# Equations

"Defining Variables" discussed *assignments* such as which *set* x equal to y. Here we discuss *equations*, which *test* equality. The equation *tests* whether x is equal to y.

This

*tests* whether

and

are equal. The result is the symbol

True.

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It is very important that you do not confuse with . While is an *imperative* statement that actually causes an assignment to be done, merely *tests* whether x and y are equal, and causes no explicit action. If you have used the C programming language, you will recognize that the notation for assignment and testing in *Mathematica* is the same as in C.

x=y | assigns x to have value y |

x==y | tests whether x and y are equal |

Assignments and tests.

This

*assigns* to have value

.

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If you ask for

, you now get

.

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This

*tests* whether

is equal to

. In this case, it is.

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This removes the value assigned to

.

The tests we have used so far involve only numbers, and always give a definite answer, either True or False. You can also do tests on symbolic expressions.

*Mathematica* cannot get a definite result for this test unless you give

a specific numerical value.

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If you replace

by the specific numerical value

, the test gives

False.

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Even when you do tests on symbolic expressions, there are some cases where you can get definite results. An important one is when you test the equality of two expressions that are *identical*. Whatever the numerical values of the variables in these expressions may be, *Mathematica* knows that the expressions must always be equal.

The two expressions are

*identical*, so the result is

True, whatever the value of

may be.

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*Mathematica* does not try to tell whether these expressions are equal. In this case, using

Expand would make them have the same form.

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Expressions like represent *equations* in *Mathematica*. There are many functions in *Mathematica* for manipulating and solving equations.

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You can assign a name to the equation.

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If you ask for

, you now get the equation.

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