@acer Thank you so much for your quick reply.

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

Thanks hirnyk!

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

Thanks hirnyk!

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.

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 for your time.

Ozgur

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

Ozgur

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]?

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. Thank you.

Ozgur

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

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

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?