Assumptions can be given both as an argument and as an option value:
When assumptions are given as an argument,
$Assumptions is used as well:
Specifying assumptions as an option value prevents
Simplify from using
$Assumptions:
The default
ComplexityFunction counts the subexpressions and digits of integers:
LeafCount counts only the number of subexpressions:
This complexity function makes
Abs more expensive than
Times:
This gives no simplification:
Excluding transformations of
(x - 2)^10 allows
Simplify to expand the remaining terms:
This takes a long time, due to trigonometric expansion, but does not yield a simplification:
Use
TimeConstraint to limit the time spent on any single transformation:
A similar example, where the transformation yields a simplification:
In this case setting
TimeConstraint prevents some simplification:
Here
Simplify uses
t as the only transformation:
Here
Simplify uses both
t and all built-in transformations:
By default
Simplify uses trigonometric identities:
With
Trig->False,
Simplify does not use trigonometric identities:
Integers, and logical combinations of these. 
EXAMPLES
Basic Examples 
Scope 