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Context: I'm using Maxima on a platform that also uses KaTeX. For various reasons related to content management, this means that we are regularly using Maxima functions to generate the necessary KaTeX commands.
I'm currently trying to develop a group of functions that will facilitate generating different sets of strings corresponding to KaTeX commands for various symbols related to vectors.
Problem
I have written the following function makeKatexVector(x), which takes a string, list or list-of-lists and returns the same type of object, with each string wrapped in \vec{} (i.e. makeKatexVector(string) returns \vec{string} and makeKatexVector(["a","b"]) returns ["\vec{a}", "\vec{b}"] etc).
/* Flexible Make KaTeX Vector Version of List Items */
makeKatexVector(x):= block([ placeHolderList : x ],
if stringp(x) /* Special Handling if x is Just a String */
then placeHolderList : concat("\vec{", x, "}")
else if listp(x[1]) /* check to see if it is a list of lists */
then for j:1 thru length(x)
do placeHolderList[j] : makelist(concat("\vec{", k ,"}"), k, x[j] )
else if listp(x) /* check to see if it is just a list */
then placeHolderList : makelist(concat("\vec{", k, "}"), k, x)
else placeHolderList : "makeKatexVector error: not a list-of-lists, a list or a string",
return(placeHolderList));
Although I have my doubts about the efficiency or elegance of the above code, it seems to return the desired expressions; however, I would like to modify this function so that it can distinguish between single- and multi-character strings.
In particular, I'd like multi-character strings like x_1 to be returned as \vec{x}_1 and not \vec{x_1}.
In fact, I'd simply like to modify the above code so that \vec{} is wrapped around the first character of the string, regardless of how many characters there may be.
My Attempt
I was ready to tackle this with brute force (e.g. transcribing each character of a string into a list and then reassembling); however, the real programmer on the project suggested I look into "Regular Expressions". After exploring that endless rabbit hole, I found the command regex_subst; however, I can't find any Maxima documentation for it, and am struggling to reproduce the examples in the related documentation here.
Once I can work out the appropriate regex to use, I intend to implement this in the above code using an if statement, such as:
if slength(x) >1
then {regex command}
else {regular treatment}
If anyone knows of helpful resources on any of these fronts, I'd greatly appreciate any pointers at all.
Looks like you got the regex approach working, that's great. My advice about handling subscripted expressions in TeX, however, is to avoid working with names which contain underscores in Maxima, and instead work with Maxima expressions with indices, e.g. foo[k] instead of foo_k. While writing foo_k is a minor convenience in Maxima, you'll run into problems pretty quickly, and in order to straighten it out you might end up piling one complication on another.
E.g. Maxima doesn't know there's any relation between foo, foo_1, and foo_k -- those have no more in common than foo, abc, and xyz. What if there are 2 indices? foo_j_k will become something like foo_{j_k} by the preceding approach -- what if you want foo_{j, k} instead? (Incidentally the two are foo[j[k]] and foo[j, k] when represented by subscripts.) Another problematic expression is something like foo_bar_baz. Does that mean foo_bar[baz], foo[bar_baz] or foo_bar_baz?
The code for tex(x_y) yielding x_y in TeX is pretty old, so it's unlikely to go away, but over the years I've come to increasing feel like it should be avoided. However, the last time it came up and I proposed disabling that, there were enough people who supported it that we ended up keeping it.
Something that might be helpful, there is a function texput which allows you to specify how a symbol should appear in TeX output. For example:
(%i1) texput (v, "\\vec{v}");
(%o1) "\vec{v}"
(%i2) tex ([v, v[1], v[k], v[j[k]], v[j, k]]);
$$\left[ \vec{v} , \vec{v}_{1} , \vec{v}_{k} , \vec{v}_{j_{k}} ,
\vec{v}_{j,k} \right] $$
(%o2) false
texput can modify various aspects of TeX output; you can take a look at the documentation (see ? texput).
While I didn't expect that I'd work this out on my own, after several hours, I made some progress, so figured I'd share here, in case anyone else may benefit from the time I put in.
to load the regex in wxMaxima, at least on the MacOS version, simply type load("sregex");. I didn't have this loaded, and was trying to work through our custom platform, which cost me several hours.
take note that many of the arguments in the linked documentation by Dorai Sitaram occur in the reverse, or a different order than they do in their corresponding Maxima versions.
not all the "pregexp" functions exist in Maxima;
In addition to this, escaping special characters varied in important ways between wxMaxima, the inline Maxima compiler (running within Ace editor) and the actual rendered version on our platform; in particular, the inline compiler often returned false for expressions that compiled properly in wxMaxima and on the platform. Because I didn't have sregex loaded on wxMaxima from the beginning, I lost a lot of time to this.
