Re: Mutiple delete in lists

*To*: mathgroup at CHRISTENSEN.CYBERNETICS.NET*Subject*: [mg374] Re: [mg360] Mutiple delete in lists*From*: Dana_Scott at POP.CS.CMU.EDU*Date*: Wed, 28 Dec 94 13:41:11 EST

The problem in understanding selections is that there is an inconsitency in the design of Mathmeatica. You should have looked at the on-line help to check the syntax. We find: In[1]:= ??Delete Delete[expr, n] deletes the element at position n in expr. If n is negative, the position is counted from the end. Delete[expr, {i, j, ...}] deletes the part at position {i, j, ...}. Delete[expr, {{i1, j1, ...}, {i2, j2, ...}, ...}] deletes parts at several positions. Attributes[Delete] = {Protected} This means that the "official" notation for a delete of the nth term of an expression is actually Delete[expr, {{n}}]. This is clearly too tiresome to type, so we abbreviate it as Delete[expr, n] with a cute expansion of meaning to the negative numbers (as in Drop). Now a list such as {i, j, ...} is a PATH in a "tree". This is nice, since all expressions are of the form Head[Part1, Part2, ...], where each Parti is again of the same form until we come to a symbol (= atom). Therefore, {i, j, ...} means to take the ith part of the expression, then take the jth part of that, and then the next part as indicated, and so on. Hence, the offical notation for removing a deeply embedded subtree is Delete[expr, {{i, j, ...}}], but again, two curlies are too much to type, so we use an abbrivated form Delete[expr, {i, j, ...}]. Finally, when we want to drop a whole batch of subtrees, we just have to go ahead and type Delete[expr, {{i1, j1, ...}, {i2, j2, ...},...}]. So here is what you wanted to do first: In[2]:= Delete[Range[10], {{2},{3}}] Out[2]= {1, 4, 5, 6, 7, 8, 9, 10} But if we have a real tree and not just a flat list, then we get a result like this: In[3]:= Delete[{{1,2},{3,4}}, {2,1}] Out[3]= {{1, 2}, {4}} Understand?? Well, now look at the explanation of Part: In[9]:= ??Part expr[[i]] or Part[expr, i] gives the ith part of expr. expr[[-i]] counts from the end. expr[[0]] gives the head of expr. expr[[i, j, ...]] or Part[expr, i, j, ...] is equivalent to expr[[i]] [[j]] .... expr[[ {i1, i2, ...} ]] gives a list of the parts i1, i2, ... of expr. Attributes[Part] = {Protected} This shows a QUITE DIFFERENT convention of using curlies that does not agree with the Delete conventions at all. Moreover, there is no simple notation for getting a list of several subtrees. Look, WRI, if Delete gives an expression with a selection of subtrees removed, then Part should have a facility for exactly getting just the subtrees that were removed. There ought to be a natural ecology of expressions as trees! And if we can write Part[expr, i, j, ...] for moving down a path, we ought to have been able to write something like Delete[expr, i, j, ...] for the corresponding destruction operation. Do people agree that there is a design fault here?

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