Sum in Mathcad Prime

[ValeryOchkov]

Is it an error in Mathcad Prime?

[StuartBruff]

Odd, Valery.  It seemed to work on my Prime 7.0.0.0 Trial.

Stuart

[LucMeekes]

Stuart,

Not odd. The 'magic' is in the fact that Valery put an evaluation (=) after the range definition of i. That changes the range to a vector. This is a special feature of Prime.

With that evaluation your sheet shows:

The summation with a single i at its bottom, requires i to be a range; vector is not allowed.

Success!
Luc

[StuartBruff]

---

@LucMeekes wrote:

Stuart,

Not odd. The 'magic' is in the fact that Valery put an evaluation (=) after the range definition of i. That changes the range to a vector. This is a special feature of Prime.

With that evaluation your sheet shows:

The summation with a single i at its bottom, requires i to be a range; vector is not allowed.

Success!
Luc

---

Ah, of course.  Thanks, Luc.  I definitely need those new glasses! 

I did know about this "feature", but I tend to avoid putting evaluation operators at the end of definitions, precisely because of such side effects.   I don't think that it's entirely clear from the rhs of the evaluation what the definition will actually assign to the variable.

IMO, for this purpose, they'd have been better off implementing a vec function that converts any argument to a vector. 

I believe that I've suggested in the past that Mathcad ought to auto-iterate over vectors (or arrays, in general) in such cases.   I vaguely recall having a discussion about this some time ago and there being some objections - but I can't remember what they were.  I'll have to have a think about it.  I vaguely recall Tom Gutman and jMG commenting ...

However, the feature request for an automatic vector product still stands.  🙂

Cheers,

Stuart

(I also wonder if min and max ought to return the first and last elements of a range ...I can think of a few uses for this capability?)

[ValeryOchkov]

Thanks, Luc and Stuart!
But my thanks are not simple, but ironic!
Previously, I had one question, and following your response, I have two questions!

[StuartBruff]

---

@ValeryOchkov wrote:

Thanks, Luc and Stuart!
But my thanks are not simple, but ironic!
Previously, I had one question, and following your response, I have two questions!

---

Затем после нескольких ваших вопросов, вы будете иметь много, много вопросов, чтобы думать!  😈

Stuart

[LucMeekes]

"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 tend to avoid putting evaluation operators at the end of definitions" :

I fully agree, it is a common source of problems, occasionally seen here on the forum.

"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. To get the first of a vector V you simply use V[ORIGIN and the last is had with V[last(V).

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...

Luc

[o.svahn]

Hi there 

see attached 

Regards 

Owe 

[StuartBruff]

<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>

[StuartBruff]

Whilst noting Luc's ( @LucMeekes ) comments below, I thought I'd revisit the notion of min and max applied to a range, and added the string type so it didn't feel left out.  I've used the MP11 built-in function vec to handle the conversion from range to vector, rather than the previous iteration over the range.

Of note is that the max and min values given for a range are not the start and end values of the range, but, rather, the minimum and maximum values of the expanded range (which might not include the end value). 

And a slight addendum to handle nested arrays.

Just food for thought ...

Stuart

[Werner_E]

😈👿👹😈👿👹😈👿👹😈👿👹😈👿👹

[StuartBruff]

Hi Werner,

I was just thinking about posting a version using my range-expanding, nested version of vec. That seemed reasonable, and I’ll add it when I’m next near a computer.

I wasn’t sure, however, about the validity of finding the min & max of an array whose elements are of mixed types (eg, real & complex, or real & string).

Complex numbers don’t have a natural sort order, although I’d be tempted to opt for sorting on real then imaginary rather than modulus then argument.

Strings and traps have several obvious options. First, squawk like a drunk parrot and raise an error (status quo). Second, return separate max and min, NaN for no value if string/number not present. Third, min/max on numbers and character code points. Fourth, min/max on numbers and string representations of numbers (eg, “3” > 2), and the Third option for mother strings. I’m sure there are other possibilities.

Stuart

(Sent from iPhone)

[Werner_E]

I was just in the mood to be a little mean. 😉

BTW, I just asked the KI of DeepL to rephrase the above sentence and had chosen 'Academic' style.

One of the proposals was

"The impetus behind this decision was a spontaneous inclination towards inflicting a degree of unpleasantness upon the subject."

Wow! I needed a translation app to understand what it means ....

According the desired results when given mixed numbers and strings I sure don't know what a max or min function actually should return - replace characters by ASCII or UNIcode? Error message, try to interpret the the string like in

? 🙂

Guess the error message given by Prime is good as any. Interesting is that we get different error messages depending on if we mix scalars and ranges or rather scalars and strings. haven't thought about non-real numbers -  already had too much red wine (or as DeepL's KI phrases: "It has been determined that a considerable amount of red wine has already been consumed.") 😉

Well, then .. Cheers!

BTW, Prime's "sort" follows the algorithm you outline - sorting for real parts and only if they are equal consider the imaginary part. Personally I would see more logic (if any) in sorting by magnitude and consider the argument in case of equal magnitude. This would mean that a number is "larger" the further away its from the origin.