simplify - Maple Programming Help

simplify

apply simplification rules to an expression

 Calling Sequence simplify(expr)

Parameters

 expr - any expression

Basic Information

Description

 • The simplify command is used to apply simplification rules to an expression.

Output

 • The simplify routine searches the expression for function calls, square roots, radicals, and powers and invokes the appropriate simplification procedures.

Details

 For detailed information on the simplify command, see simplify/details.

Examples

Basic example

 > $\mathrm{simplify}\left({4}^{\frac{1}{2}}+3\right)$
 ${5}$ (1)

Simplifying exponentials and logarithms

 > $\mathrm{simplify}\left({ⅇ}^{a+\mathrm{ln}\left(b{ⅇ}^{c}\right)}\right)$
 ${b}{}{{ⅇ}}^{{a}{+}{c}}$ (2)

Controlling which simplification rules to use

 > $\mathrm{simplify}\left({\mathrm{sin}\left(x\right)}^{2}+\mathrm{ln}\left(2x\right)+{\mathrm{cos}\left(x\right)}^{2}\right)$
 ${1}{+}{\mathrm{ln}}{}\left({2}\right){+}{\mathrm{ln}}{}\left({x}\right)$ (3)
 When trig is specified as the second argument, only the trigonometric expressions are simplified.
 > $\mathrm{simplify}\left({\mathrm{sin}\left(x\right)}^{2}+\mathrm{ln}\left(2x\right)+{\mathrm{cos}\left(x\right)}^{2},\mathrm{trig}\right)$
 ${1}{+}{\mathrm{ln}}{}\left({2}{}{x}\right)$ (4)

Using the assume option

 When you use the assume=property option as the last argument, all the indeterminate variables in expr are assumed to have the property when simplifying the expression. In the following example, x is assumed to be positive. For more information, see the simplify/details page.
 > $\mathrm{simplify}\left(\sqrt{{x}^{2}},\mathrm{assume}=\mathrm{positive}\right)$
 ${x}$ (5)

Simplifying with respect to side relations

 The command simplify can perform simplification with respect to side relations.  For details, see simplify/siderels.
 > $\mathrm{eqns}≔\left\{{\mathrm{sin}\left(x\right)}^{2}+{\mathrm{cos}\left(x\right)}^{2}=1\right\}:$
 > $e≔{\mathrm{sin}\left(x\right)}^{3}-11{\mathrm{sin}\left(x\right)}^{2}\mathrm{cos}\left(x\right)+3{\mathrm{cos}\left(x\right)}^{3}-\mathrm{sin}\left(x\right)\mathrm{cos}\left(x\right)+2$
 ${e}{≔}{{\mathrm{sin}}{}\left({x}\right)}^{{3}}{-}{11}{}{{\mathrm{sin}}{}\left({x}\right)}^{{2}}{}{\mathrm{cos}}{}\left({x}\right){+}{3}{}{{\mathrm{cos}}{}\left({x}\right)}^{{3}}{-}{\mathrm{sin}}{}\left({x}\right){}{\mathrm{cos}}{}\left({x}\right){+}{2}$ (6)
 > $\mathrm{simplify}\left(e,\mathrm{eqns}\right)$
 ${14}{}{{\mathrm{cos}}{}\left({x}\right)}^{{3}}{-}{{\mathrm{cos}}{}\left({x}\right)}^{{2}}{}{\mathrm{sin}}{}\left({x}\right){-}{\mathrm{sin}}{}\left({x}\right){}{\mathrm{cos}}{}\left({x}\right){-}{11}{}{\mathrm{cos}}{}\left({x}\right){+}{\mathrm{sin}}{}\left({x}\right){+}{2}$ (7)
 > $\mathrm{simplify}\left(e,\mathrm{eqns},\left[\mathrm{sin}\left(x\right),\mathrm{cos}\left(x\right)\right]\right)$
 ${14}{}{{\mathrm{cos}}{}\left({x}\right)}^{{3}}{-}{{\mathrm{cos}}{}\left({x}\right)}^{{2}}{}{\mathrm{sin}}{}\left({x}\right){-}{\mathrm{sin}}{}\left({x}\right){}{\mathrm{cos}}{}\left({x}\right){-}{11}{}{\mathrm{cos}}{}\left({x}\right){+}{\mathrm{sin}}{}\left({x}\right){+}{2}$ (8)
 Simplify with respect to cos(x) first.
 > $\mathrm{simplify}\left(e,\mathrm{eqns},\left[\mathrm{cos}\left(x\right),\mathrm{sin}\left(x\right)\right]\right)$
 ${-}{14}{}{{\mathrm{sin}}{}\left({x}\right)}^{{2}}{}{\mathrm{cos}}{}\left({x}\right){+}{{\mathrm{sin}}{}\left({x}\right)}^{{3}}{-}{\mathrm{sin}}{}\left({x}\right){}{\mathrm{cos}}{}\left({x}\right){+}{3}{}{\mathrm{cos}}{}\left({x}\right){+}{2}$ (9)