@digerdiga We can compare the residual sums of squares, and the nonlinear fit is better, but only slightly better.

Download Linearized_Fit.mw

I updated the procedure substantially to include the eigenvalues, and I added some color to improve the eye-tracking of the circles. I also added a second example, where the disks are more separated.

I updated the procedure substantially to include the eigenvalues, and I added some color to improve the eye-tracking of the circles. I also added a second example, where the disks are more separated.

@DJJerome1976 

I agree with DJ Jerome's skepticism about RealDomain. I am particularly skeptical about RealDomain:-solve. That's why I said to put

with(RealDomain, `^`);

rather than

with(RealDomain);

into your initialization file. The former will overload only the `^` operator, which is enough to accomplish everything discussed in this thread and which doesn't introduce any problems that I know of.

@DJJerome1976 

I agree with DJ Jerome's skepticism about RealDomain. I am particularly skeptical about RealDomain:-solve. That's why I said to put

with(RealDomain, `^`);

rather than

with(RealDomain);

into your initialization file. The former will overload only the `^` operator, which is enough to accomplish everything discussed in this thread and which doesn't introduce any problems that I know of.

@Alina8faq Yes, there is a way that you can use I as a variable in Maple 13. First, choose a symbol to use as the imaginary unit. Let's say that you choose J (although it need not be a single letter). Then give the command

interface(imaginaryunit= J);

Now you are free to use I however you like.

Even though you use the I with subscripts, it is still confusing to algsubs. But all will be okay if you give the command above.

@Alina8faq Yes, there is a way that you can use I as a variable in Maple 13. First, choose a symbol to use as the imaginary unit. Let's say that you choose J (although it need not be a single letter). Then give the command

interface(imaginaryunit= J);

Now you are free to use I however you like.

Even though you use the I with subscripts, it is still confusing to algsubs. But all will be okay if you give the command above.

@ANANDMUNAGALA Please note that I have significantly updated the procedure since you posted the above Reply.

@ANANDMUNAGALA Please note that I have significantly updated the procedure since you posted the above Reply.

@oxy Even using a variety of assumptions, I cannot simplify the expression or convert it to StandardFunctions.

@oxy Even using a variety of assumptions, I cannot simplify the expression or convert it to StandardFunctions.

@spradlig RealDomain does make your plot work the way that you want, and it does make 4^(1/2) evaluate to 2. Did you try it? If you want these behaviours to be the default, then include this line in your initialization file:

with(RealDomain, `^`):

@spradlig RealDomain does make your plot work the way that you want, and it does make 4^(1/2) evaluate to 2. Did you try it? If you want these behaviours to be the default, then include this line in your initialization file:

with(RealDomain, `^`):

It will work for the plain numeric expressions, but not the plots.

It will work for the plain numeric expressions, but not the plots.