QuotientRemainder¶

Status: Stable

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

Description¶

QuotientRemainder[m, n]

gives the pair {Quotient[m, n], Mod[m, n]}, so the quotient is floored and the remainder carries the sign of n.

Notes

QuotientRemainder is Listable; non-numeric arguments are left unevaluated.

Examples (3)¶

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

Applications (3)¶

In[1]:= QuotientRemainder[17, 5]
Out[1]= {3, 2}

In[2]:= QuotientRemainder[-17, 5]
Out[2]= {-4, 3}

In[3]:= QuotientRemainder[17, -5]
Out[3]= {-4, -3}

Implementation notes¶

builtin_quotientremainder returns the pair {Quotient[m, n], Mod[m, n]}, sharing the floored-division and Gaussian-integer conventions of its two components, so the remainder always carries the sign of the divisor. Registered PROTECTED | NUMERICFUNCTION | LISTABLE; non-numeric arguments are left unevaluated.

Attributes: Listable, NumericFunction, Protected.

References¶

See also: Mod, Quotient, Union, Tally, DeleteDuplicates

Source: src/core.c
Specification: docs/spec/builtins/arithmetic.md
Tests: tests/test_core.c
Tests: tests/test_eval.c
Tests: tests/test_expr_sharing.c
Tests: tests/test_ndsolve_compile.c

Notes & additional examples¶

Notes¶

QuotientRemainder[m, n] returns the quotient and remainder together as {Quotient[m, n], Mod[m, n]}. Because the quotient is floored and the remainder takes the sign of the divisor n, the two always reconstruct the dividend: n q + r == m. So QuotientRemainder[-17, 5] = {-4, 3} (a non-negative remainder) while QuotientRemainder[17, -5] = {-4, -3} (a non-positive one).