 Equalities and Inequalities - Maple Help

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Equalities and Inequalities in the Simple Units Environment Description

 • In the Simple Units environment, any verifications of valid dimensions ignore so-called Unit annotations.
 • In the Simple Units environment, the equality and inequality relators ($=,<,\le ,>,\ge$, and$\ne$) are modified so that they perform the necessary operations on expressions with units.
 • Every command in the Simple Units environment that needs to determine whether an expression is valid or not, does so using the Units[TestDimensions] command.
 • The properties of these relators are:

$A\mathrm{Unit}\left(a\right)=B\mathrm{Unit}\left(b\right)\to A=rB$

$A\mathrm{Unit}\left(a\right)

$A\mathrm{Unit}\left(a\right)\le B\mathrm{Unit}\left(b\right)\to A\le rB$

$A\mathrm{Unit}\left(a\right)>B\mathrm{Unit}\left(b\right)\to A>rB$

$A\mathrm{Unit}\left(a\right)\ge B\mathrm{Unit}\left(b\right)\to A\ge rB$

$A\mathrm{Unit}\left(a\right)\ne B\mathrm{Unit}\left(b\right)\to A\ne rB$

 where $a$ and $b$ are units; $A$ and $B$ are coefficients; and $r$ is the conversion factor from the unit $b$ to the unit $a$. Examples

Notes:

 – To enter a unit in 2-D Math input, select the unit from the appropriate Units palette. If the unit you want is not there, select $\mathrm{unit}$ and then enter the unit.
 – When you edit a unit, double brackets appear around it.
 > $\mathrm{with}\left(\mathrm{Units}\left[\mathrm{Simple}\right]\right):$
 > $3\mathrm{Unit}\left('\mathrm{ft}'\right)=\mathrm{Unit}\left('\mathrm{yd}'\right)$
 ${3}{=}{3}$ (1)
 > $\mathrm{evalb}\left(\right)$
 ${\mathrm{true}}$ (2)
 > $1.60\mathrm{Unit}\left('m'\right)<\mathrm{Unit}\left('\mathrm{mi}'\right)$
 ${1.60}{<}\frac{{201168}}{{125}}$ (3)
 > $\mathrm{evalb}\left(\right)$
 ${\mathrm{true}}$ (4)
 > $30.48\mathrm{Unit}\left('\mathrm{cm}'\right)=\mathrm{Unit}\left('\mathrm{ft}'\right)$
 ${30.48}{=}\frac{{762}}{{25}}$ (5)
 > $\mathrm{evalb}\left(\right)$
 ${\mathrm{true}}$ (6)
 > $3\mathrm{Unit}\left('\mathrm{ft}'\right)+3\mathrm{Unit}\left('\mathrm{inch}'\right)=\mathrm{Unit}\left('m'\right)$
 $\frac{{4953}}{{5000}}{=}{1}$ (7)
 > $\mathrm{evalb}\left(\right)$
 ${\mathrm{false}}$ (8)
 >