Please Help !!! - Problem in Plot
- To: mathgroup@smc.vnet.net
- Subject: [mg11600] Please Help !!! - Problem in Plot
- From: Jae Sung Lee <jslee@kuccnx.korea.ac.kr>
- Date: Tue, 17 Mar 1998 10:43:34 -0500
- Organization: System Engineering Research Institute (SERI)
I am to solve the following formula ;
soln1=Solve[x*(1-x)^(z-2)==y*(1-y)^(z-2), x]
where z = 6, and it is expected that x is the function of y.
and got the following six solutions ;
Out[]=
({{x -> y}, {
x ->
(4 - y)/4 -
1/2[Sqrt]((
( - 6) + 1/4(((-4) + y))^2 + 4 y - y^2 + 1/3((6 - 4 y +
y^2)) +
((2*2^(1/3)(((-1) + y))^2 y(((-6) + 5 y)
)))/((3(((-45) y^2 + 160\ y\^3 - 210\ y\^4 +
120\ y\^5 - 25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\
y\^5 -
443340\ y\^6 + 611280\ y\^7 -
563922\ y\^8 + 348192\ y\^9 -
138780\ y\^10 + 32400\ y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\) +
\(1\/\(3\ 2\^\(1/3\)\)\((
\((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 + 120\ y\^5
-
25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\ y\^5 -
443340\ y\^6 + 611280\ y\^7 - 563922\
y\^8 +
348192\ y\^9 - 138780\ y\^10 + 32400\
y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\)\))\) -
1\/2\ \[Sqrt]\((
\( - 6\) + 1\/2\ \((\(-4\) + y)\)\^2 + 4\ y - y\^2 +
1\/3\ \((\(-6\) + 4\ y - y\^2)\) -
\((2\ 2\^\(1/3\)\ \((\(-1\) + y)\)\^2\ y\ \((\(-6\) +
5\ y)
\))\)/\((
3\ \((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 +
120\ y\^5 - 25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\
y\^5 -
443340\ y\^6 + 611280\ y\^7 -
563922\ y\^8 + 348192\ y\^9 -
138780\ y\^10 + 32400\ y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\) -
\(1\/\(3\ 2\^\(1/3\)\)\((
\((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 + 120\ y\^5
-
25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\ y\^5 -
443340\ y\^6 + 611280\ y\^7 - 563922\
y\^8 +
348192\ y\^9 - 138780\ y\^10 + 32400\
y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\)\) -
\((\(-\((\(-4\) + y)\)\^3\) +
4\ \((\(-4\) + y)\)\ \((6 - 4\ y + y\^2)\) -
8\ \((\(-4\) + 6\ y - 4\ y\^2 + y\^3)\))\)/
\((4\ \[Sqrt]\((
\( - 6\) + 1\/4\ \((\(-4\) + y)\)\^2 + 4\ y
-
y\^2 + 1\/3\ \((6 - 4\ y + y\^2)\) +
\((2\ 2\^\(1/3\)\ \((\(-1\) + y)\)\^2\ y\
\((
\(-6\) + 5\ y)\))\)/
\((3\ \((
\(-45\)\ y\^2 + 160\ y\^3 -
210\ y\^4 + 120\ y\^5 - 25\ y\^6
+
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 +
207360\ y\^5 - 443340\ y\^6 +
611280\ y\^7 - 563922\ y\^8 +
348192\ y\^9 - 138780\ y\^10 +
32400\ y\^11 - 3375\
y\^12)\))\)^
\((1/3)\))\) +
\(1\/\(3\ 2\^\(1/3\)\)\((
\((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4
+
120\ y\^5 - 25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 +
207360\ y\^5 - 443340\ y\^6 +
611280\ y\^7 - 563922\ y\^8 +
348192\ y\^9 - 138780\ y\^10 +
32400\ y\^11 - 3375\
y\^12)\))\)^
\((1/3)\))\)\))\))\))\)}, {
x ->
(4 - y)/4 -
