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RationalQ

Status: Experimental

present and registered, but lightly documented and not yet covered by dedicated tests.

Description

RationalQ[expr]

gives True if expr is an exact rational number, False otherwise.

Rational[p, q]. Returns False on reals and on symbolic expressions.

Notes True for an Integer or BigInt (an integer is rational) and for a

Examples (4)

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

Applications (4)

An exact Rational[3, 4]

In[1]:= RationalQ[3/4]
Out[1]= True

An integer is rational

In[2]:= RationalQ[7]
Out[2]= True

A machine real is not, even with a rational value

In[3]:= RationalQ[2.5]
Out[3]= False

An irrational constant is not rational

In[4]:= RationalQ[Pi]
Out[4]= False

Implementation notes

Algorithm. builtin_rationalq returns True when its one argument is an exact rational number. That is exactly two cases, tested directly: the argument is integer-like (expr_is_integer_like ā€” an EXPR_INTEGER or a GMP EXPR_BIGINT, since every integer is rational) or it has head Rational (core_head_is(arg, SYM_Rational), a Rational[p, q]). Otherwise False.

Data structures. None beyond the argument. Two cheap tests ā€” a type tag check and an interned-pointer head comparison ā€” then a fresh True/False symbol.

Complexity / limits. O(1). Reals and MPFR numbers are not rational here (2.5 is False) even when they have an exact rational value, because the test is on representation; an irrational constant such as Pi, and any non-numeric expression, is False. A call that is not single-argument declines and stays symbolic.

Attributes: Protected.

References

Notes & additional examples

Notes

RationalQ[expr] is True for exactly the exact rationals: any integer (Integer or big BigInt) and any Rational[p, q]. It is a representation test, so reals and MPFR numbers are False regardless of their value, and irrational constants and symbolic expressions are False as well. Non-single-argument calls are left unevaluated.