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Formatted Tables
To summarize a set of results, it is useful to display them in a table. Consider the following set of values.
When displaying tabular output, we often need to pad all numeric values in each column to the same length. **PaddedForm** controls the number of displayed digits and **ToString** converts all numbers to strings.
We project out the *n*th column of **data** as a (column) matrix using , *e.g.*,
and specify a different number of displayed digits for each column.
Using **GridBox** and **StyleBox** allows fine control of the display of tabular data to produce a more distinctive table.
**FilterOptions** passes valid options from **opts** to **GridBox** and **StyleBox** respectively. For example,
It is easy to add other descriptive columns to tables. Defining
converts strings to vertical **GridBox**es.
We now display the following data,
in a tabular format.
The final example is taken from group theory. The Euclidean Lie algebra has the Lie subalgebras and known as and which generate rotations and translations respectively. In terms of infinitesimal generators, we have
and
*Mathematica* implementation of these differential operators is straightforward.
Note that we associate the rotation operators with *R* and the translation operators with *P** *(see Section 2.4.10 of *The Mathematica Book*). This way we can clear all translation operators using **Clear[***P***]**.
Introducing the commutator operator as
the following routine equates the commutator of two differential operators, , to an arbitrary linear combination of all the operators in an algebra and then determines the coefficients (**c**) using **SolveAlways**.
For example, in the Euclidean Lie algebra (keeping the operators in unevaluated form using **HoldForm** and **Unevaluated**),
we find that .
Here is the table of commutators in an easily readable format.
It is apparent from this table that translation operators commute but rotation operators do not.
Converted by *Mathematica*
May 8, 2000
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