Any way to solve parametric inequations?
09-14-2021, 09:35 AM
Post: #11
 Albert Chan Senior Member Posts: 1,846 Joined: Jul 2018
RE: Any way to solve parametric inequations?
(09-14-2021 05:13 AM)jte Wrote:
(09-13-2021 07:42 PM)Albert Chan Wrote:
CAS> assume(y≥0)
CAS> solve(x*y/(x+y)^2 ≤ 0, x) ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → {x<(-y),(x>(-y)) AND (x≤0)}

(It seems to me that the x>0,y=0 portion is missing.)

Good catch ! Another bug report ...

Perhaps it should be setup with 2 assumes (y≥0, y≤0), like ti-89 solution.
Or, "safer" assumes (y>0, y<0), and handle y==0 edge case separately.
Better yet, implement CAS do assume stuff automatically !

(09-13-2021 07:42 PM)Albert Chan Wrote:  Or, for y≠0, reduce to simple inequality, with t = x/y

CAS> solve(t/(t+1)^2 ≤ 0, t) ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → {t<-1,(t>-1) AND (t≤0)}

Translate t = x/y back to (x,y) world ...
First, edge case out of the way: if (y==0) then return (x!=0)

(SIGN(x)!=SIGN(y)) AND (x!=-y)

With SIGN(), we could remove test for edge case
Unfortunately, CAS SIGN() have bugs (HOME side, SIGN() seems OK)

CAS> SIGN([-1E-10, 0., 1E-10] ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → [-1., 0., -1.]
CAS> SIGN([-1E-12, 0., 1E-12]) ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → [0., 0., 0.]
CAS> SIGN(+inf) ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → 1
CAS> SIGN(1E400) ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → undef
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 Messages In This Thread Any way to solve parametric inequations? - dah145 - 09-04-2021, 02:49 AM RE: Any way to solve parametric inequations? - jte - 09-05-2021, 04:30 PM RE: Any way to solve parametric inequations? - dah145 - 09-07-2021, 09:48 PM RE: Any way to solve parametric inequations? - jte - 09-12-2021, 11:42 PM RE: Any way to solve parametric inequations? - parisse - 09-13-2021, 04:49 PM RE: Any way to solve parametric inequations? - roadrunner - 09-13-2021, 06:39 PM RE: Any way to solve parametric inequations? - Albert Chan - 09-13-2021, 07:42 PM RE: Any way to solve parametric inequations? - jte - 09-13-2021, 09:33 PM RE: Any way to solve parametric inequations? - Albert Chan - 09-14-2021, 12:55 AM RE: Any way to solve parametric inequations? - jte - 09-14-2021, 05:13 AM RE: Any way to solve parametric inequations? - Albert Chan - 09-14-2021 09:35 AM RE: Any way to solve parametric inequations? - Albert Chan - 09-14-2021, 10:23 AM RE: Any way to solve parametric inequations? - jte - 09-14-2021, 10:58 PM RE: Any way to solve parametric inequations? - parisse - 09-15-2021, 04:53 AM

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