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Sign

Status: Stable

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

Description

Sign[x] gives -1, 0, or 1 for real numeric x according to its sign, and z/Abs[z] for a nonzero numeric complex z.

Examples

No verified examples yet for this function.

Implementation notes

builtin_sign returns the sign (-1/0/1) of a real number — direct comparisons for EXPR_INTEGER/EXPR_REAL (and Rational by sign of numerator×denominator), mpz_sgn for BigInt, mpfr_sgn for MPFR. For a numeric Complex[re, im] with both parts numeric it returns the unit-modulus direction z/Abs[z] (short-circuiting 0+0I -> 0); MPFR components take a fast path computing the direction directly via mpfr_hypot and division at the combined working precision rather than building the symbolic z·Power[Abs[z], -1] tree. Non-numeric arguments return NULL (unevaluated).

Attributes: Listable, NumericFunction, Protected.

Implementation status

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

References

Notes & additional examples

Worked examples

In[1]:= Sign[-7]
Out[1]= -1

In[2]:= Sign[0]
Out[2]= 0

In[3]:= Sign[{-2, 0, 5}]
Out[3]= {-1, 0, 1}

In[1]:= Sign[3 + 4 I]
Out[1]= 3/5 + 4/5*I

In[1]:= Sign[(1 + I)^2]
Out[1]= I

In[2]:= Sign[2 - 2 I]
Out[2]= (1/2 - 1/2*I) Sqrt[2]

Notes

For real x, Sign[x] is -1, 0, or 1. For a nonzero complex z it returns the unit-modulus direction z/Abs[z]: (1+I)^2 = 2I points straight up the imaginary axis (I), while 2 - 2I lies on the diagonal and returns the exact unit vector (1 - I)/Sqrt[2]. Sign is Listable.