Greater¶

Status: Stable

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

Description¶

x > y or Greater[x, y] yields True if x is strictly greater than y on numeric inputs, False if strictly less or equal, otherwise unevaluated. Chained forms become Inequality. Per IEEE 754, an Indeterminate argument gives False.

Examples (4)¶

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

Applications (4)¶

In[1]:= 3 > 2
Out[1]= True

In[2]:= 5 > 5
Out[2]= False

In[3]:= Greater[5, 3]
Out[3]= True

In[4]:= x > 2
Out[4]= x > 2

Implementation notes¶

builtin_greater delegates to the shared evaluate_inequality(res, 1, 1), which walks adjacent argument pairs and calls compare_numeric (exact GMP for integer-like, exact cross-multiplied long double for rationals, 2^-46 relative tolerance for inexact reals; returns -1/0/+1). A pair is accepted only when the sign is +1 (strictly greater). All pairs strictly decreasing → True; any 0/-1 pair → False; any non-comparable (symbolic) pair → NULL (chain left unevaluated). This is the chained a > b > c semantics. Shares its implementation with Less/LessEqual/GreaterEqual via different accepted-sign arguments.

Attributes: Protected.

References¶

Source: src/comparisons.c
Specification: docs/spec/builtins/comparisons.md
Tests: tests/test_comparisons.c
Tests: tests/test_deriv.c
Tests: tests/test_parse.c
Tests: tests/test_readwrite.c

Notes & additional examples¶

Notes¶

> is the operator form of Greater. On purely numeric arguments it decides to True or False; if an argument is symbolic and the relation cannot be settled, the expression is returned unevaluated.