Function ISOL on HP 50 g
in [HP48]
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From: andreito on 21 Dec 2009 09:42 I am in the process of learning the feautures of this calculator (Ihave been using the 41c for many years but eventually it died for the last time and it was not worth to have it repaired-another time, i.e.) My problem is: When trying to solve for t the equation of chapter 6 of the manual: a*t^3-b*t=0 by using function ISOL, I get only one solution, i.e. t=0, while the other two t= - sqrt(a-b)/a and t= sqrt(a-b)/a do not appear. They do, however , if I use SOLVE. Analog problem with SOLVEX , which gives me invariably no result { }, while with SOLVE (and adding 'x', of course) I get the correct result (s). I have tried with CAS->Complex on and off, but it looks like there is no difference. Is anybody out there who could hopefully and thankfully help ? Sorry if, by being a newbie in this forum, I might have done something incorrect. andreito
From: John H Meyers on 21 Dec 2009 21:47 On Mon, 21 Dec 2009 08:42:02 -0600, andreito wrote: > When trying to solve for t the equation of chapter 6 of the manual: > > a*t^3-b*t=0 > > by using function ISOL, I get only one solution, i.e. t=0, while the > other two t= - sqrt(a-b)/a and t= sqrt(a-b)/a do not appear. > They do, however , if I use SOLVE. ISOL is not intended to find all possible solutions. The original command, as it existed even in the original HP48 series, is meant to do what its name implies, if possible -- manipulate the expression or equation to ISOLate the selected variable on one side of the equation. The result in the original HP48 series is: 'a*t^3-b*t=0' 't' ISOL -> Error: Unable to Isolate IMO, the HP49/50 series _should_ do the same for this equation, and I would consider the result 't=0' to be a bug! > Analog problem with SOLVEX , which gives me invariably no result { }, > while with SOLVE (and adding 'x', of course) I get the correct result (s) There is no SOLVEX (which you imagine to mean 'X' SOLVE), although you could create one for yourself: \<< 'X' SOLVE \>> 'SOLVEX' STO There is instead a more general SOLVEVX command, equivalent to RCLVX SOLVE (do this manually, and you will see what's really happening) Any variable name at all may be pre-stored into the 'VX' variable, most easily via 'anyvar' STOVX The CASCFG command (set up CAS in "standard" way) also stores 'X' into 'VX' Menu 120 shows SOLVE twice -- the original HP48 never allowed any menu to be thus so ambiguous, but always made menu labels which made clear what function was meant (the first, above the letter "E," is actually SOLVEVX, while SOLVE is associated with the "F" key) [r->] [OFF]
From: andreito on 22 Dec 2009 15:09 Thanks so much for the kind answer. I apologize for having written SOLVEX instead of SOLVEVX,which is what I meant (mere typing mistake). I am aware of the VX variable (defaulting to X) and I have been using correctly SOLVEVX and not SOLVEX as I erroneously wrote. Now (and thanks to your explanations) I have re-checked everything and found that the discrepancy was due to the letter x not being capitalized. I have always been accustomed to use x and not X for variable. By substituting X to x in the equation, SOLVEVX works now OK. So this problem is over. (my fault!) As far as ISOL is concerned, I am little puzzled, because instructions on page 6-1 and 6-2 of the HP 50g User´s Manual , confirmed by same pages of User's Guide, state : "Function ISOL (Equation,variable) will produce the solution(s) to Equation by isolating variable". (please note it mentions solution(s) and not solution ) Statement is followed by an example , reporting the equation I quoted and the three solutions (which are the same I get by using SOLVE) and not only one of them. However,even by writing different equations, I invariably get only the first solution and never the other two( in case of a third degree equation) or one (in case of a second degree equation). Hence my request , as I thought that maybe I was doing something wrong or that the other solution(s) could be found somewhere else in the calculator by pressing the appropriate keys. Again thanks andreito On Dec 22, 3:47 am, "John H Meyers" <jhmey...(a)nomail.invalid> wrote: > On Mon, 21 Dec 2009 08:42:02 -0600, andreito wrote: > > When trying to solve for t the equation of chapter 6 of the manual: > > > a*t^3-b*t=0 > > > by using function ISOL, I get only one solution, i.e. t=0, while the > > other two t= - sqrt(a-b)/a and t= sqrt(a-b)/a do not appear. > > They do, however , if I use SOLVE. > > ISOL is not intended to find all possible solutions. > > The original command, as it existed even in the original HP48 series, > is meant to do what its name implies, if possible -- manipulate > the expression or equation to ISOLate the selected variable > on one side of the equation. > > The result in the original HP48 series is: > > 'a*t^3-b*t=0' 't' ISOL -> Error: Unable to Isolate > > IMO, the HP49/50 series _should_ do the same for this equation, > and I would consider the result 't=0' to be a bug! > > > Analog problem with SOLVEX , which gives me invariably no result { }, > > while with SOLVE (and adding 'x', of course) I get the correct result (s) > > There is no SOLVEX (which you imagine to mean 'X' SOLVE), > although you could create one for yourself: > \<< 'X' SOLVE \>> 'SOLVEX' STO > > There is instead a more general SOLVEVX command, equivalent to RCLVX SOLVE > (do this manually, and you will see what's really happening) > > Any variable name at all may be pre-stored into the 'VX' variable, > most easily via 'anyvar' STOVX > > The CASCFG command (set up CAS in "standard" way) > also stores 'X' into 'VX' > > Menu 120 shows SOLVE twice -- the original HP48 never allowed > any menu to be thus so ambiguous, but always made menu labels > which made clear what function was meant > (the first, above the letter "E," is actually SOLVEVX, > while SOLVE is associated with the "F" key) > > [r->] [OFF]
