How to construct pure expressions

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg631] How to construct pure expressions
• From: Xah Y Lee <xyl10060 at fhda.edu>
• Date: Sun, 2 Apr 1995 21:08:39 -0700 (PDT)

```How to write a function ExprGenerator[] such that, for example

ExprGenerator[x,{3,3,3,3}] will return

x[
x1[
x11[
x111[ x1111, x1112, x1113],
x112[ x1121, x1122, x1123],
x113[ x1131, x1132, x1133]
],
x12[
x121[ x1211, x1212, x1213],
x122[ x1221, x1222, x1223],
x123[ x1231, x1232, x1233]
],
x13[
x131[ x1311, x1312, x1313],
x132[ x1321, x1322, x1323],
x133[ x1331, x1332, x1333]
]
],
x2[
x21[
x211[ x2111, x2112, x2113],
x212[ x2121, x2122, x2123],
x213[ x2131, x2132, x2133]
],
x22[
x221[ x2211, x2212, x2213],
x222[ x2221, x2222, x2223],
x223[ x2231, x2232, x2233]
],
x23[
x231[ x2311, x2312, x2313],
x232[ x2321, x2322, x2323],
x233[ x2331, x2332, x2333]
]
]
];

In general, the list will have following properties:
* All expressions has a head that starts with the letter x.

* The number after x correspond to the position list of that element. For
example, x211 is an element with position {2,1,1}.

* The number of digits following x correspond to the level of that element.
For example,  x111, x211 are elements in level 3, x1 or x2 is in level 1,
x is in level 0 because it has zero digits following x.

I spend 2 hours on this with no clear solution. But, one learns a lot
about mma structures and commands that manipulate them.

Xah Lee
Venus & Xah Love Factory
Quote of the day: To understand infinity, you need to know love. --Venus.

```

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