|Complex number capability in non-HP machines|
Message #1 Posted by Palmer O. Hanson, Jr. on 5 July 2008, 11:13 p.m.
In a May 17 thread "HP 35s successor?" Rodger Rosenbaum asked:
Since no one else has responded to Roger's question with respect to non-HP calculators I decided to try. My answer is limited to machines to which I have access. I wrote separately to Rodger noting that several machines in the TI product line had what I thought were substantial complex number capabilities. He responded
Has there ever been a non-HP calculator with excellent complex number capability?
The ones I've seen have been abysmal.
I have a TI86, and as you say, it has comprehensive complex variable
capability. But, my experience with calculators other than HP or TI
has been that if they have any complex capability at all, it is rudimentary.
My Casio fx-115D offers the four arithmetic functions and 1/x.
My Casio fx-115ES (currently available) offers the four arithmetic functions, 1/x, x^2, x^3, argument and conjugate.
My Sharp EL-515S has a complex mode which offers only the four arithmetic functions.
My Sharp PC-1261 Pocket Computer does not offer a built-in complex capability. The PC-1260/1261 Instruction Manual includes fifteen sample programs none of which provide complex number capabilities. Sharp's Application Software for PC-1250/CE-125 includes twenty BASIC programs. Again, none of them provide complex number capabilities. The book Mathematics Library - Application Software for the Sharp EL-5500 and PC-1403 Scientific Computers by Maurice E. T. Swinnen and David Thomas (Systems Publications, 1987) offers five BASIC programs for complex number calculations:
Program 1. Sine, cosine and tangent and the inverses.
Program 2. The four arithmetic functions plus polar to rectangular and rectangular to polar conversions.
Program 3. Square, square root, reciprocal, natural log, e^x, plus polar to rectangular and rectangular conversions.
Program 4. y^x, y^(1/x), log to the base y of x, plus polar to rectangular and rectangular to polar conversions.
Program 5. Complex Roots
These programs should be compatible with the PC-1261. I have successfully run parts of the first three on my PC-1261. I have successfully run the Simultaneous Equation program from the book on my PC-1261 and converted it for use with my Radio Shack Model 100 and with my Texas Instruments CC-40.
The book provides example calculations which can be used to verify that the programs have been entered correctly. For the first program the sine of 3 - 5i is calculated as 3.883848618 -74.10151768i which does NOT agree with the result obtained with my TI-85 and HP-28S. The first line of the program sets degree mode. If I set radian mode instead I get results which agree with my TI-85 and HP-28S. Degree mode is also set at the beginning of programs 3 and 4. As a result the example calculation for any function which uses real trigonometric functions as a part of its solution will not agree with results from machines which use radian mode. Setting radian mode will result in agreement. I leave any discussion over the merits of the use of degree or radian mode to others more skilled in the use of complex functions than I am.
To demonstrate the arcsine fnction the book asks the user to enter 3.8838 - 74.1i (a truncated version of the sine of 3 - 5i when using degree mode) and see 3.000023834 - 4.99997943i as the answer. There is a better way to demonstrate the arcsine after having calculated the sine. The input routine stores the real part in R and the imaginary part in M. Each complex trigonometric function stops with the real part in O and the imaginary part in P. Since the PC-1261 accepts variables as the response to INPUT statements the user can enter the complete answer from a previous trigonometric function by responding with O and P for the real and imaginary inputs. A user who does that to calculate the arcsine after having calculated the sine of 3 - 5i in degree mode will see the result 3.000000101 - 4.999999881 .
The arithmetic functions in the second program stop with the result in the locations where the first complex number is entered for an arithmetic function. The INPUT statement of the PC-1261 does not display those values; however, if ENTER is pressed the INPUT statement essentailly acts as a non-operation and the existing values in the input locations are preserved. The INPUT statement on my Radio Shack Model 100 reacts in the same way. To preserve the previously stored values on the CC-40 the user must use the response Shift ENTER.
I have not worked with the fifth program.
The TI Machines:
Rodger noted that the TI-86 has a comprehensive capability. Several other TI machines also offer comprehensive capability.
The TI-58/58C/59 offer complex calculations if either the Master Library module or the Electrical Engineering module is in place. Three sub-programs offer the four arithmetic functions, x^2, square root, 1/x, e^x, ln x and sin, cos, tan and the
inverses. The functions are selected from sub-programs with the user defined keys (A through E and A' through E'). Prompting to the display is not available since the TI-59 does not offer alphanumerics in the display. The user can use the label card in the slot above the top row of keys. That requires shuffling the appropriate cards in and out of the slot. Frank Fujimoto recognized the various limitations of that method and wrote a Complex Keyboard program which was published in the Volume 4 Number 4 (July/August 1980) issue of PPX Exchange. His program offers access to all of the complex functions in the memory module. Seven complex memory registers are provided which can be accessed with Store, Recall, Exchange, Sum, Inverse Sum, Product and Inverse Product functions. I recommend that the user change step 026 of the program from B to INV and step 117 of the program from INV to B. Then the user can perform complex mathematics with the same keyboard sequences that would be used for real functions except that SBR must be pressed before each complex function.
The CC-40, the TI-74 and the TI-95 all offer an extended capability as part of their Mathematics Library modules including x^2, SQRT, 1/x, LN, EXP, SIN, COS, TAN, ASIN, ACOS, ATAN, y^x and x root of y. The CC-40 and the TI-95 also offer LOGyX. The TI-74 does not. A curious addendum to the TI-74 manual states:
The addendum then goes on to offer a program to calculate LOGyX. Somehow, I believe that a user of the complex capability will be able to keep track of which function to use.
The Complex Functions Program (COMPF) contains two complex logarithm options, LN(X) and LOGyX . LOGyX calculations are needed less often than LN(X) calculations. To prevent you from accidentally selecting LOGyX when you intend to calculate LN(X), th LOGyX option (Option 20) has been disabled. Selecting this option results in an 'E1 Syntax' error message.
The TI-95 also offers the hyperbolics and their inverses. The CC-40 and the TI-74 offer a Complex Systems program (COMPS) which solve a system of nxn simultaneous equations with complex coefficients. The baseline 6K versions of the machines will handle up to 12x12 complex systems. The program is easy to use with excellent prompting.
The first page of the section on complex numbers in the TI-68 Guidebook states: "A major innovation of the TI-68 is its extensive complex number capability. You have the freedom to enter complex numbers wherever they are applicable without 'mode' limitations. Few other calculators evn approach the versatility of complex numbers provided by the TI-68." How much salesmanship and how much actual capability? I haven't done any substantial amount of work with the TI-68. I do know that the method of entering and displaying is similar to the HP-48. I can't compare with the HP-15 or the HP-42 since I don't have either of those.
Many of the TI graphic machines offer complex number capabilities. The TI-83 offers a relatively wide range of functions but it does not offer the trigonometric functions. I have not tested my TI-84. The TI-85 offers all the capabilites of the TI-83 and adds the trigonometric and hyperbolic functions and their inverses, polynomial solutions, simultaneous equation solutions, sorting based on modulus, and the sum or product of the elements of a list.
A Question on HP Capabilities
I haven't been able to use memory register arithmetic with complex functions in Algebraic mode on the HP-35S. I haven't found a reference in the manual which indicates that should be so. I may be doing something incorrectly. If anyone knows how to do that please let me know.