Questions about DownValues which specify function definitions for symbols.

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18
votes
3answers
549 views

What are the requirements for a well behaved indexed variable? Subscript, ToExpression, Downvalue?

On writing this answer I needed to call a function, (NonlinearModelFit) with an unknown number of parameters. We have learned that we should not use ...
19
votes
5answers
3k views

The difference between 0. and 0

I have a function for which 0 is a special case: f[A___, 0, B___] := 0 But since I am doing numerics, sometimes in the course ...
45
votes
2answers
1k views

How is pattern specificity decided?

Mathematica has a notion of pattern specificity, which is a partial ordering on patterns. The rules (e.g. DownValues, SubValues,...
9
votes
2answers
581 views

How to get the list of defined values for an indexed variable?

I would like a table with rational indexes - thus it would be practical to use a dictionary, which, in Mathematica are implemented with the indexed variables. I would like to be able to do: ...
2
votes
1answer
142 views

How do I constrain movement for lists of Locators using 2nd argument of Dynamic?

I need to display edge labels of a graph in a way that allows the edge labels to be moved. Locator seems the simplest and most obvious function to use. My ...
2
votes
2answers
219 views

How to unprotect GeneratingFunction

I'm trying to add custom downvalues for GeneratingFunction, and to do so I thought I just had to Unprotect it. However, that ...
2
votes
1answer
142 views

Can a Symbol own OwnValues that don't evaluate when it's the head of an expression?

I believe this a question that most of us have encountered when we were beginners but forgot when we got more familiar with Mathematica. We know the notation $y=y(x)$ for functions, where $y$ here ...
11
votes
1answer
398 views

Selectively clear DownValues

How can I clear a subset of a symbol's DownValues ? For example, suppose I have created some DownValues for $f$ like this: ...
0
votes
3answers
121 views

How to initialize downvalues from a list?

The For expression below initializes downvalues of a variable a from the values in a list ...
4
votes
4answers
379 views

How to do memoization together with evaluation of a complicated function

UPDATE 2: much shorter version Given a list of paired indices {i, j}={{1,2}, {3,4}, …}, I need to first evaluate a rather complicated function test[i,j,x] (because ...
6
votes
1answer
203 views

How can I define a ⊕ operator?

What is wrong with the following code? CirclePlus := SparseArray[Band[{1, 1}] -> {##}] & a_ ⊕ b_ := CirclePlus[a, b] SetDelayed::write: Tag Function in ...
4
votes
1answer
159 views

Multiple down-values with exactly the same lefthand side

I was working on an answer to this question, when I was sidetracked by what I bring up here. I wanted a function, which when given a string representing a binary number, would convert the string to a ...
4
votes
2answers
401 views

Overloading conjugate operator for a particular function

I trying to modify the behaviour of the built-in Conjugate[] operator on a particular function I have defined, to take into account that some of its variables are ...