1\/2\ \[Sqrt]\((
\( - 6\) + 1\/4\ \((\(-4\) + y)\)\^2 + 4\ y - y\^2 +
1\/3\ \((6 - 4\ y + y\^2)\) +
\((2\ 2\^\(1/3\)\ \((\(-1\) + y)\)\^2\ y\ \((\(-6\) +
5\ y)
\))\)/\((
3\ \((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 +
120\ y\^5 - 25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\
y\^5 -
443340\ y\^6 + 611280\ y\^7 -
563922\ y\^8 + 348192\ y\^9 -
138780\ y\^10 + 32400\ y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\) +
\(1\/\(3\ 2\^\(1/3\)\)\((
\((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 + 120\ y\^5
-
25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\ y\^5 -
443340\ y\^6 + 611280\ y\^7 - 563922\
y\^8 +
348192\ y\^9 - 138780\ y\^10 + 32400\
y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\)\))\) +
1\/2\ \[Sqrt]\((
\( - 6\) + 1\/2\ \((\(-4\) + y)\)\^2 + 4\ y - y\^2 +
1\/3\ \((\(-6\) + 4\ y - y\^2)\) -
\((2\ 2\^\(1/3\)\ \((\(-1\) + y)\)\^2\ y\ \((\(-6\) +
5\ y)
\))\)/\((
3\ \((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 +
120\ y\^5 - 25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\
y\^5 -
443340\ y\^6 + 611280\ y\^7 -
563922\ y\^8 + 348192\ y\^9 -
138780\ y\^10 + 32400\ y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\) -
\(1\/\(3\ 2\^\(1/3\)\)\((
\((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 + 120\ y\^5
-
25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\ y\^5 -
443340\ y\^6 + 611280\ y\^7 - 563922\
y\^8 +
348192\ y\^9 - 138780\ y\^10 + 32400\
y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\)\) -
\((\(-\((\(-4\) + y)\)\^3\) +
4\ \((\(-4\) + y)\)\ \((6 - 4\ y + y\^2)\) -
8\ \((\(-4\) + 6\ y - 4\ y\^2 + y\^3)\))\)/
\((4\ \[Sqrt]\((
\( - 6\) + 1\/4\ \((\(-4\) + y)\)\^2 + 4\ y
-
y\^2 + 1\/3\ \((6 - 4\ y + y\^2)\) +
\((2\ 2\^\(1/3\)\ \((\(-1\) + y)\)\^2\ y\
\((
\(-6\) + 5\ y)\))\)/
\((3\ \((
\(-45\)\ y\^2 + 160\ y\^3 -
210\ y\^4 + 120\ y\^5 - 25\ y\^6
+
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 +
207360\ y\^5 - 443340\ y\^6 +
611280\ y\^7 - 563922\ y\^8 +
348192\ y\^9 - 138780\ y\^10 +
32400\ y\^11 - 3375\
y\^12)\))\)^
\((1/3)\))\) +
\(1\/\(3\ 2\^\(1/3\)\)\((
\((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4
+
120\ y\^5 - 25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 +
207360\ y\^5 - 443340\ y\^6 +
611280\ y\^7 - 563922\ y\^8 +
348192\ y\^9 - 138780\ y\^10 +
32400\ y\^11 - 3375\
y\^12)\))\)^
\((1/3)\))\)\))\))\))\)}, {
x ->
(4 - y\)\/4 +
1\/2\ \[Sqrt]\((
\( - 6\) + 1\/4\ \((\(-4\) + y)\)\^2 + 4\ y - y\^2 +
1\/3\ \((6 - 4\ y + y\^2)\) +
\((2\ 2\^\(1/3\)\ \((\(-1\) + y)\)\^2\ y\ \((\(-6\) +
5\ y)
\))\)/\((
3\ \((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 +
120\ y\^5 - 25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\
y\^5 -
443340\ y\^6 + 611280\ y\^7 -
563922\ y\^8 + 348192\ y\^9 -
