71 & 75 Math ROMs, Series 80 Matrix ROM

[Valentin Albillo]

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Hi, J-F:

(06-02-2018 01:27 PM)J-F Garnier Wrote:  Updated document with full comparison of all the features of the 71 and 75 Math ROMs :
hp71_75.pdf

Thanks for this second draft, which surely is quickly approaching v1.0. A few comments in an eminently constructive mood, please don´t take any of it as criticism or patronizing on my part or anything such.

1) As far as I remember, you could also specify zero rows and or zero columns whole matrices, not just subarrays. You could even matrix-multiply, say, a 5x0 matrix and a 0x3 matrix, in that order, and you'd get a 5x3 matrix as a result (all its elements "created out of nowhere" would be assigned the value 0).

2) The HP-71B Math ROM can't compute the determinant of a complex matrix. For example:

      1 DESTROY ALL @ OPTION BASE 1 @ COMPLEX A(3,3) @ MAT A=IDN @ MAT DISP A;
      2 DISP DET(A)

      >RUN

             (1,0) (0,0) (0,0)
             (0,0) (1,0) (0,0)
             (0,0) (0,0) (1,0)

      ERR L2:Data Type

Yet another useful, expected feature missing for unfathomable reasons (remember those 5K of ROM unforgivably left to waste ?).

3) The ease of use of complex functionalities in the HP-71B is an order of magnitude over the ones in the HP-75C, which are clumsy, time-wasting and RAM-wasting in the extreme. With the 75C Math ROM , computing any non-trivial expression involving complex values becomes an extreme chore which eats tons of RAM if programmed (think evaluating the Mach number's formula featured in many classic Owner's Handbooks using complex values).

Besides, the functions left out in the 75C's, namely SIGN and ABS aren't as trivial as those for the real case. For instance, for real numbers, ABS(X) is just X if positive, -X if negative, but for the complex case ABS(Z) = SQR(REPT(Z)^2+IMPT(Z)^2), which is significantly harder to evaluate and thus more useful if available as a keyword. Same with SIGN for the complex case as compared to the real case. There's also the point of IMAGE with complex specifiers, which the 71B has but not the 75C, further complicating the essential output of complex scalars, vectors and matrices.

4) The implementation of FNROOT and INTEGRAL in the HP-71B Math ROM is not just "better" than the one for the HP-75C, it's dramatically better, actually on a completely different league, considering that:

      - 75C: you can't use them right from the keyboard, you must create a program with at least one or more lines to define your function and at least an additional line including the FNROOT/INTEGRAL call.

      - 71C: you can do that, of course, but you can also use the FNROOT/INTEGRAL right from the keyboard with no need to create any program or UDF whatsoever. For instance, to find a root of x\(^3\)-6*x-2 = 0, simply execute this from the command line:

      >FNROOT(0,3,FVAR^3-6*FVAR-2)

             2.60167913189

As seen in my latest challenge, S&SMC#23, the length of the expression being solved/integrated is limited only by available memory, with no program or user-defined function needed.

      - 75C: you can't nest FNROOT with other FNROOT or INTEGRAL with other INTEGRAL, which means you can solve just a single equation in a single variable or compute a simple integral, not a double, triple, etc. integral. Further, you can call FNROOT from INTEGRAL and vice versa, but you must write a program and create at least two User-defined functions.

      - 71B: you can nest FNROOT up to 5 levels, which allows you to solve a non-linear system of up to 5 equations in 5 unknows, and you can nest INTEGRAL up to 5 levels as well, which allows computing double, triple, up to quintuple integrals. For instance, you can compute this double integral from the command line:

      >INTEGRAL(0,1,0,SIN(IVAR^2*INTEGRAL(0,IVAR,0,EXP(IVAR^2))))

             .280631692621

This is too much of an improvement over the 75C's, not only in ease of use but essentially in capabilities, to label it simply as "better" and so its importance ought to be pointed out.

Finally, I feel that there are probably many other significant differences in functionality in both the functions already considered and the ones left untouched, for instance in how FOUR works with real and complex data, if the tricks available in the 71B also work in the 75C, how MAT A=PROOT exactly works, and how matrix conjugate transposes work in the 75C, but without having either a 75C (real or emulated) at hand or studying the 75C Math ROM in depth I can't say for sure.

Thanks again for your effort in producing this excellent document, which will surely become a worthwhile reference.

Regards and have a nice weekend.
V.
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