Documentation

=, _equal

Equations (equal)

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x = y
_equal(x, y)

Description

x = y defines an equation.

x = y is equivalent to the function call _equal(x, y).

The operator = returns a symbolic expression representing an equation. The resulting expression can be evaluated to TRUE or FALSE by the function bool. It also serves as control conditions in if, repeat, and while statements. In all these cases, testing for equality is a purely syntactical test. For example, bool(0.5 = 1/2) returns FALSE although both numbers coincide numerically. Further, Boolean expressions can be evaluated to TRUE, FALSE, or UNKNOWN by the function is. Tests using is are semantic comparing x and y applying mathematical considerations.

Equations have two operands: the left side and the right side. Use lhs and rhs to extract these operands.

The boolean expression not x = y is always converted to x <> y. The expression not x <> y is always converted to x = y.

Examples

Example 1

In the following example, note the difference between syntactical and numerical equality. The numbers 1.5 and coincide numerically. However, 1.5 is of domain type DOM_FLOAT, whereas is of domain type DOM_RAT. Consequently, they are not regarded as equal in the following syntactical test:

1.5 = 3/2;
bool(%)  For equations with floating-point numbers, use the operator ~= instead of =. The functions bool and is test whether the floating-point approximations coincide up to the relative precision given by DIGITS:

1.5 ~= 3/2;
bool(1.5 ~= 3/2);
is(1.5 ~= 3/2);   The following expressions coincide syntactically:

_equal(1/x, diff(ln(x),x));
bool(%)  The Boolean operator not converts equalities and inequalities:

not a = b, not a <> b Example 2

In this example, use the operator = to compare non-mathematical objects:

if "text" = "t"."e"."x"."t" then "yes" else "no" end Example 3

Test equality of these expressions by using the syntactical test via bool and the semantic test via testeq:

bool(1 = x/(x + y) + y/(x + y)),
testeq(1 = x/(x + y) + y/(x + y)) Example 4

Equations are typical input objects for system functions, such as solve:

solve(x^2 - 2*x = -1, x) Parameters

 x, y Arbitrary MuPAD® objects

Return Values

Expression of type "_equal".