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SolveTools

  

CancelInverses

  

normalize expression by canceling functions inverse to each other

 

Calling Sequence

Parameters

Description

Examples

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

with(SolveTools):

CancelInverses(1+exp(-x^2));

1+1ⅇx2

(1)

CancelInverses(arccos(cos(x-y*2)));

x2y

(2)

CancelInverses(tan(arctan(x-y*2)));

x2y

(3)

CancelInverses(ln(exp(x-y*2)));

x2y

(4)

CancelInverses(exp(ln(x-y*2)));

x2y

(5)

CancelInverses(ln(LambertW(exp(a+b^2+c^3))));

c3+b2+aLambertWⅇc3+b2+a

(6)

CancelInverses(exp(LambertW(a+b^2+c^3)));

c3+b2+aLambertWc3+b2+a

(7)

CancelInverses(g(1-cos(x+y+z)^2));

gsinx+y+z2

(8)

CancelInverses((-5)^(1/2));

I5

(9)

CancelInverses(((x*sin(x))^(1/2))^3);

xsinx32

(10)

CancelInverses(exp(ln(x)+ln(y+z)+t));

ⅇty+zx

(11)

CancelInverses(exp(2*ln(x)+3*ln(y+z)-4*t));

ⅇ4ty+z3x2

(12)

CancelInverses(exp(2*ln(sin(x))));

sinx2

(13)

CancelInverses(ln(exp(c*k)^z*exp(b*t)));

zck+bt

(14)

CancelInverses(ln(z^(3/2)*x));

lnx+3lnz2

(15)

CancelInverses(ln((z^(3/2))^5*x));

lnx+15lnz2

(16)

CancelInverses(ln(exp(z)^cos(x)));

cosxz

(17)

CancelInverses(ln((s^f(x))^g(z)));

gzfxlns

(18)

CancelInverses(x^((x+1)/ln(x)+(x-1)/ln(x)));

ⅇ2x

(19)

CancelInverses(arctan(-sin(b), cos(b)));

b

(20)

CancelInverses(arctan(cos(b), sin(b)));

π2b

(21)

CancelInverses(ln(exp(x))+cos(arccos(x)));

2x

(22)

CancelInverses(ln(exp(x))+cos(arccos(x)),'safe');

lnⅇx+x

(23)

See Also

exp

SolveTools

SolveTools[Combine]