e] is True exactly when e is an exact integer — a machine Integer or an arbitrary-precision bigint — and False for everything else, including reals at integral values, rationals, and symbols. Like the other *Q predicates it always returns a boolean; it never stays unevaluated.

Use it to test exactness: IntegerQ[5.0] is False because 5.0 is a machine real, not an integer.