BUILT-IN MATHEMATICA SYMBOL

ConditionalExpression

is a symbolic construct that represents the expression expr when the condition cond is True.

MORE INFORMATION

ConditionalExpression[expr, True] evaluates to expr.

ConditionalExpression[expr, False] evaluates to Undefined.

ConditionalExpression is automatically propagated from the arguments of mathematical functions, equations and inequalities, and Boolean operators, i.e., is transformed to ConditionalExpression.

If a function takes assumptions then the conditional part of ConditionalExpression arguments gets added to the assumptions.

Algebraic transformation functions applied to a conditional expression apply to the first argument.

EXAMPLES

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Basic Examples (2)

There is a solution only when

:

The answer is valid when the condition

is satisfied:

There is a solution only when

:

In[1]:=

Out[1]=

The answer is valid when the condition

is satisfied:

In[1]:=

Out[1]=

Scope (16)

Conditional solutions:

Parametrized solutions:

Conditionally valid integration results:

Conditionally valid summation results:

Conditionally valid Fourier series:

ConditionalExpression with True or False conditions:

Mathematical functions with ConditionalExpression arguments:

Boolean combinations of equations and inequalities involving ConditionalExpression:

Contradictory conditions:

Inverse of a function with a restricted domain:

Simplify a conditional expression:

Find solutions of equations involving conditional expressions:

Plot a function with a restricted domain:

Piecewise function involving conditional expressions:

Transform a conditionally valid expression:

Conditionally valid expressions in calculus functions:

Properties & Relations (4)

ConditionalExpression with True condition evaluates to its first argument:

ConditionalExpression with False condition evaluates to Undefined:

ConditionalExpression is propagated from the arguments of mathematical functions:

ConditionalExpression is propagated from the arguments of equations and inequalities:

ConditionalExpression is propagated from the arguments of Boolean functions:

For functions taking the Assumptions option, argument conditions are used as assumptions:

Refine, Simplify, and FullSimplify use the conditions to transform the values:

Possible Issues (1)

For functions taking the Assumptions option, argument conditions are used as assumptions:

ConditionalExpression subexpressions that are not arguments are not used: