dwrfielder@dahlia.waterloo.edu (Dave Fielder) (06/22/91)
Does anyone know as to why the 48sx does not like negatives in the COMB function. They should be valid. eg. COMB(-8,4) should return (-8)(-9)(-10)(-11)/(4!) = 330. It isn't like HP to screw up on important functions like this. Or, then again, is it...Hmmm :^). --Dave. PS. What happened to the guy who was going to post those stats routines of his. I'm still interested if you can still post them.
Dan_Ciarniello@cc.sfu.ca (06/22/91)
>Does anyone know as to why the 48sx does not like negatives >in the COMB function. They should be valid. > >eg. COMB(-8,4) should return (-8)(-9)(-10)(-11)/(4!) = 330. > >It isn't like HP to screw up on important functions like this. >Or, then again, is it...Hmmm :^). > > >--Dave. HP didn't screw up on this function. COMB(x,y) returns the number of possible combinations of x distinct objects taken y at a time. In this context negative numbers make no sense (how many objects are -8). Also, the factorial function is defined only for the positive integers (including 0). It is not defined for the negative integers. The gamma function *is* defined for negative numbers but it is undefined for the negative integers (the 48 gives an Infinite Result error). Dan Ciarniello Physics Department Capilano College North Vancouver, B. C.
dwrfielder@dahlia.waterloo.edu (Dave Fielder) (06/26/91)
In article <3238343@cc.sfu.ca> Dan_Ciarniello@cc.sfu.ca writes: >>Does anyone know as to why the 48sx does not like negatives >>in the COMB function. They should be valid. >> >>eg. COMB(-8,4) should return (-8)(-9)(-10)(-11)/(4!) = 330. >> >HP didn't screw up on this function. COMB(x,y) returns the number of >possible combinations of x distinct objects taken y at a time. In >this context negative numbers make no sense (how many objects are >-8). > >Also, the factorial function is defined only for the positive integers >(including 0). It is not defined for the negative integers. The gamma >function *is* defined for negative numbers but it is undefined for the >negative integers (the 48 gives an Infinite Result error). > Well, perhaps then COMB should not be defined only for the positive integers but rather be extended. (r) ie. n is a symbol read "n to r factors", is defined as follows: (r) n =n(n-1)(n-2)...(n-r+1), r>0 (0) n =1. (r) If n is a non-negative integer, n is the number of arrangements, or permutations, of n different things taken r at a time, for which another common symbol is nPr. In particular, (n) n = nPn is the number of arrangements or permutations of n different things taken all at a time, and is given a special symbol n! called "n factorial". (r) "n choose r" is then defined as: n for r>= 0. ----- r! If r and n are non-negative integers, then "n choose r" is the number of ways to choose r items from n when the order of choice is unimportant. This is sometimes referred to as the number of combinations of n things taken r at a time, and another frequently used symbol is nCr. Excerpts taken from: Probability and Statistical Inference Volume 1: Probability by non other than J.G. Kalbfleisch. Dean of Faculty of Mathematics at U of W. (God I hate this textbook!) :^). Now, the whole point of all this is that is possible to take n as being negative in "n choose r", and this is really useful when you get into the binomial theorum for statistics, and combinatorics and optomizations. ie. n ___ / \ r (1+t) = \_ | n | t /__ | r | r>=0 \ / I find it suprizing that HP restricted the domain of COMB(n,r) such that n is a positive integer rather than a real. Just my $.02 worth. --Dave Hubert 3A Math Non-Specailist Faculty of Mathematics University of Waterloo, Canada.
