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.

$\mathrm{with}\left(\mathrm{MathematicalFunctions}\right)\:$

$\mathrm{c\_\_1}≔\mathrm{And}\left(b<a\&comma;b=a\right)$

$\mathrm{c\_\_1}≔b<a\wedge b=a$

$\mathrm{c\_\_2}≔\mathrm{And}\left(a<b\&comma;b=a\right)$

$\mathrm{c\_\_2}≔a<b\wedge b=a$

$\mathrm{Or}\left(\mathrm{c\_\_1}\&comma;\mathrm{c\_\_2}\right)$

$\left(b<a\wedge b=a\right)\vee \left(a<b\wedge b=a\right)$

$\mathrm{Coulditbe}\left(\right)$

$\mathrm{false}$

$\mathrm{Is}\left(\right)=\left(\mathbf{not}\mathrm{Coulditbe}\left(\mathrm{Not}\left(\right)\right)\right)$

$\mathrm{false}=\mathrm{false}$

$\mathrm{c\_\_3}≔\mathrm{And}\left(a\le b\&comma;b=a\right)$

$\mathrm{c\_\_3}≔a\le b\wedge b=a$

$\mathrm{Or}\left(\mathrm{c\_\_1}\&comma;\mathrm{c\_\_2}\&comma;\mathrm{c\_\_3}\right)$

$\left(b<a\wedge b=a\right)\vee \left(a<b\wedge b=a\right)\vee \left(a\le b\wedge b=a\right)$

$\mathrm{Coulditbe}\left(\right)$

$\mathrm{true}$

$\mathrm{Is}\left(\right)=\left(\mathbf{not}\mathrm{Coulditbe}\left(\mathrm{Not}\left(\right)\right)\right)$

$\mathrm{false}=\mathrm{false}$

$\left[a\&comma;b\&comma;c\right]\ne \left[A\&comma;B\&comma;C\right],\left[a\&comma;b\&comma;c\right]=\left[A\&comma;B\&comma;C\right]$

$\left[a\&comma;b\&comma;c\right]\ne \left[A\&comma;B\&comma;C\right],\left[a\&comma;b\&comma;c\right]=\left[A\&comma;B\&comma;C\right]$

$\mathrm{Coulditbe}\left(\right)$

$\mathrm{true}$

$\mathrm{Not}\left(\left[a\&comma;b\&comma;c\right]\ne \left[A\&comma;B\&comma;C\right]\right),\mathrm{Not}\left(\left[a\&comma;b\&comma;c\right]=\left[A\&comma;B\&comma;C\right]\right)$

$\neg \left(\left[a\&comma;b\&comma;c\right]\ne \left[A\&comma;B\&comma;C\right]\right),\neg \left(\left[a\&comma;b\&comma;c\right]=\left[A\&comma;B\&comma;C\right]\right)$

$\mathrm{Is}\left(\right)=\left(\mathbf{not}\mathrm{Coulditbe}\left(\right)\right)$

$\mathrm{false}=\mathrm{false}$

$\mathrm{Coulditbe}\left(\mathrm{And}\left(\right)\right)$

$\mathrm{false}$

$\mathrm{Coulditbe}\left(\&comma;1=0\right)$

$\mathrm{false}$

$\mathrm{Coulditbe}\left(\mathrm{Or}\left(\&comma;1=0\right)\right)$

$\mathrm{true}$

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.