In almost any mathematical formulation in Physics or when working with MathematicalFunctions, there are variables that are real, positive, or represent angles that have a restricted range. For example: Planck's constant, time, the mass and position of particles, spherical coordinates, the domain of some special function parameters, etc. One typically perform algebraic computations with these variables, and at some point wants to place assumptions on them, because the results appear somewhat unsimplified, under the generic assumption that every name represents a complex variable defined over the whole complex plane.

Assume is a command for placing these assumptions on variables and is the preferred command for this purpose when working with the Physics and MathematicalFunctions packages. Assume also includes the functionality of the additionally command. All the assumptions placed using Assume are taken into account by the commands coulditbe, is, getassumptions and assuming (with option additionally), and through them by the whole Maple library, in exactly the same way they are taken into account when placed using assume.

To understand the motivation for Assume note that when placing assumptions using the assume command, expressions entered before placing the assumptions cannot be reused and results involving assumed variables, obtained after placing the assumptions, cannot be reused in case the assumptions are removed, or more or different assumptions are placed on the same variables. This is so because assume redefines the variables receiving assumptions each time you place assumptions on them.

These restrictions do not exist when placing assumptions with Assume, because it does not redefine the variables receiving assumptions - it only places the assumptions - and in that way allows for reusing expressions entered before placing assumptions, or reusing results that involve assumed variables after removing or changing the assumptions to something more precise/appropriate. This is a typical situation when working on Physics problems or performing algebraic exploration with mathematical functions.

More important, when using assume, because the variables receiving assumptions get redefined, geometrical coordinates (spacetime, Cartesian, cylindrical and spherical) loss their identity and are not recognized anymore by the Physics package commands or those from the VectorCalculus package. This is not an issue when placing assumptions with Assume because it does not redefine the variables, they remain the same, before, during and after removing the assumptions placed, in some way implementing the concept of an assuming command of extended action.

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

$\mathrm{Setup}\left(\mathrm{mathematicalnotation}=\mathrm{true}\right)$

$\left[\mathrm{mathematicalnotation}=\mathrm{true}\right]$

$\mathrm{about}\left(x\right)$

x:
  nothing known about this object

$\mathrm{addressof}\left(x\right)$

$36893628512123923548$

$\mathrm{assume}\left(0<x\mathbf{and}x<\frac{1}{2}\mathrm{\pi }\right)$

$\mathrm{addressof}\left(x\right)$

$36893628512000574044$

$\mathrm{about}\left(x\right)$

Originally x, renamed x~:
  is assumed to be: RealRange(Open(0),Open(1/2*Pi))

$x≔'x'$

$x≔x$

$\mathrm{addressof}\left(x\right)$

$36893628512123923548$

All the equations/expressions, entered before placing the assumptions on $x$ using assume, involve a variable $x$ that is different than the one that exists after placing the assumptions. So, these previous expressions cannot be reused, because they involve a different variable.

Because, after placing the assumptions using assume, $x$ refers to a different variable, programs that depend on the $x$ that existed before placing the assumptions (e.g. the spacetime metric g_, general relativity tensors, Physics:-Vectors and VectorCalculus commands) do not recognize the new $x$ redefined by assume.

$\mathrm{simplify}\left(\arccos \left(\cos \left(x\right)\right)\right)$

$\arccos \left(\cos \left(x\right)\right)$

$\mathrm{Assume}\left(0<x\mathbf{and}x<\frac{1}{2}\mathrm{\pi }\right)$

$\left\{x::\left(0\&comma;\frac{\mathrm{\pi }}{2}\right)\right\}$

$\mathrm{addressof}\left(x\right)$

$36893628512123923548$

$\mathrm{about}\left(x\right)$

Originally x, renamed x:
  is assumed to be: RealRange(Open(0),Open(1/2*Pi))

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

$x$

$\mathrm{Assume}\left(\mathrm{clear}=x\right)$

$\varnothing$

$\mathrm{about}\left(x\right)$

x:
  nothing known about this object

$\mathrm{Assume}\left(x::\mathrm{positive}\right)$

$\left\{x::\left(0\&comma;\mathrm{\infty }\right)\right\}$

$\mathrm{about}\left(x\right)$

Originally x, renamed x:
  is assumed to be: RealRange(Open(0),infinity)

$\mathrm{Assume}\left(\mathrm{additionally}\&comma;x<1\right)$

$\left\{x::\left(0\&comma;1\right)\right\}$

$\mathrm{about}\left(x\right)$

Originally x, renamed x:
  is assumed to be: RealRange(Open(0),Open(1))

$\mathrm{addressof}\left(x\right)$

$36893628512123923548$