Finally, the regex expression that achieved the desired substitution, in my case, was:
regex_subst("\vec{\\1}", "([[:alpha:]])", "v_1");
which returns vec{v}_1 in wxMaxima (N.B. none of my attempts to get wxMaxima to return \vec{v}_1 were successful; escaping the backslash just does not seem to work; fortunately, the usual escaped version \\vec{\\1} does return the desired form).
I have yet to adjust the code for the rest of the function, but I doubt that will be of use to anyone else, and wanted to be sure to post an update here, before anyone else took time to assist me.
Always interested in better methods / practices or any other pointers / feedback.
Seeing as the Maybe type is isomorphic to the set of null and singleton lists, why would anyone ever want to use the Maybe type when I could just use lists to accomodate absence?
Because if you match a list against the patterns [] and [x] that's not an exhaustive match and you'll get a warning about that, forcing you to either add another case that'll never get called or to ignore the warning.
Matching a Maybe against Nothing and Just x however is exhaustive. So you'll only get a warning if you fail to match one of those cases.
If you choose your types such that they can only represent values that you may actually produce, you can rely on non-exhaustiveness warnings to tell you about bugs in your code where you forget to check for a given a case. If you choose more "permissive" types, you'll always have to think about whether a warning represents an actual bug or just an impossible case.
You should strive to have accurate types. Maybe expresses that there is exactly one value or that there is none. Many imperative languages represent the "none" case by the value null.
If you chose a list instead of Maybe, all your functions would be faced with the possibility that they get a list with more than one member. Probably many of them would only be defined for one value, and would have to fail on a pattern match. By using Maybe, you avoid a class of runtime errors entirely.
Building on existing (and correct) answers, I'll mention a typeclass based answer.
Different types convey different intentions - returning a Maybe a represents a computation with the possiblity of failing while [a] could represent non-determinism (or, in simpler terms, multiple possible return values).
This plays into the fact that different types have different instances for typeclasses - and these instances cater to the underlying essence the type conveys. Take Alternative and its operator (<|>) which represents what it means to combine (or choose) between arguments given.
Maybe a Combining computations that can fail just means taking the first that is not Nothing
[a] Combining two computations that each had multiple return values just means concatenating together all possible values.
Then, depending on which types your functions use, (<|>) would behave differently. Of course, you could argue that you don't need (<|>) or anything like that, but then you are missing out on one of Haskell's main strengths: it's many high-level combinator libraries.
As a general rule, we like our types to be as snug fitting and intuitive as possible. That way, we are not fighting the standard libraries and our code is more readable.
Lisp, Scheme, Python, Ruby, JavaScript, etc., manage to get along with just one type each, which you could represent in Haskell with a big sum type. Every function handling a JavaScript (or whatever) value must be prepared to receive a number, a string, a function, a piece of the document object model, etc., and throw an exception if it gets something unexpected. People who program in typed languages like Haskell prefer to limit the number of unexpected things that can occur. They also like to express ideas using types, making types useful (and machine-checked) documentation. The closer the types come to representing the intended meaning, the more useful they are.
Because there are an infinite number of possible lists, and a finite number of possible values for the Maybe type. It perfectly represents one thing or the absence of something without any other possibility.
Several answers have mentioned exhaustiveness as a factor here. I think it is a factor, but not the biggest one, because there is a way to consistently treat lists as if they were Maybes, which the listToMaybe function illustrates:
listToMaybe :: [a] -> Maybe a
listToMaybe [] = Nothing
listToMaybe (a:_) = Just a
That's an exhaustive pattern match, which rules out any straightforward errors.
The factor I'd highlight as bigger is that by using the type that more precisely models the behavior of your code, you eliminate potential behaviors that would be possible if you used a more general alternative. Say for example you have some context in your code where you uses a type of the form a -> [b], though the only correct alternatives (given your program's specification) are empty or singleton lists. Try as hard as you may to enforce the convention that this context should obey that rule, it's still possible that you'll mess up and:
Somehow a function used in that context will produce a list of two or more items;
And somehow a function that uses the results produced in that context will observe whether the lists have two or more items, and behave incorrectly in that case.
Example: some code that expects there to be no more than one value will blindly print the contents of the list and thus print multiple items when only one was supposed to be.
But if you use Maybe, then there really must be either one value or none, and the compiler enforces this.
