@wlferguson19 It's a dimensionless number, in this case a ratio of two things with the same units. I think that the Units package can only handle units on the ratio scale of measurement (I'll put a Wikipedia link when I get a chance). AFAIK, it can't handle other scales such as ordinal (e.g., Mohs hardness), difference (e.g., calendar year), or logarithmic (e.g., pH).

@MapleEnthusiast Your expression is simply a polynomial with a huge number of variables  (when you count the indices), a huge number of terms, no coefficients, and a low degree (4 or 5). simplify is too generic to be of much help. Actually, I think that it might make patterns even harder to see. The relevant patterns are in the indices, which simplify won't even look at. Perhaps something can be achieved by encoding the indices as exponents.

Were you able to make use of the sorting procedures that I posted for you in another thread?

I suppose that you've been given a Maple procedure text2num? Have you also been given its inverse num2text? Or are you supposed to write it? Due to the simplicity of the text-to-number encoding, I was able to write num2text without seeing text2num.

Hint: My num2text took 3 lines of code. The most important part is a convert(..., base, ...) command. The rest of the decoding took only one line of code, the central part of which is a solve command for the equations, then applying num2text to the numbers found for x, y, and z, then inserting spaces between the words.

@user-JG I strongly disagree with these statements of yours:

•  While Maple has friendly routines to deal with decomposing polynomials, the analogous
  handling of integer numbers does not seem to have been implemented yet.

• A proper implementation of routines for dealing with decomposition of numbers would be a nice addition to Maple. Algebra is good, arithmetics is missing.

I think that you're simply unaware of the commands available. Please describe some operations on integers that you'd like, and I'll tell you how to do them.

My question was Why do you want the form
    base, exponent, base, exponent, ....?
The form
    base,        base,        ...
    exponent, exponent, ...
is much more convenient.

Oddly enough, two days ago I started having a similar problem in MaplePrimes, not Maple. This part is exactly as you described: "It looks like the local refreshing problem is following the cursor of the mouse." I'm using Chrome as my browser. I have not had this problem on any other web pages.

@greatpet Maple's applyrule would work for this also were it not for the serious localization bug that I pointed out. My guess is that this bug would be easy to fix. However, subsindets and evalindets are much more reliable than applyrule. Unfortunately, the coding needed to use them is substantially more complicated in this case than that needed for applyrule. For other cases, it's often no more complicated.

@acer It's interesting that ifactors works by calling ifactor and restructuring its output. I would've expected that to be the other way around.

@user-JG I understand why you'd want to remove the initial 1, but why would you want to unpair the exponents from their bases?

Use the green uparrow on the toolbar to attach that as a worksheet.

@tomleslie The Vectorfield command in your procedure f is not needed. The Gradient command already returns a vector field.

@mon And that form from that thesis is not the polynomial given by form= MOD2? Can you show me a small example of the desired form? How about doing it for modus ponens:

((p implies q) and p) implies q 

(just the first thing I thought of). Or you may choose a better example, perhaps directly from that thesis.

@mon It would be easier if you specified the form that you want to convert to.

The graph of a paraboloid is not bounded: It extends to +infinity. So what do you mean by "I want the full paraboloid to show"?

I don't think that you ask an excessive number of questions. There's no need to be shy.

@aoakindele I have not read the code, so I'm not sure about the finer details of this, but this is my best guess at Maple's numeric BVP algorithm based on many years of experience using it. (And you learn a lot more about the inner workings from the error messages than when it runs smoothly.)

1. The system of ODEs is converted to a first-order system by introducing new dependent variables.

2. The derivatives are replaced by finite-difference approximations, so now it's a system of algebraic equations.

3. A mesh of evenly spaced points is defined on the solution interval. 

4. The algebraic equations are solved at the mesh points by Newton's method.

5. The mesh is doubled. Interpolation is used to obtain a Newton's method initial guess at the new points. Go back to step 4, or quit if sufficient accuracy has been obtained.

From the point of view of the parts of Maple that perform polynomial algebra, such as factor, your expression is identical to

f(4*x) + 2*f(2*x) + 1

for some arbitrary symbol f. This is why it isn't immediately factored.