<I wrote this at the time but forgot to push the Post button>
@LucMeekes wrote:
"I did know about this "feature",":
It's not a feature. The evaluation of a range turning it into a vector is not on the published list of methods to create a vector (See Prime Help under: Vectors, Matrices, and Tables > Creating Arrays and Tables > Methods for Defining Arrays), so it's an undocumented side effect that creates problems for users
I believe the traditional name for such cases is "undocumented feature". "Undocumented side-effect" sounds less ... positive. I quoted "feature" to imply that I was aware of its status.
"I also wonder if min and max ought to return the first and last elements of a range ...":
No, certainly not. min() and max() serve to get the lowest and highest values of an array (vector or matrix). Those are not necessarily the first and the last respectively.
After a few hours sleep, I agree that min and max are the wrong choices for the first and last elements of a range variable. However, that's more for a technical reason than the underlying principle. What I believe should happen is:
Given that:
- a range is a Mathcad distinct data object,
- a range is an implicit specification for a sequence of values,
- the range specification is either start..stop or start,step..stop,
- a range variable holds a range,
- rv is a variable that holds a range (ie, is a range variable),
then:
first(rv) should return the start value of the range.
last(rv) should return the stop value of the range.
<suggest name, second?> should return the second value of the range.
min(rv) should return the minimum value of the evaluated sequence.
max(rv) should return the maximum value of the evaluated sequence.
For. rv:=0,1..π, I'd expect:
first(rv)= 0, min(rv) = 0; last(rv) = 3.141, max(rv) = 6.
Under the symbolic processor, I'd expect:
last(rv)→π.
I'd also like a function rng2vec that, analogously to str2vec, returns a vector containing start, step, and stop. The name could be improved, as it could be interpreted as meaning it expands the range. It goes without saying, but I'll say it anyway, that there should be an inverse function vec2rng that creates a range from a 3-vector.
And while I'm high on featurehol, I'd also like range types to be a bit smarter and:
- accept string arguments, generating a suitable sequence (eg, "a","c"..g should produce ["a","c","e","g"].
- accept multiple-step arguments and generate the corresponding polynomial sequence (ie, n steps = nth order poly).
Oh, and if it helps overcome any problems with using vectors as indices, I'd like the sequence to be a specific data type, separate from the vector or array. A sequence should be an extension of a range in terms of appearance and use. That is, enter a list of values separated by commas (and possibly semicolons); (start,step..stop) type ranges should be enclosed in parentheses to remove ambiguity).
Plus, I want general sequences restored in for loops, and sequences made into a proper data type that can be assigned to variables.
"I also wonder if min and max ought to return the first and last elements of a range ...":
To get the first of a vector V you simply use V[ORIGIN and the last is had with V[last(V).
I, like you, have a library of Prime Express functions that I use to get around the lack of programming. Some of them are based upon, but not identical to, the functions that can be found in many functional programming languages, such as Haskell, or programming languages that have support for functional programming. I do, however, try to take into account that Mathcad Prime is not a true functional programming language (especially in its Express form) and that Mathcad has its differences in how data is handled.
I use head and tail to do what you suggest (a break with many conventions for tail). head(a) returns a non-array unchanged, the value of the first element of a vector, and the first row of a non-vector array. tail(a) returns "empty" for a non-array, the value of the last element of a vector, and the last row of a non-vector array.
I use first(a,n) and last(a,n) to return the first and last, respectively, n rows of array a.
Now if last() wasn't already used to get the highest index of a Vector, I might have advocated the functions first() and last() for those element values, but alas...
Pardon me whilst I recover from an outpouring of hysterical laughter. 🤣
Given Mathsoft's and PTC's penchant for breaking things, I have no problems whatsoever in changing the meaning of last - breaking sequences in for loops is an apposite example.
Compared to some of the major changes that have been made to Mathcad over the years, some requiring significant rewrites, I'll hazard that this change should be almost trivial for most users. I've always found the name unintuitive for its purpose, anyway, and hardly ever use it.
It would (should!) be easy enough to change last upon reading older worksheets to some suitable new name (eg, end, lastindex) and annotating the change. Indeed, I vaguely recall discussion along the lines of just missing the value out and Mathcad inferring that the author means the last element. I normally use -1 in my functions (in general, being a zero-index aficionado, I use negative numbers to count backward from the end of an array dimension).
Stuart
See https://support.ptc.com/help/mathcad/r7.0/en/index.html#page/PTC_Mathcad_Help%2Frange_operators.html%23wwID0E6LZR
Note that a range is specific data type in the Mathcad Prime 7 XML worksheet format.
<ml:define>
<ml:id xml:space="preserve" labels="VARIABLE">k</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:apply>
<ml:minus/>
<ml:id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">n</ml:id>
<ml:real>1</ml:real>
</ml:apply>
</ml:range>
</ml:define>
Interestingly, the word sequence crops up for a function's parameter list, which is one of the potential uses I had in mind for sequences (primarily as a means of implementing variable number parameter lists).
<ml:define>
<ml:function>
<ml:id xml:space="preserve" labels="VARIABLE">ints</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve" labels="VARIABLE">n</ml:id>
</ml:boundVars>
</ml:function>
<ml:apply>
<ml:id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">matrix</ml:id>
<ml:sequence>
<ml:id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">n</ml:id>
<ml:real>1</ml:real>
<ml:id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">max</ml:id>
</ml:sequence>
</ml:apply>
</ml:define>
