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MathematicalFunctions

  

Assume

  

place assumptions without redefining the variables receiving assumptions - suitable for working with the MathematicalFunctions, Physics and VectorCalculus packages

  

Coulditbe

  

determine whether given variables could satisfy given properties

  

Is

  

determine whether given variables certainly satisfy given properties

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Assume(x::A, y::B, ...)

Coulditbe(x::A, y::B, ...)

Is(x::A, y::B, ...)

Parameters

x, y, ...

-

any variables receiving assumptions, these can be names or functions

A, B, ...

-

properties, the assumptions to be placed on the variables x, y, ...

Description

• 

Assume places assumptions similar to what the assume command does but without redefining the variables. This is particularly useful when working with packages that require some variables with special meaning to not be redefined, as is the case for instance with DifferentialGeometry, VectorCalculus, and Physics. Also, it is possible to reuse expressions entered before placing the assumptions and the result can be reused after removing the assumptions, computing as in an extended-assuming context.

  

Note: Results cached in remember tables before placing the assumptions, or after removing the assumptions, are always cleared.

• 

Coulditbe and Is compute boolean answers (as do the coulditbe and is commands respectively), but also handle a sequence of an arbitrary number of nested conditionals, which possibly include And, Or, and Not (see also convert/boolean_function to relate these boolean functions to and, or, and not).

• 

Regarding their implementation, all of Assume, Coulditbe and Is only manipulate their input before sending it to the corresponding lowercase commands, assume, coulditbe and is, in order to extend their functionality as explained above.

Examples

withMathematicalFunctions:

For examples about Assume, see the Examples section of Physics:-Assume. Regarding Coulditbe and Is, these commands permit computing with an arbitrary number of conditions to be tested, that could be nested with no restrictions, involving And and Or.

Consider the two conditions

c__1b<ab=a

c__1b<ab=a

(1)

c__2a<bb=a

c__2a<bb=a

(2)

None of them can be true, so if the question is about c1 or c2,

c__1c__2

b<ab=aa<bb=a

(3)

Coulditbe

false

(4)

The Is command is entirely based on Coulditbe so that Is(A, B, ...) = not Coulditbe(Not(A), Not(B), Not(...)). This is a generalization to many arguments of the relationship between the output of the standard is and coulditbe commands. Hence

Is=notCoulditbe¬

false=false

(5)

Add a third condition

c__3abb=a

c__3abb=a

(6)

We see that c3 can be true, therefore:

c__1c__2c__3

b<ab=aa<bb=aabb=a

(7)

Coulditbe

true

(8)

Is=notCoulditbe¬

false=false

(9)

Coulditbe also accepts a sequence of arguments (statements), in which case it only returns true if it would return true for each of the arguments received. In this example, the following two conditions cannot be true at the same time, but either of them by itself can be true.

a&comma;b&comma;cA&comma;B&comma;C,a&comma;b&comma;c=A&comma;B&comma;C

a&comma;b&comma;cA&comma;B&comma;C,a&comma;b&comma;c=A&comma;B&comma;C

(10)

Coulditbe

true

(11)

To see the output of Is with the same input, first negate these conditions

¬a&comma;b&comma;cA&comma;B&comma;C,¬a&comma;b&comma;c=A&comma;B&comma;C

¬a&comma;b&comma;cA&comma;B&comma;C,¬a&comma;b&comma;c=A&comma;B&comma;C

(12)

Is=notCoulditbe

false=false

(13)

Note the difference between this result and the one you would get using And

CoulditbeAnd

false

(14)

Add now a condition that cannot be true:

Coulditbe&comma;1=0

false

(15)

Note the difference between this result and the one you would get using Or

Coulditbe1=0

true

(16)

Compatibility

• 

The MathematicalFunctions[Assume], MathematicalFunctions[Coulditbe] and MathematicalFunctions[Is] commands were introduced in Maple 2015.

• 

For more information on Maple 2015 changes, see Updates in Maple 2015.

See Also

assume

coulditbe

is

MathematicalFunctions

Physics[Assume]