138780\ y\^10 + 32400\ y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\) +
\(1\/\(3\ 2\^\(1/3\)\)\((
\((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 + 120\ y\^5
-
25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\ y\^5 -
443340\ y\^6 + 611280\ y\^7 - 563922\
y\^8 +
348192\ y\^9 - 138780\ y\^10 + 32400\
y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\)\))\) -
1\/2\ \[Sqrt]\((
\( - 6\) + 1\/2\ \((\(-4\) + y)\)\^2 + 4\ y - y\^2 +
1\/3\ \((\(-6\) + 4\ y - y\^2)\) -
\((2\ 2\^\(1/3\)\ \((\(-1\) + y)\)\^2\ y\ \((\(-6\) +
5\ y)
\))\)/\((
3\ \((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 +
120\ y\^5 - 25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\
y\^5 -
443340\ y\^6 + 611280\ y\^7 -
563922\ y\^8 + 348192\ y\^9 -
138780\ y\^10 + 32400\ y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\) -
\(1\/\(3\ 2\^\(1/3\)\)\((
\((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 + 120\ y\^5
-
25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\ y\^5 -
443340\ y\^6 + 611280\ y\^7 - 563922\
y\^8 +
348192\ y\^9 - 138780\ y\^10 + 32400\
y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\)\) +
\((\(-\((\(-4\) + y)\)\^3\) +
4\ \((\(-4\) + y)\)\ \((6 - 4\ y + y\^2)\) -
8\ \((\(-4\) + 6\ y - 4\ y\^2 + y\^3)\))\)/
\((4\ \[Sqrt]\((
\( - 6\) + 1\/4\ \((\(-4\) + y)\)\^2 + 4\ y
-
y\^2 + 1\/3\ \((6 - 4\ y + y\^2)\) +
\((2\ 2\^\(1/3\)\ \((\(-1\) + y)\)\^2\ y\
\((
\(-6\) + 5\ y)\))\)/
\((3\ \((
\(-45\)\ y\^2 + 160\ y\^3 -
210\ y\^4 + 120\ y\^5 - 25\ y\^6
+
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 +
207360\ y\^5 - 443340\ y\^6 +
611280\ y\^7 - 563922\ y\^8 +
348192\ y\^9 - 138780\ y\^10 +
32400\ y\^11 - 3375\
y\^12)\))\)^
\((1/3)\))\) +
\(1\/\(3\ 2\^\(1/3\)\)\((
\((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4
+
120\ y\^5 - 25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 +
207360\ y\^5 - 443340\ y\^6 +
611280\ y\^7 - 563922\ y\^8 +
348192\ y\^9 - 138780\ y\^10 +
32400\ y\^11 - 3375\
y\^12)\))\)^
\((1/3)\))\)\))\))\))\)}, {
x ->
(4 - y\)\/4 +
1\/2\ \[Sqrt]\((
\( - 6\) + 1\/4\ \((\(-4\) + y)\)\^2 + 4\ y - y\^2 +
1\/3\ \((6 - 4\ y + y\^2)\) +
\((2\ 2\^\(1/3\)\ \((\(-1\) + y)\)\^2\ y\ \((\(-6\) +
5\ y)
\))\)/\((
3\ \((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 +
120\ y\^5 - 25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\
y\^5 -
443340\ y\^6 + 611280\ y\^7 -
563922\ y\^8 + 348192\ y\^9 -
138780\ y\^10 + 32400\ y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\) +
\(1\/\(3\ 2\^\(1/3\)\)\((
\((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 + 120\ y\^5
-
25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\ y\^5 -
443340\ y\^6 + 611280\ y\^7 - 563922\
y\^8 +
348192\ y\^9 - 138780\ y\^10 + 32400\
y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\)\))\) +
1\/2\ \[Sqrt]\((
\( - 6\) + 1\/2\ \((\(-4\) + y)\)\^2 + 4\ y - y\^2 +
