normalize expression by canceling functions inverse to each other - Maple Help

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SolveTools[CancelInverses] - normalize expression by canceling functions inverse to each other

Calling Sequence

CancelInverses(expr)

CancelInverses(expr,'safe')

Parameters

expr

-

expression

'safe'

-

'safe'

Description

• 

The CancelInverses command performs cancellation of the functions that are inverse to each other.

• 

The following simplifications are made:

trigarctrigsubexprsubexpr

arctrigtrigsubexprsubexpr

lnⅇsubexprsubexpr

ⅇlnsubexprsubexpr

lnLambertWⅇsubexprsubexprLambertWⅇsubexpr

ⅇintegerLambertWsubexprsubexprintegerLambertWsubexprinteger

1sinsubexpr2cossubexpr2

1cossubexpr2sinsubexpr2

subexpr12subexpr

subexprrationalintegersubexprrationalinteger

  

Any combinations of the previous simplifications are made.  Also, arctan of two arguments is simplified if it contains sin(subexpr).

  

Note: Not all simplifications are valid everywhere. You should be aware of this when calling CancelInverses, if option 'safe' is given, then only valid simplifications are applied.

Examples

withSolveTools:

CancelInverses1+ⅇx2

1+1ⅇx2

(1)

CancelInversesarccoscosxy2

x2y

(2)

CancelInversestanarctanxy2

x2y

(3)

CancelInverseslnⅇxy2

x2y

(4)

CancelInversesⅇlnxy2

x2y

(5)

CancelInverseslnLambertWⅇa+b2+c3

c3+b2+aLambertWⅇc3+b2+a

(6)

CancelInversesⅇLambertWa+b2+c3

c3+b2+aLambertWc3+b2+a

(7)

CancelInversesg1cosx+y+z2

gsinx+y+z2

(8)

CancelInverses512

I5

(9)

CancelInversesxsinx123

xsinx3/2

(10)

CancelInversesⅇlnx+lny+z+t

ⅇty+zx

(11)

CancelInversesⅇ2lnx+3lny+z4t

ⅇ4ty+z3x2

(12)

CancelInversesⅇ2lnsinx

sinx2

(13)

CancelInverseslnⅇckzⅇbt

ckz+bt

(14)

CancelInverseslnz32x

lnx+32lnz

(15)

CancelInverseslnz325x

lnx+152lnz

(16)

CancelInverseslnⅇzcosx

cosxz

(17)

CancelInverseslnsfxgz

gzfxlns

(18)

CancelInversesxx+1lnx+x1lnx

ⅇ2x

(19)

CancelInversesarctansinb,cosb

b

(20)

CancelInversesarctancosb,sinb

12πb

(21)

CancelInverseslnⅇx+cosarccosx

2x

(22)

CancelInverseslnⅇx+cosarccosx,'safe'

lnⅇx+x

(23)

See Also

exp, SolveTools, SolveTools[Combine]


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