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Newsgroups: comp.soft-sys.math.maple
From: Thomas Dean <tomd...@speakeasy.net>Date: Fri, 20 Jan 2012 20:43:53 -0800
Local: Fri, Jan 20 2012 11:43 pm
Subject: Solve Polynomial
Maple 15 does not produce a solution to diff(eq,x)=0; But, one exists.
eqn := (2*x^2-5*x+2)/(5*x^2-7*x-6);
deq:=diff(eqn,x);
solve(deq=0,x);
# returns no solution
eq2 := op(1, deq) = op(2, deq);
solve(eq2,x,AllSolutions);
returns two solutions as I expect.
numer(eqn) is zero at x=2 and x=1/2
denom(eqn) is zero at x=2 and x=-3/5
eqn is zero at x=1/2 and undefined at x=2 and x=-3/5. I assume 0/0 is
undefined.
limit(eqn,x=2) is 3/13.
How can I use solve to do produce a solution for diff(eq,x)=0?
Tom Dean
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Newsgroups: comp.soft-sys.math.maple
From: "Nasser M. Abbasi" <n...@12000.org>Date: Fri, 20 Jan 2012 23:52:33 -0600
Local: Sat, Jan 21 2012 12:52 am
Subject: Re: Solve Polynomial
On 1/20/2012 10:43 PM, Thomas Dean wrote:
> Maple 15 does not produce a solution to diff(eq,x)=0; But, one exists.
> eqn := (2*x^2-5*x+2)/(5*x^2-7*x-6);
> deq:=diff(eqn,x);
> solve(deq=0,x);
> # returns no solution
I think if you plot deq as function of x you'll see why
there is no solution. deq is positive for all x.
> eq2 := op(1, deq) = op(2, deq);
> solve(eq2,x,AllSolutions);
> returns two solutions as I expect.
> numer(eqn) is zero at x=2 and x=1/2
> denom(eqn) is zero at x=2 and x=-3/5
> eqn is zero at x=1/2 and undefined at x=2 and x=-3/5. I assume 0/0 is
> undefined.
> limit(eqn,x=2) is 3/13.
> How can I use solve to do produce a solution for diff(eq,x)=0?
> Tom Dean
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Newsgroups: comp.soft-sys.math.maple
From: "G. A. Edgar" <ed...@math.ohio-state.edu.invalid>Date: Sat, 21 Jan 2012 07:35:15 -0700
Local: Sat, Jan 21 2012 9:35 am
Subject: Re: Solve Polynomial
In article <jfdjr1$sm ...@speranza.aioe.org>, Nasser M. Abbasi
<n ...@12000.org> wrote:
> On 1/20/2012 10:43 PM, Thomas Dean wrote:
> > Maple 15 does not produce a solution to diff(eq,x)=0; But, one exists.
> > eqn := (2*x^2-5*x+2)/(5*x^2-7*x-6);
> > deq:=diff(eqn,x);
> > solve(deq=0,x);
> > # returns no solution
> I think if you plot deq as function of x you'll see why
> there is no solution. deq is positive for all x.
and, simplified, deq = 11/(5*x+3)^2, so we can see it is never zero.
However, it has a pole at x=-3/5, maybe that is what you want to find?
> > eq2 := op(1, deq) = op(2, deq);
> > solve(eq2,x,AllSolutions);
> > returns two solutions as I expect.
> > numer(eqn) is zero at x=2 and x=1/2
> > denom(eqn) is zero at x=2 and x=-3/5
> > eqn is zero at x=1/2 and undefined at x=2 and x=-3/5. I assume 0/0 is
> > undefined.
> > limit(eqn,x=2) is 3/13.
> > How can I use solve to do produce a solution for diff(eq,x)=0?
