Refine¶

Simplifies expressions using assumptions.

$ wo 'Refine[x]'
x

A finite factor with a known sign collapses factor * Infinity to the correctly-signed infinity:

$ wo 'Refine[a*Infinity, a > 0]'
Infinity

$ wo 'Refine[a*Infinity, a < 0]'
-Infinity

A condition the assumption settles collapses the head around it:

$ wo 'Refine[Boole[x > 0], x > 0]'
1

$ wo 'Refine[If[x > 0, a, b], x < 0]'
b

Step functions resolve once the assumption fixes the sign of the argument:

$ wo 'Refine[UnitStep[x], x < 0]'
0

A chained inequality settles the rounding functions whenever the range cannot straddle a boundary:

$ wo '{Refine[Floor[x], 0 < x < 1], Refine[Ceiling[x], 0 < x < 1], Refine[IntegerPart[x], -1 < x < 0]}'
{0, 1, 0}

A range that can straddle one is left alone — x may be 1 below, and Round turns over at ½:

$ wo '{Refine[Floor[x], 0 < x <= 1], Refine[Round[x], 0 < x < 1]}'
{Floor[x], Round[x]}

The sign such a range implies reaches the other refinements too:

$ wo '{Refine[Sign[x], 0 < x < 1], Refine[Abs[x], 0 < x < 1]}'
{1, x}