Re¶

Status: Stable

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

Description¶

Re[z] gives the real part of numeric z; Re[Re[z]], Re[Im[z]], Re[Abs[z]], Re[Arg[z]] fold since those heads are real-valued.

Examples¶

No verified examples yet for this function.

Implementation notes¶

builtin_re returns the real part. It returns the argument itself for real numeric kinds (EXPR_INTEGER/EXPR_REAL/EXPR_MPFR/Rational) and for real-valued head calls (Re/Im/Abs/Arg, via is_real_valued_head_call); for a Complex[re, im] literal it returns re; and for an expression complex_decompose splits into numeric real/imaginary parts, it returns the real part. Otherwise (genuinely symbolic) it returns NULL and the call stays unevaluated.

Attributes: Listable, NumericFunction, Protected.

Implementation status¶

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

References¶

Source: src/complex.c
Specification: docs/spec/builtins/arithmetic.md

Notes & additional examples¶

Worked examples¶

In[1]:= Re[3 + 4 I]
Out[1]= 3

In[2]:= Re[7]
Out[2]= 7

Being Listable, Re maps over a list of complex numbers, and it sees through exact arithmetic — (1 + I)^10 = 32 I is purely imaginary, so its real part is exactly 0:

In[1]:= Re[{1 + I, 2 - 3 I, 5}]
Out[1]= {1, 2, 5}

In[2]:= Re[(1 + I)^10]
Out[2]= 0

It also rationalises quotients to extract an exact real part:

In[1]:= Re[1/(2 + 3 I)]
Out[1]= 2/13

Notes¶

Re[z] extracts the real part of numeric z; a purely real argument is returned unchanged. It is Listable.