> > Tom Dean
-- G. A. Edgar http://www.math.ohio-state.edu/~edgar/
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Newsgroups: comp.soft-sys.math.maple
From: Thomas Dean <tomd...@speakeasy.net>Date: Sat, 21 Jan 2012 10:01:53 -0800
Local: Sat, Jan 21 2012 1:01 pm
Subject: Re: Solve Polynomial
On 01/20/12 20:43, Thomas Dean wrote:
> eq2 := op(1, deq) = op(2, deq);
> solve(eq2,x,AllSolutions);
eqn := (2*x^2-5*x+2)/(5*x^2-7*x-6);
2
2 x - 5 x + 2
eqn := --------------
2
5 x - 7 x - 6
deq:=diff(eqn,x);
2
4 x - 5 (2 x - 5 x + 2) (10 x - 7)
deq := -------------- - ---------------------------
2 2 2
5 x - 7 x - 6 (5 x - 7 x - 6)
solve(deq=0,x);
eq2 := op(1, deq) = op(2, deq);
2
4 x - 5 (2 x - 5 x + 2) (10 x - 7)
eq2 := -------------- = - ---------------------------
2 2 2
5 x - 7 x - 6 (5 x - 7 x - 6)
solve(eq2,x,AllSolutions);
1/2 1/2
37 2649 37 2649
-- - -------, -- + -------
80 80 80 80
evalf(%);
-0.1808554616, 1.105855462
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Newsgroups: comp.soft-sys.math.maple
From: acer <ma...@rogers.com>Date: Sat, 21 Jan 2012 10:04:56 -0800 (PST)
Local: Sat, Jan 21 2012 1:04 pm
Subject: Re: Solve Polynomial
Did you not forget a minus sign, when you wrote, eq2 := op(1, deq) = op(2, deq);
for `deq` a sum of two operands?
acer
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Newsgroups: comp.soft-sys.math.maple
From: Thomas Dean <tomd...@speakeasy.net>Date: Sat, 21 Jan 2012 10:09:31 -0800
Local: Sat, Jan 21 2012 1:09 pm
Subject: Re: Solve Polynomial
On 01/21/12 10:01, Thomas Dean wrote:
> On 01/20/12 20:43, Thomas Dean wrote:
>> eq2 := op(1, deq) = op(2, deq);
>> solve(eq2,x,AllSolutions);
> eqn := (2*x^2-5*x+2)/(5*x^2-7*x-6);
> 2
> 2 x - 5 x + 2
> eqn := --------------
> 2
> 5 x - 7 x - 6
> deq:=diff(eqn,x);
> 2
> 4 x - 5 (2 x - 5 x + 2) (10 x - 7)
> deq := -------------- - ---------------------------
> 2 2 2
> 5 x - 7 x - 6 (5 x - 7 x - 6)
> solve(deq=0,x);
> eq2 := op(1, deq) = op(2, deq);
> 2
> 4 x - 5 (2 x - 5 x + 2) (10 x - 7)
> eq2 := -------------- = - ---------------------------
> 2 2 2
> 5 x - 7 x - 6 (5 x - 7 x - 6)
> solve(eq2,x,AllSolutions);
> 1/2 1/2
> 37 2649 37 2649
> -- - -------, -- + -------
> 80 80 80 80
> evalf(%);
> -0.1808554616, 1.105855462
oops - I should have used -op(2,deq)
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Newsgroups: comp.soft-sys.math.maple
From: Peter Pein <pet...@dordos.net>Date: Sat, 21 Jan 2012 19:50:13 +0100
Local: Sat, Jan 21 2012 1:50 pm
Subject: Re: Solve Polynomial
Am 21.01.2012 19:01, schrieb Thomas Dean:
> On 01/20/12 20:43, Thomas Dean wrote:
>> eq2 := op(1, deq) = op(2, deq);
>> solve(eq2,x,AllSolutions);
> eqn := (2*x^2-5*x+2)/(5*x^2-7*x-6);
> 2
> 2 x - 5 x + 2
> eqn := --------------
> 2
> 5 x - 7 x - 6
> deq:=diff(eqn,x);
> 2
> 4 x - 5 (2 x - 5 x + 2) (10 x - 7)
> deq := -------------- - ---------------------------
> 2 2 2
> 5 x - 7 x - 6 (5 x - 7 x - 6)
> solve(deq=0,x);
> eq2 := op(1, deq) = op(2, deq);
> 2
> 4 x - 5 (2 x - 5 x + 2) (10 x - 7)
> eq2 := -------------- = - ---------------------------
> 2 2 2
> 5 x - 7 x - 6 (5 x - 7 x - 6)
> solve(eq2,x,AllSolutions);
> 1/2 1/2
> 37 2649 37 2649
> -- - -------, -- + -------
> 80 80 80 80
> evalf(%);
> -0.1808554616, 1.105855462
If you want deq=0, you should look at
eq2 := op(1, deq) = -op(2, deq);
(please note the sign of op(2,deq);
Cheers,
Peter
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