Re: Re: My problem when solving a system of equations

• To: mathgroup at smc.vnet.net
• Subject: [mg78137] Re: [mg78071] Re: My problem when solving a system of equations
• From: DrMajorBob <drmajorbob at bigfoot.com>
• Date: Sat, 23 Jun 2007 07:20:30 -0400 (EDT)
• References: <f5dkv7\$13j\$1@smc.vnet.net> <9728183.1182542882326.JavaMail.root@m35>

```Same output here, in v5.2, no errors in v6.

The v6 outputs are

{{p -> 2.29251}}

{{pA -> 4.44537, p1 -> 2.31915, p2 -> 2.25392,
disA -> 0.996607}, {pA -> 3.97324, p1 -> 4.9583, p2 -> 2.9492,
disA -> 1.73173}}

For simplicity and convenience, I'd write the Select and DeleteCases cal=
ls  =

this way:

SNB = DeleteCases[NB, {_ -> _Complex}]

BR = DeleteCases[B, {(_ -> _Complex) ..}];

and

SB = Select[DeleteCases[BR, {___, _ -> _?Negative, ___}],
pA > disA /. # &]

or

SB = DeleteCases[
BR, {___, _ -> _?Negative, ___} | _?(pA <= disA /. # &)]

Bobby

On Fri, 22 Jun 2007 05:40:52 -0500, dimitris <dimmechan at yahoo.com> wrote=
:

> Hi.
>
> Quit the session.
> This is what I got.
>
> In[1]:=
> a = 24;
> b = 5;
> c = 25;
> d = 4;
> cA = 3;
> cB = 2;
> t = 5;
> alpha = 0;
> bta = 0.6;
> NB = NSolve[{-d(p - cB) + c - d*p == (p - cB)(c - d*p)^2/t}, {p}=
];
> SNB = DeleteCases[NB, {p -> _Complex}]
> B = NSolve[{(alpha + (1 - alpha - bta)*(0.5 - ((d/
> 2)*(p1^2 - p2^2) - c*(p1 - p2))/(2t) - ((b/2)*((
> pA - disA)^2 - pA^2) + a*disA)/(2t)))*(a - b*pA - b*(pA -
> cA)) - (1 - alpha - bta)*((p1 - cB)*(c - d*
> p1) + (pA - disA - cA)*(a - b*(pA -
> disA)) - (pA - cA)*(a - b*pA))*(-(
> a - b*pA)/(
> 2t)) == 0, (1 - alpha - bta)*((a - b*(pA -
> disA) -
> b(pA - disA - cA))*(0.5 + ((d/2)*(
> p1^2 - p2^2) - c*(
> p1 - p2))/(2t) + ((b/2)*((pA -
> disA)^2 - pA^2) + a*disA)/(2t)) +
> ((
> p1 - cB)*(c -
> d*p1) + (pA - disA - cA)(a - b*(pA - disA)) - (pA -
> cA)(a - b*pA))*(-(a - b*(pA - disA))/(
> 2t))) == 0, (1 - alpha)*((c - d*p1 - d*(p1 -
> cB))*(0.5 + ((d/2)*(p1^2 - p2^2) - c*(p1 -
> p2))/(2t)) + (p1 - cB)*(c - d*p1)*(-
> c + d*p1)/(2t)) + (1 -
> alpha - bta)*(((pA - disA - cA)*(a -
> b*(pA - disA)) - (pA - cA)*(a - b*
> pA))*(-c + d*p1)/(2t) + (c - d*p1 - d(
> p1 - cB))*((
> b/2)((pA - disA)^2 - pA^2) + a*disA)/(2t)) ==
> 0, (1 - alpha)*((c - d*p2 - d(p2 - cB))*(
> 0.5 - ((d/
> 2)*(p1^2 - p2^2) - c*(p1 - p2))/(2t)) + (
> p2 - cB)*(c - d*p2)*(-c + d*p2)/(
> 2t)) - (1 - alpha - bta)*(c - d*p2 - d(p2 -
> cB))*((
> b/2)*((pA - disA)^2 - pA^2) + a*disA)/(
> 2t) == 0}, {pA, p1, p2, disA}];
> BR = DeleteCases[B, {pA -> _Complex, p1 -> _Complex,
> p2 -> _Complex, disA -> _Complex}];
> SB = Select[BR, And @@ (({pA > 0, p1 > 0, p2 >
> 0, disA > 0, pA - disA > 0} /. #)) &]
>
>
> Out[11]=
> {{p\[Rule]2.29251}}
>
>> From In[1]:=
> \!\(\*
>   RowBox[{\(General::"ovfl"\), \(\(:\)\(\ \)\), "\<\"Overflow occurred=

> in
>       computation. \\!\\(\\*
,
> \
> ButtonFrame->None, ButtonData:>\\\"General::ovfl\\\"]\\)\"\>"}]\)
>
>> From In[1]:=
> \!\(\*
>   RowBox[{\(General::"ovfl"\), \(\(:\)\(\ \)\), "\<\"Overflow occurred=

> in
>       computation. \\!\\(\\*
,
> \
> ButtonFrame->None, ButtonData:>\\\"General::ovfl\\\"]\\)\"\>"}]\)
>
>> From In[1]:=
> \!\(\*
>   RowBox[{\(General::"ovfl"\), \(\(:\)\(\ \)\), "\<\"Overflow occurred=

> in
>       computation. \\!\\(\\*
,
> \
> ButtonFrame->None, ButtonData:>\\\"General::ovfl\\\"]\\)\"\>"}]\)
>
>> From In[1]:=
> \!\(\*
>   RowBox[{\(General::"stop"\), \(\(:\)\(\ \)\), "\<\"Further output
>     of \\!\\(General :: \\\"ovfl\\\"\\) will be suppressed during this=

> \
> calculation. \\!\\(\\*ButtonBox[\\\"More...\\\", \
> ButtonData:>\\\"General::stop\\\"]\\)\"\>"}]\)
>
> Out[14]=
> {{pA\[Rule]3.\
> 9732432017395564125192881280440459970239458049155570290659727205464200=
58294383\
> 598890842765930734752225321438217919715672292159,p1\[Rule]4.\
> 9583020205953198426844437490276847987374968830138184752206982442835052=
99552283\
> 746464263057828871991290065319494660363196793637,p2\[Rule]2.\