mueller@schaefer.math.wisc.edu (Carl Mueller) (06/26/91)
In article <1991Jun25.171406.17170@watdragon.waterloo.edu> dwrfielder@dahlia.waterloo.edu (Dave Fielder) writes: >In article <3238343@cc.sfu.ca> Dan_Ciarniello@cc.sfu.ca writes: >>>Does anyone know as to why the 48sx does not like negatives >>>in the COMB function. They should be valid. >>> >>>eg. COMB(-8,4) should return (-8)(-9)(-10)(-11)/(4!) = 330. >>> >>HP didn't screw up on this function. >I find it suprizing that HP restricted the domain of COMB(n,r) such that >n is a positive integer rather than a real. > Well, I'd say HP did the right thing. Most people who use the COMB function are using it in its usual sense. Thus the 48 SHOULD indicate that something is wrong if it is being fed negative or fractional values as input. If you want the extended version, you can program it yourself. >Just my $.02 worth. > >--Dave Hubert > 3A Math Non-Specailist > Faculty of Mathematics > University of Waterloo, Canada. Adding my $.02. Carl Mueller (mueller@math.wisc.edu)
ags@seaman.cc.purdue.edu (Dave Seaman) (06/26/91)
In article <1991Jun25.191006.4983@schaefer.math.wisc.edu> mueller@schaefer.UUCP (Carl Mueller) writes: >Well, I'd say HP did the right thing. Most people who use the COMB function >are using it in its usual sense. Thus the 48 SHOULD indicate that something >is wrong if it is being fed negative or fractional values as input. If you want >the extended version, you can program it yourself. Applying the same reasoning, the 48 SHOULD indicate that something is wrong if it is fed complex values as input to functions such as SIN or LN, since most people use these functions only on real values and they should be told when they are probably making a mistake. If you want the SIN of a complex number, you can program it yourself, just like on all those ordinary calculators. If we keep extending this line of reasoning, we should be able to reduce the HP48 to a simple four-function calculator. -- Dave Seaman ags@seaman.cc.purdue.edu
grue@cs.uq.oz.au (Frobozz) (06/26/91)
In <1991Jun25.191006.4983@schaefer.math.wisc.edu> mueller@schaefer.math.wisc.edu (Carl Mueller) writes: ]>I find it suprizing that HP restricted the domain of COMB(n,r) such that ]>n is a positive integer rather than a real. ]> ]Well, I'd say HP did the right thing. Most people who use the COMB function ]are using it in its usual sense. Thus the 48 SHOULD indicate that something ]is wrong if it is being fed negative or fractional values as input. If you want ]the extended version, you can program it yourself. Then why did they include the gamma function instead of a simple factorial? Pauli seeya Paul Dale | Internet/CSnet: grue@cs.uq.oz.au Dept of Computer Science| Bitnet: grue%cs.uq.oz.au@uunet.uu.net Uni of Qld | JANET: grue%cs.uq.oz.au@uk.ac.ukc Australia, 4072 | EAN: grue@cs.uq.oz | UUCP: uunet!munnari!cs.uq.oz!grue f4e6g4Qh4++ | JUNET: grue@cs.uq.oz.au --
mueller@schaefer.math.wisc.edu (Carl Mueller) (06/26/91)
In article <13978@mentor.cc.purdue.edu> ags@seaman.cc.purdue.edu (Dave Seaman) writes: >In article <1991Jun25.191006.4983@schaefer.math.wisc.edu> mueller@schaefer.UUCP (Carl Mueller) writes: > >>Well, I'd say HP did the right thing. Most people who use the COMB function >>are using it in its usual sense. > >Applying the same reasoning, the 48 SHOULD indicate that something is wrong if >it is fed complex values as input to functions such as SIN or LN, since most >people use these functions only on real values and they should be told when >they are probably making a mistake. > >If we keep extending this line of reasoning, we should be able to reduce the >HP48 to a simple four-function calculator. > Well, I'm not convinced that complex number support in basic functions can properly be compared to an extended version of the COMBINATION function whose mathematical definition is in terms of integers, but I'm willing to concede that it is saying too much to say that HP did the right thing. It would also be wrong to say that they did the wrong thing. It was a judgement call and I think that I would have made the same decision. >-- >Dave Seaman >ags@seaman.cc.purdue.edu Carl Mueller (mueller@math.wisc.edu)
mueller@schaefer.math.wisc.edu (Carl Mueller) (06/26/91)
In article <2141@uqcspe.cs.uq.oz.au> grue@cs.uq.oz.au writes: >In <1991Jun25.191006.4983@schaefer.math.wisc.edu> mueller@schaefer.math.wisc.edu (Carl Mueller) writes: > [STUFF DELETED] > >Then why did they include the gamma function instead of a simple factorial? > OK, maybe this will clear stuff up. They includede BOTH the gamma function and the factorial function. The factorial function requires non-negative integers as input (or should ... I don't have my calculator [can we call it that?] with me to check), the gamma function requires anything but negative integers as input. The factorial function is simply no defined for fractional or negative numbers. Thus the gamma function is provided. Perhaps HP should have provided a generalized COMB function in addition to the COMB function that is provided which (apparently -- though I haven't checked) is defined only for integers. > > Pauli >seeya > Carl Mueller (mueller@math.wisc.edu)
akcs.vttoth@hpcvbbs.UUCP (Viktor T. Toth) (06/30/91)
Lines: 7 Well, here is something else for you guys. How about the analytic continuation of the gamma function? While I never before saw COMB extended to negative numbers, applying the gamma function to complex numbers is fairly commonplace. In fact, in the few occasions when I needed the gamma function myself, I had to program it from scratch. HP, please, why did you not include a gamma function routine that is a.) extended over the complex plane and b.) differentiable?