1\/3\ \((\(-6\) + 4\ y - y\^2)\) -
\((2\ 2\^\(1/3\)\ \((\(-1\) + y)\)\^2\ y\ \((\(-6\) +
5\ y)
\))\)/
\((3\ \((
\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 +
120\ y\^5 - 25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\
y\^5 -
443340\ y\^6 + 611280\ y\^7 -
563922\ y\^8 + 348192\ y\^9 -
138780\ y\^10 + 32400\ y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\) -
\(1\/\(3\ 2\^\(1/3\)\)\((
\((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4 + 120\ y\^5
-
25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 + 207360\ y\^5 -
443340\ y\^6 + 611280\ y\^7 - 563922\
y\^8 +
348192\ y\^9 - 138780\ y\^10 + 32400\
y\^11 -
3375\ y\^12)\))\)^\((1/3)\))\)\) +
\((\(-\((\(-4\) + y)\)\^3\) +
4\ \((\(-4\) + y)\)\ \((6 - 4\ y + y\^2)\) -
8\ \((\(-4\) + 6\ y - 4\ y\^2 + y\^3)\))\)/
\((4\ \[Sqrt]\((
\( - 6\) + 1\/4\ \((\(-4\) + y)\)\^2 + 4\ y
-
y\^2 + 1\/3\ \((6 - 4\ y + y\^2)\) +
\((2\ 2\^\(1/3\)\ \((\(-1\) + y)\)\^2\ y\
\((
\(-6\) + 5\ y)\))\)/
\((3\ \((
\(-45\)\ y\^2 + 160\ y\^3 -
210\ y\^4 + 120\ y\^5 - 25\ y\^6
+
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 +
207360\ y\^5 - 443340\ y\^6 +
611280\ y\^7 - 563922\ y\^8 +
348192\ y\^9 - 138780\ y\^10 +
32400\ y\^11 - 3375\
y\^12)\))\)^
\((1/3)\))\) +
\(1\/\(3\ 2\^\(1/3\)\)\((
\((\(-45\)\ y\^2 + 160\ y\^3 - 210\ y\^4
+
120\ y\^5 - 25\ y\^6 +
\[Sqrt]\((
6912\ y\^3 - 56727\ y\^4 +
207360\ y\^5 - 443340\ y\^6 +
611280\ y\^7 - 563922\ y\^8 +
348192\ y\^9 - 138780\ y\^10 +
32400\ y\^11 - 3375\
y\^12)\))\)^
\((1/3)\))\)\))\))\))\)}}\)
I make the pure function R[x], later it should be used in another
expression, as follows;
R[x_]:=soln1[[2]] /.y->x
Problem occurred when I plot this function
Plot[R[x], {x,0,1}]
Mathematica displays following messages ;
Plot::plnr:
"R[x] is not a machine-size real number at x =
4.16666666666666607`*^-8
Plot::plnr:
R[x] is not a machine-size real number at x = 0.0405669915729157892
Plot::plnr:
R[x] is not a machine-size real number at x = 0.0848087998593736713
General::stop:
Further output of (Plot :: plnr) will be suppressed during this
calculation.
and in Front End Message is as follows
******************************************************************************
Front End Message
The string '\!\(R[x]\) is not a machine-size real number at x =
4.16666666666666607`*^-8' cannot be displayed with
ShowStringCharacters->False due to an error in the string.
******************************************************************************
However, when these values are put into R[x]
In[1]:=r[4.16666666666666607`*^-8]
Out[1]={x -> 0.985661}
In[2]:=r[0.0405669915729157892]
Out[2]={x -> 0.4836810121606896}
In[3]:=r[0.0848087998593736713]
Out[3]={x ->0.3642868596845246}
What is the meaning of above Front End Message ? What is wrong?
Please help me !!!!
Thanks for reading.