compute the value of an expression under assumptions - Maple Help

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assuming - compute the value of an expression under assumptions

Calling Sequence

expression assuming property

Parameters

expression

-

expression or input to be evaluated

property

-

name; property

Description

• 

The expression assuming property calling sequence evaluates the expression under the assumption property on all names in expression.

• 

The property parameter can be a type, inequation, or other property to be assumed on a name or expression involving names.

  

Note: Computations performed using assuming do not affect computations performed before or after calling assuming.

Examples

Find the square root of a2 under the assumption that a is a positive, real constant.

a2assuming0<a

a

(1)

a2

a2

(2)

You can determine the value of an expression under the assumption that all its variables are real.

e1:=ln&ExponentialE;k1t

e1:=ln&ExponentialE;k1t

(3)

e1assumingreal

k1t

(4)

Using the assuming command does not update e1.

e1

ln&ExponentialE;k1t

(5)

The assumptions are valid only during the computation of one input statement, and no assumptions are placed on the variables.

e2:=lnyxlny&plus;lnx

e2:=lnyxlny&plus;lnx

(6)

simplifye2assumingx::positive

0

(7)

simplifye2assumingy::positive

ln1x&plus;lnx

(8)

simplifysubsx&equals;x&comma;e2assumingx::posint&comma;y::posint

2I&pi;

(9)

aboutx&colon;

x:
  nothing known about this object

abouty

y:
  nothing known about this object

Using the value command, you can evaluate an inert integral. This evaluation can be performed under assumptions.

e3:=&int;0&infin;&ExponentialE;uxx13&DifferentialD;x

e3:=&int;0&infin;&ExponentialE;uxx1&sol;3&DifferentialD;x

(10)

valuee3assuming0u

29&pi;3&Gamma;23u4&sol;3

(11)

valuee3assumingu<0

&infin;

(12)

The variable a is inside the body of f; the assumption that a>0 is not effectively used when computing f(1).

f:=x&rarr;a2&plus;x

f:=x&rarr;a2&plus;x

(13)

f1assuming0<a

a2&plus;1

(14)

For these purposes, use assume.

assume0<a

f1

a~&plus;1

(15)

Details

  

For detailed information including:

• 

How to evaluate expressions under assumptions applied to specific variables

• 

Detailed information on how the assuming command computes under assumptions

• 

How to use the assuming command in conjunction with the assume command

  

see the assuming/details help page.

See Also

assume, Physics[Assume], type, value


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