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NonPositive

Status: Stable

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

Description

NonPositive[x]

gives True if x is a real number that is negative or zero, and False

Notes if x is a manifestly positive real number or a non-real complex number. For non-numeric x the expression is left unevaluated. NonPositive is Listable, so it threads over lists element by element.

Examples (8)

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

Basic examples (3)

In[1]:= NonPositive[{1.6, 3/4, Pi, 0, -5, 1 + I, Sin[10^5]}]
Out[1]= {False, False, False, True, True, False, False}

In[2]:= NonPositive[{x, Sin[y]}]
Out[2]= {NonPositive[x], NonPositive[Sin[y]]}

In[3]:= NonPositive[1 - Pi]
Out[3]= True

Applications (5)

Zero is included

In[4]:= NonPositive[0]
Out[4]= True

In[5]:= NonPositive[1 - Pi]
Out[5]= True

In[6]:= NonPositive[3]
Out[6]= False

Listable

In[7]:= NonPositive[{1.6, 3/4, Pi, 0, -5, 1 + I, Sin[10^5]}]
Out[7]= {False, False, False, True, True, False, False}

Non-numeric argument stays symbolic

In[8]:= NonPositive[x]
Out[8]= NonPositive[x]

Implementation notes

Algorithm. builtin_nonpositive (src/core.c) decides whether a numeric quantity is real and <= 0. It gates on is_numeric_quantity (a non-numeric argument returns NULL and stays unevaluated), then classifies with the shared numeric_real_sign helper: exact EXPR_INTEGER / EXPR_BIGINT / Rational / EXPR_REAL (and EXPR_MPFR) read directly via expr_numeric_sign, everything else numericalized at machine precision. A non-real complex value answers False; otherwise the verdict is sign <= 0, so zero is included.

Data structures. All Expr. A packed list or NDArray is read in one pass by ndint_sign_predicate(res, NDSP_NONPOSITIVE) (src/ndinteger.c) into a List of True/False; complex buffers, rank > 1, and Indeterminate elements are declined, with ndarray_delist_and_reeval falling back to the scalar path that Listable threading reaches for an unpacked list.

Complexity / limits. O(1) per scalar, O(n) over a buffer. For inexact or symbolic-constant inputs the verdict rests on a machine-precision numericalization. Attributes Listable, Protected.

Attributes: Listable, Protected.

References

See also: NumericQ

Notes & additional examples

Notes

NonPositive[x] is True for a real numeric quantity that is negative or zero; it differs from Negative only at zero. A non-real complex value gives False. Exact inputs are decided exactly, inexact and symbolic-constant inputs by their machine-precision value, and a non-numeric argument is left unevaluated. NonPositive is Listable and reads a packed list or NDArray straight off the buffer.