Is there a way for the solve app to use exact figures?

10222020, 03:03 AM
Post: #1




Is there a way for the solve app to use exact figures?
Hi there.
I am trying to solve this equation: a^2+b^2+c^2+6=a given that b=6 and c=31. I'm particularly having trouble trying to get the given parts of that equation to work I know how to do this via the solve app, but I can't get exact figures with the app, and it doesn't play nice with nonlinear equations. So is there a different way solve that equation and still get exact figures? 

10222020, 04:11 AM
(This post was last modified: 10222020 06:41 AM by Stevetuc.)
Post: #2




RE: Is there a way for the solve app to use exact figures?
(10222020 03:03 AM)Lord_Spooglypuff Wrote: [....] There are 2 ways I found: Code: exact(proot([1,1,6^2+31^2])) Code: exact(QuadSolve(1,1,6^2+31^2)) Code: [(6188390727*i)/12376,(6188+390727*i)/12376] 

10222020, 04:36 PM
Post: #3




RE: Is there a way for the solve app to use exact figures?
(10222020 04:11 AM)Stevetuc Wrote: exact(proot([1,1,6^2+31^2])) 2 issues: 1). you missed the +6 for the constant term. 2). approximate solutions, then apply exact, does not give exact solutions. (some cases do work, if exact solutions are "simple" rational; but not in general) BTW, exact is a bad name. It really meant float2rational (conversion likely *not* exact) I don't have HP Prime, but in XCas, you can use solve (with complex ON) XCas> eqn := subst(a^2+b^2+c^2+6a, [b,c]=[6,31]) → a^2a+1003 XCas> solve(eqn=0, a) → \([{1+i\sqrt{4011} \over 2}, {1i\sqrt{4011} \over 2}]\) 

10222020, 05:47 PM
Post: #4




RE: Is there a way for the solve app to use exact figures?
(10222020 04:36 PM)Albert Chan Wrote:(10222020 04:11 AM)Stevetuc Wrote: exact(proot([1,1,6^2+31^2])) Thanks Albert, I learnt something! 

10222020, 07:19 PM
(This post was last modified: 10222020 07:34 PM by Albert Chan.)
Post: #5




RE: Is there a way for the solve app to use exact figures?
Knowing the limitation of proot and exact, we can use it to get exact results.
But, it required confirmations. Example: find roots of x^2 + (1+i)*x + (3i) = 0 XCas> [r1, r2] := proot([1, 1+i, 3i]) → [0.9207742662342.28242839495*i , 0.0792257337659+1.28242839495*i] Quadratic roots should have a form of c ± √d = (r1+r2)/2 ± √((r1r2)/2)² We use the "inexact" nature of exact, to our advantage. (If results look messy, we can use the even more "inexact" version, float2rational) XCas> c := exact((r1+r2)/2) → 1/(1i) = 1/2i/2 XCas> d := exact(((r1r2)/2)^2) → (6+3i)/2 = 3+3i/2 Confimation steps: XCas> simplify(2*c) → 1+i, matching linear coefficient. XCas> simplify(c*cd) → 3i, matching constant term. → x roots = c ± √d = (1/2i/2) ± √(3+3i/2) For quadratics, this is stupid. We get faster results applying quadratic formula. But, it is useful for simplifying cubics and beyond. Example: ³√(1859814842094  59687820010√415) = 11589  145√415 RHS (actually, just 11589) was originally a guess. Then we confirm it. 

10222020, 07:43 PM
Post: #6




RE: Is there a way for the solve app to use exact figures?
Using CAS on the Prime:
b:=6 c:=31 solve(a^2+b^2+c^2+6=a,a) Result: (1/2)*(i*sqrt(4011)+1),(1/2)*((−i)*sqrt(4011)+1) Thibault  not collector but in love with the few HP models I own  Also musician : http://walruspark.co 

10252020, 09:27 PM
Post: #7




RE: Is there a way for the solve app to use exact figures?
(10222020 04:36 PM)Albert Chan Wrote: BTW, exact is a bad name. It really meant float2rational (conversion likely *not* exact) For what it's worth (apologies if this is too offtopic, just ignore), my notes on exact() — largely pinched from Joe Horn; all mistakes are mine — say: The abc key in CAS for Real input, executes exact() exact() uses a simple continuedfraction algorithm; not as good as Joe's PDQ algorithm. The accuracy of exact() is controlled by CAS Settings — Epsilon, but has limited range. Joe says: The exact() function in CAS has three shortcomings  it only finds answers which are principal convergents  it only allows the tolerance (epsilon) to lie between 10^6 and 10^14  it sometimes returns incorrect answers (outside the specified tolerance) PDQ has none of these shortcomings It always finds the unique best answer for any target and tolerance. PDQ: https://www.hpmuseum.org/forum/thread61.html Cambridge, UK 41CL/DM41X 12/15C/16C DM15/16 71B 17B/BII/bII+ 28S 42S/DM42 32SII 48GX 50g 35s 30b/WP34S Prime G2 & Casios, Rockwell 18R :) 

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