# Physics updates (Oct/2) and products of powers of same base

October 02 2013
Maple

4

Hi

It's been 1 and 1/2 months since updates for the Maple Physics package have been distributed in the Maplesoft webpage "Maple Physics: Research & Development".  The number of Mapleprimes Physics posts that got rapidly addressed in this way is already large, some of them are listed here.

The experience has been great. Suggestions are implemented and problems are fixed in a couple of days since they were posted here, and the changes are made available to everybody right away. This is moving the focus of developments into the topics people are actually working on, with feedback and related downloadable updates happening every week.

The recent Physics updates are mostly related to quantum mechanics, an advanced topic, but part of the resulting functionality is interesting for algebraic computations in general. To mention but one: the "automatic combination of products of powers of same base" is now optional.

Recalling, by default, in Maple, if you enter xn xm, in order to receive x(n+m). you need to use the combine command (the same happens with products of exponentials). The idea behind the Maple approach is to give you more control over the steps. On the other hand, depending on your problem, the automatic combination of powers of the same base is a desired automatic simplification - this is for instance the Mathematica approach.

In today's update of Physics, a new Setup option, 'combinepowersofsamebase', is implemented, so that this automatic simplification is now optional. If set to true (> Setup(combine = true))you enter xn xm or exp(A) exp(B) and you respectively receive x(n+m) and exp(A+B). Being able to turn this automatic simplification ON and OFF comes in handy in varied situations.

Those more familiar with noncommutative objects (e.g. Matrices), also know that the combination of exp(A) exp(B) is not valid when the exponents A and B do not commute, unless A and B commute with their commutator AB - BA, in which case the combination can be done using Glauber's formula (also related to Hausdorff's formula). All of these cases have been implemented too.

In summary, in the latest update of Physics the combination and expansion of powers and exponentials using combine and expand now takes into account the noncommutative character of the exponents and the value of their commutator, and there is the option of having this combination happening automatically, for both noncommutative and commutative algebraic objects in general.

Other relevant changes more related to Physics are described in the PhysicsUpdates.mw distributed inside the zip that contains the updated Physics.mla linked in the "Maple Physics: Research & Development" webpage.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

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