## 78 Reputation

16 years, 60 days

## @acer Thank you so much for your quick r...

@acer Thank you so much for your quick reply.

## Yeah......

I feel embarrassed when I see that the answers to my questions are so obvious.

Thanks hirnyk!

## Yeah......

I feel embarrassed when I see that the answers to my questions are so obvious.

Thanks hirnyk!

## one more question......

Thank you Joe, this works great.

Is it at all possible to display y1, y2 etc. right next to the lines on the plot, rather than below the plot as legends? I'm using Maple 12 by the way.

## one more question......

Thank you Joe, this works great.

Is it at all possible to display y1, y2 etc. right next to the lines on the plot, rather than below the plot as legends? I'm using Maple 12 by the way.

## That's very helpful. Thanks a lot again ...

That's very helpful. Thanks a lot again for your time.

Ozgur

## That's very helpful. Thanks a lot again ...

That's very helpful. Thanks a lot again for your time.

Ozgur

## It works!...

Thank you pagan!

Mine is an expression. I am trying to see how the derivative of an expression behaves (positive or negative), when I vary 2 of its variables (fixing the rest, of course). For example:

I don't exactly understand your code, but it works!

If I want to change the colors from the default green/red to, say, black/blue, how do I do it?

Also, doesn't color=[signum@fexpr,-signum@fexpr,0] mean either color=[1,-1,0] or color=[-1, 1, 0]? Why doesn't it work when I write, say, color=[-1, 1, 0]?

## It works!...

Thank you pagan!

Mine is an expression. I am trying to see how the derivative of an expression behaves (positive or negative), when I vary 2 of its variables (fixing the rest, of course). For example:

I don't exactly understand your code, but it works!

If I want to change the colors from the default green/red to, say, black/blue, how do I do it?

Also, doesn't color=[signum@fexpr,-signum@fexpr,0] mean either color=[1,-1,0] or color=[-1, 1, 0]? Why doesn't it work when I write, say, color=[-1, 1, 0]?

## Oh, I see. Now it's clear....

Oh, I see. Now it's clear. Thank you.

Ozgur

## what if the function is not cubic anymor...

Hi Robert,

I worked on your algorithm for a while, and I think I wrote something which would invert cubic functions, which are monotone decreasing in the first quadrant. However, I cannot find the inverse of piecewise(x <= 2, 10/x^0.7e-1+3-7*x+4*x^2-x^3, x <= 3, 10/x^0.7e-1-49.13953960-((-1)*65.1860528)*x-29.0813981*x^2-((-1)*4.01162830)*x^3, x <= 9, 10/x^0.7e-1-1.986362376-2.47249394*x-((-1)*.306573983)*x^2-0.1316006154e-1*x^3) because now the function is not cubic. It is monotone decreasing though, hence should have an inverse.

Solving each piece separately and then picking the branch which gives the smallest error for f^(-1)(f(x))-x does not work anymore, because I get RootOf expressions and Maple tends to return only one value when I evaluate a list of solutions.

Do you have any idea?

Thank you,

Ozgur

## what if the function is not cubic anymor...

Hi Robert,

I worked on your algorithm for a while, and I think I wrote something which would invert cubic functions, which are monotone decreasing in the first quadrant. However, I cannot find the inverse of piecewise(x <= 2, 10/x^0.7e-1+3-7*x+4*x^2-x^3, x <= 3, 10/x^0.7e-1-49.13953960-((-1)*65.1860528)*x-29.0813981*x^2-((-1)*4.01162830)*x^3, x <= 9, 10/x^0.7e-1-1.986362376-2.47249394*x-((-1)*.306573983)*x^2-0.1316006154e-1*x^3) because now the function is not cubic. It is monotone decreasing though, hence should have an inverse.

Solving each piece separately and then picking the branch which gives the smallest error for f^(-1)(f(x))-x does not work anymore, because I get RootOf expressions and Maple tends to return only one value when I evaluate a list of solutions.

Do you have any idea?

Thank you,

Ozgur

## casus irreducibilis...

Thank you Robert.

If you did not include simplify( ) in your example, Maple would return roots with complex variables such as

I*((1/6)*120^(1/3)*15^(1/6)*sin(-(1/3)*arctan((1/9)*sqrt(1419))+(1/3)*Pi)-(1/180)*120^(2/3)*15^(5/6)*sin(-(1/3)*arctan((1/9)*sqrt(1419))+(1/3)*Pi)).

but this evaluates to -1.*10^(-10)*I which is very small. So I guess that is what simplify does; disregarding very small numbers, in addition to other simplifications?

## solved...

Doug and Robert, Thank you for your time; both of your suggestions are exactly what I was trying to do. It is a shame that for 6 months, since I started using Maple, I thought that I was defining an object which of type "function" when I wrote y := x-x^2; !!! I think I need to go back to the basics and study the definitions. Cheers, Ozgur

## solved...

Doug and Robert, Thank you for your time; both of your suggestions are exactly what I was trying to do. It is a shame that for 6 months, since I started using Maple, I thought that I was defining an object which of type "function" when I wrote y := x-x^2; !!! I think I need to go back to the basics and study the definitions. Cheers, Ozgur
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