relational operators - Maple Help

Equations and Inequalities, =, <>, <, <=, >, >=

Description

 • An equation is represented externally using the binary operator =. An expression which is an equation has two operands, the left-hand side and the right-hand side.  The names = and equation are known to the type function.
 • In 2-D math, when you type <>, <=, or >=, it is displayed as $\ne$, $\le$, or $\ge$, respectively.
 • There are three internal data types for inequalities, corresponding to the operators <>, <, and <=. Inequalities involving the operators > and >= are converted to the latter two cases for purposes of representation. An inequality has two operands, the left-hand side and the right-hand side. The names <>, <, <= are known to the type function.
 • Comparisons of numeric values are carried out in the corresponding numeric computation environment. For example, the test 3.141 < 3.142 is evaluated by subtraction in the floating-point environment determined by Digits. Hence, if Digits > 3, this returns true.  If Digits <= 3, this test returns false.
 • These operators are viewed as relational operators in a Boolean context or by the evalb function.  For more information, see boolean.

 • The equation and inequality operators are thread safe as of Maple 15.
 • The Equations and Inequalities, =, <>, <, <=, >, >= command is thread-safe as of Maple 15.

Examples

 > $e≔a=b$
 ${e}{≔}{a}{=}{b}$ (1)
 > $\mathrm{type}\left(e,'\mathrm{equation}'\right)$
 ${\mathrm{true}}$ (2)
 > $e≔f\left(x\right)
 ${e}{≔}{f}{}\left({x}\right){<}{g}{}\left({x}\right)$ (3)
 > $\mathrm{type}\left(e,'\mathrm{equation}'\right)$
 ${\mathrm{false}}$ (4)
 > $\mathrm{type}\left(e,\mathrm{<}\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{lhs}\left(e\right)$
 ${f}{}\left({x}\right)$ (6)
 > $\mathrm{rhs}\left(e\right)$
 ${g}{}\left({x}\right)$ (7)
 > $\mathrm{eqs}≔\left\{\mathrm{a1}=\mathrm{b1},\mathrm{a2}=\mathrm{b2},\mathrm{a3}=\mathrm{b3}\right\}$
 ${\mathrm{eqs}}{≔}\left\{{\mathrm{a1}}{=}{\mathrm{b1}}{,}{\mathrm{a2}}{=}{\mathrm{b2}}{,}{\mathrm{a3}}{=}{\mathrm{b3}}\right\}$ (8)
 > $\mathrm{map}\left(\mathrm{lhs},\mathrm{eqs}\right)$
 $\left\{{\mathrm{a1}}{,}{\mathrm{a2}}{,}{\mathrm{a3}}\right\}$ (9)
 > $a=2$
 ${a}{=}{2}$ (10)
 > $a$
 ${a}$ (11)
 > $\mathrm{assign}\left(\right)$
 > $a$
 ${2}$ (12)