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Simplify

SymPy, WMA

Simplify[expr]

simplifies expr.

Simplify[expr, assump]

simplifies expr assuming assump instead of $Assumptions.

• • Simplify[2*Sin[x]^2 + 2*Cos[x]^2]

• • Simplify[x]

• • Simplify[f[x]]

Simplify over conditional expressions uses $Assumptions, or assump
to evaluate the condition:

• • $Assumptions={a <= 0};

• • Simplify[ConditionalExpression[1, a > 0]]

The assump option override $Assumption:

• • Simplify[ConditionalExpression[1, a > 0] ConditionalExpression[1, b > 0], { b > 0 }]

On the other hand, Assumptions option does not override $Assumptions, but add to them:

• • Simplify[ConditionalExpression[1, a > 0] ConditionalExpression[1, b > 0], Assumptions -> { b > 0 }]

Passing both options overwrites $Assumptions with the union of assump the option

• • Simplify[ConditionalExpression[1, a > 0] ConditionalExpression[1, b > 0], {a>0},Assumptions -> { b > 0 }]

• • $Assumptions={};

The option ComplexityFunction allows to control the way in which the evaluator decides if one expression is simpler than another. For example, by default, Simplify tries to avoid expressions involving numbers with many digits:

• • Simplify[20 Log[2]]

This behaviour can be modified by setting LeafCount as the ComplexityFunction:

• • Simplify[20 Log[2], ComplexityFunction->LeafCount]