apply simplification rules to an expression - Maple Help

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simplify - apply simplification rules to an expression

 Calling Sequence simplify(expr, n1, n2, ...) simplify(expr, side1, side2, ...) simplify(expr, assume=prop) simplify(expr, symbolic)

Parameters

 expr - any expression n1, n2, ... - (optional) names; simplification procedures side1, side2, ... - (optional) sets or lists; side relations prop - (optional) any property

Basic Information

 • This help page contains complete information about the simplify command. For basic information on the simplify command, see the simplify help page.

Description

 • The simplify command is used to apply simplification rules to an expression.
 • The simplify/expr calling sequence searches the expression, expr, for function calls, square roots, radicals, and powers. It then invokes the appropriate simplification procedures.

Examples

Simple Example

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

Simplifying Trigonometric Expressions

 > $e:={\mathrm{cos}\left(x\right)}^{5}+{\mathrm{sin}\left(x\right)}^{4}+2{\mathrm{cos}\left(x\right)}^{2}-2{\mathrm{sin}\left(x\right)}^{2}-\mathrm{cos}\left(2x\right):$
 > $\mathrm{simplify}\left(e\right)$
 ${{\mathrm{cos}}{}\left({x}\right)}^{{4}}{}\left({\mathrm{cos}}{}\left({x}\right){+}{1}\right)$ (2)

Simplifying Exponentials and Logarithms

 > $\mathrm{simplify}\left({ⅇ}^{a+\mathrm{ln}\left(b{ⅇ}^{c}\right)}\right)$
 ${b}{}{{ⅇ}}^{{a}{+}{c}}$ (3)

Controlling Simplification Rules

 > $\mathrm{simplify}\left({\mathrm{sin}\left(x\right)}^{2}+\mathrm{ln}\left(2x\right)+{\mathrm{cos}\left(x\right)}^{2}\right)$
 ${1}{+}{\mathrm{ln}}{}\left({2}\right){+}{\mathrm{ln}}{}\left({x}\right)$ (4)
 > $\mathrm{simplify}\left({\mathrm{sin}\left(x\right)}^{2}+\mathrm{ln}\left(2x\right)+{\mathrm{cos}\left(x\right)}^{2},\mathrm{trig}\right)$
 ${1}{+}{\mathrm{ln}}{}\left({2}{}{x}\right)$ (5)
 > $\mathrm{simplify}\left({\mathrm{sin}\left(x\right)}^{2}+\mathrm{ln}\left(2x\right)+{\mathrm{cos}\left(x\right)}^{2},\mathrm{ln}\right)$
 ${{\mathrm{sin}}{}\left({x}\right)}^{{2}}{+}{\mathrm{ln}}{}\left({2}\right){+}{\mathrm{ln}}{}\left({x}\right){+}{{\mathrm{cos}}{}\left({x}\right)}^{{2}}$ (6)

Simplifying With Respect to Side Relations

 > $f:=-\frac{1{x}^{5}y}{3}+{x}^{4}{y}^{2}+\frac{1x{y}^{3}}{3}+1:$
 > $\mathrm{simplify}\left(f,\left\{{x}^{3}=xy,{y}^{2}=x+1\right\}\right)$
 ${{x}}^{{4}}{+}{{x}}^{{2}}{+}{x}{+}{1}$ (7)

Using the assume option

 > $g:=\sqrt{{x}^{2}}$
 ${g}{:=}\sqrt{{{x}}^{{2}}}$ (8)
 > $\mathrm{simplify}\left(g\right)$
 ${\mathrm{csgn}}{}\left({x}\right){}{x}$ (9)
 > $\mathrm{simplify}\left(g,\mathrm{assume}=\mathrm{real}\right)$
 $\left|{x}\right|$ (10)
 > $\mathrm{simplify}\left(g,\mathrm{assume}=\mathrm{positive}\right)$
 ${x}$ (11)
 > $\mathrm{simplify}\left(g,\mathrm{symbolic}\right)$
 ${x}$ (12)

Simplifying an Integral

 Integrands and summands are simplified taking into account the integration or sum ranges respectively. For more information, see assuming.
 > $\mathrm{expr}:={{∫}}_{1}^{4}{\left(1+{\mathrm{sinh}\left(t\right)}^{2}\right)}^{\frac{1}{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}t$
 ${\mathrm{expr}}{:=}{{∫}}_{{1}}^{{4}}\sqrt{{1}{+}{{\mathrm{sinh}}{}\left({t}\right)}^{{2}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{t}$ (13)
 > $\mathrm{simplify}\left(\mathrm{expr}\right)$
 ${{∫}}_{{1}}^{{4}}{\mathrm{cosh}}{}\left({t}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{t}$ (14)
 See Also

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