Even though isomorphic, e.g. QuickCheck will run slower because of the increase in search space.
set var1 A
set var2 {A}
Is it possible to check if variable is list in TCL? For var1 and var2 llength gives 1. I am thinking that these 2 variables are considered same. They are both lists with 1 element. Am I right?
Those two things are considered to be entirely identical, and will produce identical bytecode (except for any byte offsets used for indicating where the content of constants are location, which is not information normally exposed to scripts at all so you can ignore it, plus the obvious differences due to variable names). Semantically, braces are a quoting mechanism and not an indicator of a list (or a script, or …)
You need to write your code to not assume that it can look things up by inspecting the type of a value. The type of 123 could be many different things, such as an integer, a list (of length 1), a unicode string or a command name. Tcl's semantics are based on you not asking what the type of a value is, but rather just using commands and having them coerce the values to the right type as required. Tcl's different to many other languages in this regard.
Because of this different approach, it's not easy to answer questions about this in general: the answers get too long with all the different possible cases to be considered in general yet most of it will be irrelevant to what you're really seeking to do. Ask about something specific though, and we'll be able to tell you much more easily.
You can try string is list $var1 but that will accept both of these forms - it will only return false on something that can't syntactically be interpreted as a list, eg. because there is an unmatched bracket like "aa { bb".
I'm trying to implement a Search-Function using c++ and libpqxx.
But I've got the following problem:
The user is able to specify 4 different search patterns (each of them optional):
from date
till date
document type
document id
Each of them is optional. So if I want to use prepared statements I would need 2^4 = 16 different prepared statements. Well, it's possible, but I want to avoid this.
Here as an example what a prepared statement in libpqxx looks like:
_connection->prepare("ExampleStmnt", "SELECT * FROM foo WHERE title=$1 AND id=$2 AND date=$3")
("text", pqxx::prepare::treat_string)
("smallint", pqxx::prepare::treat_direct)
("timestamp", pqxx::prepare::treat_direct);
Therefore I also have no idea how I would piece such a prepared statement together.
Is there any other 'nice' way that I didn't think of?
The best you can do is to have four different ->prepare clauses, depending on how many search criteria are actually used, concatenate the criteria into your String, and then branch to one of the four prepare code blocks. (That will probably spook your style checker into thinking you are creating an injection vulnerability, but of course you aren't, as long as you insert only elements of the closed set os column names.)
Note that this isn't a very nice solution, but even Stephane Faroult (in The Art of SQL) says it's the best one possible, so who am I to argue?
I have a bunch of boolean options for things like "acceptable payment types" which can include things like cash, credit card, cheque, paypal, etc. Rather than having a half dozen booleans in my DB, I can just use an integer and assign each payment method an integer, like so
PAYMENT_METHODS = (
(1<<0, 'Cash'),
(1<<1, 'Credit Card'),
(1<<2, 'Cheque'),
(1<<3, 'Other'),
)
and then query the specific bit in python to retrieve the flag. I know this means the database can't index by specific flags, but are there any other drawbacks?
Why I'm doing this: I have about 15 booleans already, split into 3 different logical "sets". That's already a lot of fields, and using 3 many-to-many tables to save a bunch of data that will rarely change seems inefficient. Using integers allows me to add up to 32 flags to each field without having to modify the DB at all.
The main drawback that I can think of is maintainability. Someone writing a query against the database has to understand the bit convention rather than being able to go after a more human readable set of columns. Also, if one of the "accepted payment types" is removed, the data itself has to be migrated rather than just dropping the a column in the table.
This isn't the worst, but there might be a better way.
Define table called PaymentTypes
id, paymentId, key (string), value (boolean)
Now you just populate this table with whatever you want. No long column of booleans, and you can dynamically add new types. The drawback to this is that default of all booleans is NULL or false.
Not sure what database you're using, but MySQL has a set type.
If you could limit your use case to one or more sets of values that can only have one bit true at a time, perhaps you could use enums in your database. You would get the best of both worlds, maintainable like btreat notes, and still smaller (and simpler) than several booleans.
Since that's not possible, I'd agree with your initial assment and go with a bitfield. I would use/create a bitfield wrapper however, so that in your code you don't deal with flipping and shifting bits directly - that becomes difficult to maintain and debug, as btreat says - but instead deal with it like a list or dictionary and convert to/from a bitfield when needed.
Some commentary on enums/bitfields in Django
I think the previous posters were both correct. The cleanest way to do it in a "relational" database would be to define a new relation table that stores payment types. In practice though, this is usually more hassle than it's worth.
Using enums in your code and using something similar in the DB (check constraints in Oracle, AFAIK) should help keep it maintainable, and obvious to the poor soul who's job it will be to add a new type, many many years after you've left