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simplify

apply simplification rules to an expression

 

Calling Sequence

Parameters

Basic Information

Description

Options

Examples

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.

Options

Simplification procedures  

  

n1, n2, ...

  

Invokes only the simplification procedures specified by the additional names.

  

Further information on the simplification procedures supported is available in the help pages simplify/name where name is one of:

@

constant

constants

Ei

GAMMA

hypergeom

ln

piecewise

polar

power

radical

RootOf

rtable

siderels

size

sqrt

trig

wronskian

zero

 

  

You can extend the simplify function by defining a Maple procedure. If the procedure `simplify/f` is defined, then the function call simplify(a,f) invokes `simplify/f`(a).

  

 

Side relations

  

side1, side2,...

  

Performs simplification with respect to the side relations. For details, see simplify/siderels.

  

 

The assume option

  

assume=prop

  

When the last argument is assume=prop, all the indeterminates in expr are assumed to have the property prop when computing the simplified expression. This option is not necessary to simplify integrands and summands in definite integrals and sums taking into account the integration/summation range. For details, see the following Examples section.

  

 

The symbolic option

  

symbolic

  

Specifies that formal symbolic manipulation of expressions is allowed without regard to the analytical issue of branches for multi-valued functions. For example, the expression sqrt(x^2) simplifies to x under the symbolic option. Without this option, the simplified result must take into account the different possible values of the (complex) sign of x.

  

Note: When the symbolic option is specified, any branch of a multi-valued function can be chosen during the simplification process. The result of such an operation is in general not valid over the whole complex plane and can lead to incorrect results if you assume the expressions represent analytical functions.

Examples

Simple Example

simplify412+3

5

(1)

Simplifying Trigonometric Expressions

ecosx5+sinx4+2cosx22sinx2cos2x:

simplifye

cosx4cosx+1

(2)

Simplifying Exponentials and Logarithms

simplifyⅇa+lnbⅇc

bⅇa+c

(3)

Controlling Simplification Rules

simplifysinx2+ln2x+cosx2

1+ln2+lnx

(4)

simplifysinx2+ln2x+cosx2,trig

1+ln2x

(5)

simplifysinx2+ln2x+cosx2,ln

sinx2+ln2+lnx+cosx2

(6)

Simplifying With Respect to Side Relations

f1x5y3+x4y2+1xy33+1:

simplifyf,x3=xy,y2=x+1

x4+x2+x+1

(7)

Using the assume option

gx2

g:=x2

(8)

simplifyg

csgnxx

(9)

simplifyg,assume=real

x

(10)

simplifyg,assume=positive

x

(11)

simplifyg,symbolic

x

(12)

Simplifying an Integral

  

Integrands and summands are simplified taking into account the integration or sum ranges respectively. For more information, see assuming.

expr∫141+sinht212ⅆt

expr:=∫141+sinht2ⅆt

(13)

simplifyexpr

∫14coshtⅆt

(14)

See Also

assume

assuming

collect

combine

convert

expand

factor

normal

RealDomain

RealRange

simplify

simplify/@

simplify/Ei

simplify/GAMMA

simplify/hypergeom

simplify/ln

simplify/polar

simplify/power

simplify/radical

simplify/RootOf

simplify/rtable

simplify/sqrt

simplify/trig

 


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