From: Virgil on 22 Dec 2009 23:41 In article <op.u5c4ynptnn735j(a)miu.edu>, "John H Meyers" <jhmeyers(a)nomail.invalid> wrote: > On Tue, 22 Dec 2009 14:09:47 -0600, andreito wrote: > > > As far as ISOL is concerned, I am little puzzled, because instructions > > on page 6-1 and 6-2 of the HP 50g User�s Manual , confirmed by same > > pages of User's Guide, state : > > > > "Function ISOL (Equation,variable) will produce the solution(s) to > > Equation by isolating variable". (please note it mentions solution(s) > > and not solution ) > > > > Statement is followed by an example , reporting the equation I quoted > > and the three solutions (which are the same I get by using SOLVE) and > > not only one of them. > > The result of ISOL, > if it is to continue the function it performed on the 48 series, > must be a _single_ equation, with the variable to be isolated > on one side. > > Here is the AUR's definition of ISOL (note, by the way, > that ISOL is not listed among CAS commands, > since it is an original HP48 series command): > > Isolate Variable Command: > > 'symb1' 'global' -> 'symb2' > > Returns an algebraic symb2 that rearranges symb1 to > isolate the first occurrence of variable global. > > The result symb2 is an equation of the form 'global=expression.' > > If global appears more than once, > then symb2 is effectively the right side of an equation > obtained by rearranging and solving symb1 > to isolate the first occurrence of global on the left side of the equation. > > If symb1 is an expression, > it is treated as the left side of an equation 'symb1=0' > > If global appears in the argument of a function within symb1, > that function must be an analytic function, that is, > a function for which the hp49g+/hp48gII provides an inverse. > Thus ISOL cannot solve IP(x)=0 for x, since IP has no inverse. > > [End quote] > > The very next sentence in the AUR contradicts everything just said, > however, by saying: "ISOL is identical to SOLVE," > because the description of SOLVE (which is a CAS command), > says: "Output: A zero or solution, or a list of zeros or solutions." > > The definition of ISOL demands a single (usually analytic) function as output, > while SOLVE permits (and may deliver) a list of solution values as output, > sometimes even numeric solutions. > > My conclusions: > > The documentation contradicts itself, > the calculator contradicts the documentation, > and the ISOL command, once both fast and reliable on HP48 series, > is now left with bugs and non-usability on the 49/50 series, > its original mechanics having been stripped out and replaced > with something from the CAS which was apparently never worked out. > > I once wrote a complete "triangle solver" for the HP48. > It worked with seven equations (three "sine law," > three "cosine law," and one "sum of angles is a straight angle"). > The solution for three unknown variables was obtained by using > ISOL three times to obtain a formula for one unknown variable > at a time, in terms of known variables, then evaluating > each right side to a numeric value. > > The program can not work properly on HP49/50 series, > because the original ISOL command died with the HP48 series. > > -- Perhaps in some future version of the CAS the ISOL command can be restored to its original form.
From: John H Meyers on 22 Dec 2009 18:31
On Tue, 22 Dec 2009 14:09:47 -0600, andreito wrote: > As far as ISOL is concerned, I am little puzzled, because instructions > on page 6-1 and 6-2 of the HP 50g User�s Manual , confirmed by same > pages of User's Guide, state : > > "Function ISOL (Equation,variable) will produce the solution(s) to > Equation by isolating variable". (please note it mentions solution(s) > and not solution ) > > Statement is followed by an example , reporting the equation I quoted > and the three solutions (which are the same I get by using SOLVE) and > not only one of them. The result of ISOL, if it is to continue the function it performed on the 48 series, must be a _single_ equation, with the variable to be isolated on one side. Here is the AUR's definition of ISOL (note, by the way, that ISOL is not listed among CAS commands, since it is an original HP48 series command): Isolate Variable Command: 'symb1' 'global' -> 'symb2' Returns an algebraic symb2 that rearranges symb1 to isolate the first occurrence of variable global. The result symb2 is an equation of the form 'global=expression.' If global appears more than once, then symb2 is effectively the right side of an equation obtained by rearranging and solving symb1 to isolate the first occurrence of global on the left side of the equation. If symb1 is an expression, it is treated as the left side of an equation 'symb1=0' If global appears in the argument of a function within symb1, that function must be an analytic function, that is, a function for which the hp49g+/hp48gII provides an inverse. Thus ISOL cannot solve IP(x)=0 for x, since IP has no inverse. [End quote] The very next sentence in the AUR contradicts everything just said, however, by saying: "ISOL is identical to SOLVE," because the description of SOLVE (which is a CAS command), says: "Output: A zero or solution, or a list of zeros or solutions." The definition of ISOL demands a single (usually analytic) function as output, while SOLVE permits (and may deliver) a list of solution values as output, sometimes even numeric solutions. My conclusions: The documentation contradicts itself, the calculator contradicts the documentation, and the ISOL command, once both fast and reliable on HP48 series, is now left with bugs and non-usability on the 49/50 series, its original mechanics having been stripped out and replaced with something from the CAS which was apparently never worked out. I once wrote a complete "triangle solver" for the HP48. It worked with seven equations (three "sine law," three "cosine law," and one "sum of angles is a straight angle"). The solution for three unknown variables was obtained by using ISOL three times to obtain a formula for one unknown variable at a time, in terms of known variables, then evaluating each right side to a numeric value. The program can not work properly on HP49/50 series, because the original ISOL command died with the HP48 series. -- |