Intel has a very good math library. I hope that it is used in Windows, Mac OS X and Linux for evalhf.

Alec

I agree with that, I also think that continuity shouldn't be applied to both Int and Diff.

Alec

It also can be converted to Abel ODE in First Kind form using

convert(...,FirstKind);

Alec

That seems to be fixed in Maple 11.02. The signs are negative in Maple 12 as well, as they should.

Alec

David,

You can't see any issues?

1. Minus doesn't touch 0 in -0.5 and is not too long in -1?

2. 0 is positioned on the same level as the other coordinates on the x-axis and is not shifted to the left comparing with numbers on the y-axis?

3. The both lines %%Pages: 1 and %%Page: 1 1 are present in the eps, or only one of them?

Alec

PS Do the eps file really need comments about bugs in some windows drivers? -Alec

PPS What about the eps export in Standard Maple? Also doesn't have any issues? -Alec

PPPS Other things may be really caused by me using 30'' monitor with high resolution. They didn't look that bad in print. 2 main issues seem to be the location of 0 and the axes and tickmarks width, which, probably, should be configurable in the plot command. -Alec

 

Since that seems to be a typical issue with plot, sum, and fsolve, wouldn't it be better if the arguments were not evaluated there (like in add, for example)? The cases where such an evaluation is needed, seems to be rather rare.

Alec

Since that seems to be a typical issue with plot, sum, and fsolve, wouldn't it be better if the arguments were not evaluated there (like in add, for example)? The cases where such an evaluation is needed, seems to be rather rare.

Alec

Continuity can be visualized (it is not the definition) as follows - if 2 inputs are close to each other, then their outputs are also close. From this point of view, if 2 functions are close to each other, even if the graph of one of them looks smooth, and the graph of another one is close to it, but looks like a saw, their integrals are close to each other, so the integration operator is continuous. But their derivatives are very different, so the differentiation operator is not continuous.

Alec

Whom do you ask, me or the original poster?

If me - I don't have problems with that, just because I don't use Maple personally, for eps or other purposes, and don't have it installed.

I'm glad Maple eps works good for you.

Alec

David,

As Joe Riel said, this is for printing purposes. Try to print it. It should look good on the screen too. Are you sure that your screen settings are good?

If you look at the Postscript code, the first line draws the entire parabola as a Bezier curve. Nothing can draw parabola more smooth than that.

Other 2 lines are for the axes. I set them with width 1.5 so that the tickmarks could have width 1. Generally speaking, that should be configurable in the plot command, probably, as well as the tickmarks width.

For the line widths, 2 things should be kept in mind. First, the picture's size will be reduced in the print, it is not 1 to 1. Second, too thin lines will be barely seen in the first copies, and will completely disappear at about 100th or 200th copy. That's why it is better to have them rather more thick than not thick enough.

Certainly, I know that Times Roman can be set. Some places accept that (as the worst possible choice), but others - don't. Practically, it is better to not to include text at all - then it could be added later in another application.

Alec

PS Comparing eps from few CAS and Matlab, I would suggest using Matlab version. It looked better than others. -Alec

PPS Add showpage at the end of the Postscript code (but before %%EOF) for printing from gsview - otherwise it won't print. -Alec

Many of these seem to be wrong even for real functions. For example, constant 0 is obviously linear, but it is not StrictlyMonotonic.

Alec

And constants are not monotonic, too. I think, I mentioned about that in another thread though.

Alec

I also think that continuity should not be deducted from such things as LinearMap or PolynomialMap because they are defined in much large context including Diff and Int, for which, as we discussed, property "continuous" should not be applied.

Alec

What I meant by continuity of Int, is that, for example, on the function space of analytic functions, the integral of an analytic function is analytic, and considering "topological basis" 1, x, x^2, x^3, ... it can be deducted that it is bounded in some sense. While Diff is unbounded.

Generally speaking, in Maple terminology, both Diff and Int, being inert operators, transform any expression f to an expression of type Int(f,x), or Int(f,x=-infinity..infinity,CauchyPrincipalValue) or Int(f,x=0..1), or maybe Int(f,y,continuous). And while continuity with respect to the first argument may have some sence, the continuity with respect to second, or third argument doesn't.

I also agree with Jacques that it is useless, even if it had some sense, because Maple doesn't work with function spaces and related constructions, and it would be not that simple, probably, even to define them properly.

Alec

For functions on [0,1], for example, yes. 

The standard terminology in physics is bounded and unbounded, I think, instead of continuous and not continuous.

Some pathological examples can be constructed (such as using discrete topology in which any function (or operator in different terminology) is continuous), but I meant usually used (not pathological) function spaces.

Edit: Just noticed the word "compact" in the title. Bounded is the same as continuous (on normed spaces), but compact is even "better" property.

Thinking about that, I could just say that Diff is not continuous (usually)  because it is not bounded.

Alec