@Preben Alsholm O.K., I write whole my work for you:

restart:

with(plots, implicitplot):

eq := proc (z) options operator, arrow; (H^2+(-1)*.27*(1+z)^3-(1/20000)*(1+z)^4)/(H^2)^.1 = .7299500000 end proc;

Y := proc (z) options operator, arrow; fsolve(eq(z), H) end proc;

plot(Y, -10 .. 10, -10 .. 10);

Here is where I have the line below the x-axis. Tough I can write:

plots:-implicitplot(eq(z), z = -10 .. 10, H = -10 .. 10, grid = [150, 150]);

and obtain a more complete graph which has a line above the axis too. Then, for obtaining "diff(H(z), z)" I can write either:

plot(fdiff(Y, [1], z), z = -2 .. 2, caption = "The derivative of y using fdiff on Y");

or:

yp := implicitdiff(eq(z), H, z);

plot(eval(yp, H = 'Y(z)'), z = -3 .. 2, caption = "The derivative of y using implicitdiff and Y");

but remember in both the above procedures we have used "Y" and I think the one above has not considered in plotting  "diff(H(z), z)". Also, if now I want to plot a new function like: "w(z) :=( (1+z)*diff(H(z), z))/H(z)" I should write:

plot(eval((1+z)*yp/H, H = 'Y(z)'), z = -1 .. 5, view = -3 .. 3, caption = "The derivative of y using implicitdiff and Y");

In here, we are using "Y" which has only one below and doesn't know the one above and also "yp" where I think may not be complete(because to obtain it we have used "Y", as well).

sorry for this long message and thank you again!

@Preben Alsholm Yes, the problem is what I told you before. When I want to obtain a new function like:

w(z) := diff(H(z), z)/H(z)

I have to replace H(z) with "Y", right? Then, maple uses the "Y" that we have defined before and that "Y" only contains a line below the x-axis for my equation. This is the problem because only the one above has physical meaning for me.

Also, I still think maple is using only the one above to obtain "diff(H(z), z)".

please check the previous program for the new equation to see what I'm telling you!  

thanks. 

@Preben Alsholm Yes, the problem is what I told you before. When I want to obtain a new function like:

w(z) := diff(H(z), z)/H(z)

I have to replace H(z) with "Y", right? Then, maple uses the "Y" that we have defined before and that "Y" only contains a line below the x-axis for my equation. This is the problem because only the one above has physical meaning for me.

Also, I still think maple is using only the one above to obtain "diff(H(z), z)".

please check the previous program for the new equation to see what I'm telling you!  

thanks. 

@Preben Alsholm thanks for your reply. I think that's better I write my equation. It is:

(H^2-.27*(1+z)^3-(1/20000)*(1+z)^4)/(H^2)^.1 = .7299500000;

please check all your previous works and tell me your idea about it and also your result. Tell me that does your notation work here as well?

@Preben Alsholm thanks for your reply. I think that's better I write my equation. It is:

(H^2-.27*(1+z)^3-(1/20000)*(1+z)^4)/(H^2)^.1 = .7299500000;

please check all your previous works and tell me your idea about it and also your result. Tell me that does your notation work here as well?

@Preben Alsholm Yes, I am interested in the one above. But don't you think maple uses the one below to get

(diff(Y(x), x)? Because you are using "Y" and "Y" only have a plot below the x-axis. I think if I want to plot  (diff(Y(x), x) for the one above it gives probably another plot.

Do you think both above and below one have the same plot?

@Preben Alsholm Yes, I am interested in the one above. But don't you think maple uses the one below to get

(diff(Y(x), x)? Because you are using "Y" and "Y" only have a plot below the x-axis. I think if I want to plot  (diff(Y(x), x) for the one above it gives probably another plot.

Do you think both above and below one have the same plot?

@Preben Alsholm Hi!

I think I can't explain my question. O.K. I say in a different way. If I use your notation, at the end of program I have two similar graphs for:

plot(fdiff(Y,[1],x),x=-2..2,caption="The derivative of y using fdiff on Y");             and:

plot(eval(yp,y='Y(x)'),x=-2..2,caption="The derivative of y using implicitdiff and Y");       right?

That's true, because to definition both of them we have used "Y". But if I don't define "Y" and straightforwardly use:

implicitplot(eq(x), x=0..10,y=-10..10);

I have a more complete plot (an additional part up to the x-axis) and also, I can't use the two upper sentences to plot  " (diff(Y(x),x)) " . I think if I want to plot  " (diff(Y(x),x)) " for the more complete graph I'll have a different plot that I have now. Am I right? In other words I need to plot " (diff(Y(x),x)) ", for that part of graph which is at the top of "x-axis". 

thanks!

@Preben Alsholm Hi!

I think I can't explain my question. O.K. I say in a different way. If I use your notation, at the end of program I have two similar graphs for:

plot(fdiff(Y,[1],x),x=-2..2,caption="The derivative of y using fdiff on Y");             and:

plot(eval(yp,y='Y(x)'),x=-2..2,caption="The derivative of y using implicitdiff and Y");       right?

That's true, because to definition both of them we have used "Y". But if I don't define "Y" and straightforwardly use:

implicitplot(eq(x), x=0..10,y=-10..10);

I have a more complete plot (an additional part up to the x-axis) and also, I can't use the two upper sentences to plot  " (diff(Y(x),x)) " . I think if I want to plot  " (diff(Y(x),x)) " for the more complete graph I'll have a different plot that I have now. Am I right? In other words I need to plot " (diff(Y(x),x)) ", for that part of graph which is at the top of "x-axis". 

thanks!

Sorry, I don't know exactly how to work in "mapleprimes". Maybe this is better or not!

Anyway, I knew

implicitplot(eq(x), x=0..10,y=0..120);

and I had done it before, but the problem is when I want to use your notation

yp := implicitdiff(eq(x), y, x);

plot(eval(yp, y='Y(x)', x=-2..2));

because in this way I've not defined "Y(x)" and just after writting

eq:=x->y^(-1/5)*(y^2-(1+x)^3-(1+x)^4)=1;

I've used "implicitplot"

Thanks a lot.

Sorry, I don't know exactly how to work in "mapleprimes". Maybe this is better or not!

Anyway, I knew

implicitplot(eq(x), x=0..10,y=0..120);

and I had done it before, but the problem is when I want to use your notation

yp := implicitdiff(eq(x), y, x);

plot(eval(yp, y='Y(x)', x=-2..2));

because in this way I've not defined "Y(x)" and just after writting

eq:=x->y^(-1/5)*(y^2-(1+x)^3-(1+x)^4)=1;

I've used "implicitplot"

Thanks a lot.

Thank you very much "Preben Alsholm". Your help was very useful for me. I'm very happy now.

Thank you very much "Preben Alsholm". Your help was very useful for me. I'm very happy now.