> 9492043120958567848661780700152290929443792979472395124432261753037846=
09762982\
> 212035816978006166136210705386558781550333832228,disA\[Rule]1.\
> 7317345095455130836574595752515783213548027500930796460910004112980812=
55083276\
> 2752868835871074875089387169154659532655501459707},{pA\[Rule]4.\
> 4453741673000709391848598582133786788222599587325774958959075071516186=
91880549\
> 660415122202305507338705522502612851605862635436,p1\[Rule]2.\
> 3191544666381207575033273744035069978770949953159758125555358123091317=
09076747\
> 313776308520736763603708360710094963211884291417,p2\[Rule]2.\
> 2539202474547679263108488307500266352058951825911431165934917794312904=
07927731\
> 601498154267807767823951092934390534865277197642,disA\[Rule]0.\
> 9966066322077992533144866328594633845356760754716330960239718093767669=
93819562\
> 5934892093572991329922317150799668794322107434808}}
>
> Dimitris
>
>
> lovei... at gmail.com       :
>> Hi, guys,
>>
>> I was trying to solve a system of nonlinear equations. However,
>> whenever I run it, Mathematica always returns:
>> " ReplaceAll::reps: {-0.04\(-24 + 5\pA)\((25 - 4\p1)\(-2 + p1) - (24 =
-
>> \
>> 5\pA)\(-3 + pA) + (-3 - disA + pA)\(24 - 5\(-disA + pA))) + 0.4\(\
>> \[LeftSkeleton]1\[RightSkeleton])\(\[LeftSkeleton]1\[RightSkeleton])
>> == 0, \
>> \[LeftSkeleton]3\[RightSkeleton]} is neither a list of replacement
>> rules nor \
>> a valid dispatch table, and so cannot be used for replacing. "
>>
>> I don't know what this means and how to deal with it.
>>
>> Below is my code for your reference:
>>
>> a = 24;
>> b = 5;
>> c = 25;
>> d = 4;
>> cA = 3;
>> cB = 2;
>> t = 5;
>> alpha = 0;
>> bta = 0.6;
>> NB = NSolve[{-d(p - cB) + c - d*p == (p - cB)(c - d*p)^2/t}, {p=
}];
>> SNB = DeleteCases[NB, {p -> _Complex}]
>> B = NSolve[{(alpha + (1 - alpha - bta)*(0.5 - ((d/
>>           2)*(p1^2 - p2^2) - c*(p1 - p2))/(2t) - ((b/2)*((
>>       pA - disA)^2 - pA^2) + a*disA)/(2t)))*(a - b*pA - b*(pA -
>>     cA)) - (1 - alpha - bta)*((p1 - cB)*(c - d*
>>     p1) + (pA - disA - cA)*(a - b*(pA -
>>                    disA)) - (pA - cA)*(a - b*pA))*(-(
>>                     a - b*pA)/(
>>                         2t)) == 0, (1 - alpha - bta)*((a - b*(pA =
-
>> disA) -
>>                                b(pA - disA - cA))*(0.5 + ((d/2)*(
>>                         p1^2 - p2^2) - c*(
>>                                 p1 - p2))/(2t) + ((b/2)*((pA -
>>                                     disA)^2 - pA^2) + a*disA)/(2t)) +=

>> ((
>>                           p1 - cB)*(c -
>>               d*p1) + (pA - disA - cA)(a - b*(pA - disA)) - (pA -
>>             cA)(a - b*pA))*(-(a - b*(pA - disA))/(
>>               2t))) == 0, (1 - alpha)*((c - d*p1 - d*(p1 -
>>                   cB))*(0.5 + ((d/2)*(p1^2 - p2^2) - c*(p1 -
>>                         p2))/(2t)) + (p1 - cB)*(c - d*p1)*(-
>>                   c + d*p1)/(2t)) + (1 -
>>                      alpha - bta)*(((pA - disA - cA)*(a -
>>
>>                   b*(pA - disA)) - (pA - cA)*(a - b*
>>         pA))*(-c + d*p1)/(2t) + (c - d*p1 - d(
>>             p1 - cB))*((
>>                       b/2)((pA - disA)^2 - pA^2) + a*disA)/(2t)) ===

>>                           0, (1 - alpha)*((c - d*p2 - d(p2 - cB))*(
>>         0.5 - ((d/
>>                   2)*(p1^2 - p2^2) - c*(p1 - p2))/(2t)) + (
>>                         p2 - cB)*(c - d*p2)*(-c + d*p2)/(
>>                         2t)) - (1 - alpha - bta)*(c - d*p2 - d(p2 -
>> cB))*((
>>                               b/2)*((pA - disA)^2 - pA^2) + a*disA)/(=

>>                   2t) == 0}, {pA, p1, p2, disA}];
>> BR = DeleteCases[B, {pA -> _Complex, p1 -> _Complex,
>>              p2 -> _Complex, disA -> _Complex}];
>> SB = Select[BR, And @@ (({pA > 0, p1 > 0, p2 >
>>                0, disA > 0, pA - disA > 0} /. #)) &]
>
>
>

-- =

DrMajorBob at bigfoot.com

```

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