## 625 Reputation

17 years, 60 days

## integration variable...

I believe the problem is in your definition of B:

B:=(r,t)-> int(-Curl(E(r,t),t);

Note that t is stretched between being a dummy variable on the right side and a honest variable on the left side.

So, try something like this:

B:=(r,t)->int(-Curl(E(r,tt),tt=0..t);

## fuzzy zero...

I guess the point is that you cannot always decide if a certain number is zero. For example, think about the Goldbach number: g=0.000...x...000 etc., where the kth bit is 0 if 2*k is the sum of two odd primes (k>2), and 1 otherwise. Is g=0?

One can imagine that the Goldbach conjecture is undecidable, in which case g is not computable. Of course most people think that someday somebody will prove the conjecture, but this is a nice colloquial example. It makes the point how a well-defined number might not be computable.

## value...

It's worth a lot to know that bugs are tracked and corrected. Thanks.

## Maple 8 helps some...

Although this does not solve the challange, it is interesting that Maple 8 can re-express A1 in terms of some elementary functions and some more simple hypergeometrics...(2,1) instead of (3,2). Maple 12 does not seem to know this.

A1 := hypergeom([-1/2, 3/8, 169/88], [81/88, 19/8], z);

expand(simplify(A1)); #in Maple8

-3/8*hypergeom([-1/2, 11/8],[19/8],z)+15/8*hypergeom([-1/2, 11/8],[19/8],z)*z-319/108/(1-z)^(1/2)*z+341/216/(1-z)^(1/2)*z^2+11/8/(1-z)^(1/2)+121/1026*hypergeom([1/2, 19/8],[27/8],z)*z-55/342*hypergeom([1/2, 19/8],[27/8],z)*z^2

## yes, but...

What you write is correct.  You use the fact that diff(exp(u),u)=exp(u), together with the chain rule.

When you write out the difference quotient for this derivative of exp(u), you find that you need to know

limit(dq,h=0) where dq=(exp(h)-1)/h. This is a special case of the limit in question, when a=e.

The fact that this is equal to 1 is essentially the definition of the number e.

## yes, but...

What you write is correct.  You use the fact that diff(exp(u),u)=exp(u), together with the chain rule.

When you write out the difference quotient for this derivative of exp(u), you find that you need to know

limit(dq,h=0) where dq=(exp(h)-1)/h. This is a special case of the limit in question, when a=e.

The fact that this is equal to 1 is essentially the definition of the number e.

## I*sigh^2...

But look at this!

A:=int(sqrt(t^5+6*t)*(5*t^4+6),t=0..I) ;
#the upper limit is I=sqrt(-1) in case the font makes this unclear

B:=int(sqrt(t^5+6*t)*(5*t^4+6),t=I..1) ;

simplify(A+B);

This behavior of int returning a hypergeom that is difficult to simply to 14*sqrt(7)/3 is one of things that can make using MapleTA in calculus II frustrating.

It's hard to get Maple to  recognize that the hypegeom expression is equal to 14*sqrt(7)/3.

## I*sigh^2...

But look at this!

A:=int(sqrt(t^5+6*t)*(5*t^4+6),t=0..I) ;
#the upper limit is I=sqrt(-1) in case the font makes this unclear

B:=int(sqrt(t^5+6*t)*(5*t^4+6),t=I..1) ;

simplify(A+B);

This behavior of int returning a hypergeom that is difficult to simply to 14*sqrt(7)/3 is one of things that can make using MapleTA in calculus II frustrating.

It's hard to get Maple to  recognize that the hypegeom expression is equal to 14*sqrt(7)/3.

## you have a table, not an array...

Your initial construction of c produces a table, not an array.

for i from 1 to 5 do c[i]:=i end do;

type(c,table);
true

type(c,array);
false

Thus you can clear c by simply assigning it to be the null table:

c:=table([ ]);

There is no need for your "holding array" d.

## risk...

At the risk of being suckered into a deep question by the master, I would say that

exp(x)=13 is an equation, regardless of the context of x.

Something like exp(x)-13 would be an expression. I remember being disappointed that "expression" is not a Maple "datatype" yet the help screens give a decent defintion of expression. (I would like to define "expression" in such a way that equations and inequalities are not expressions, but so that an "expression" is somethat that could parse as one side of an "equation" or "inequality". I do see some pitfalls with this approach)

Something like unapply(exp(x)-13,x) would be a function.

It would be nice if something like this happened:

>type(x^2,expression);

true

>type(x^2, procedure);

false (this does happen, of course)

>type(unapply(x^2,x),procedure);

true (this also happens, of course)

## Too general...

Your situation is essentially the same as a general first order diffeq

x'(t)=F(t,x(t)).

If your function f is continuous, then a short time solution always exists, but it is rare that a "formula" can be written down for x(t).

You say b is small, but what about f? Look what happens if your function is a constant function, such as f(x)=1/b.

## eval vs evaluate fn...

I have never gotten into the habit of using eval. One of the things that I immediately valued about Maple was how it treated functions, and so I have always used function evaluation instead of eval. As I have read Mapleprimes, I have always been surprised at how many people prefer eval.

In this case, set up q as a proc, and there is no problem:

q := a->(6*((1/3)*a-1/9))/(36*a-116+12*sqrt(12*a^3-3*a^2-54*a+93))^(1/3);

q(1/3) ;

Error, (in q) numeric exception: division by zero

>limit(q(a),a=1/3);

undefined

So as long as q as a function works properly, I could care less about eval. But it would be nice if the two perspective were consistent.

## I miss psfrag...

Although Maple did make noble progress with the ability to put math symbols in a graph to be exported to eps, I still find it far inferior to what I used to be able to do with the LaTeX psfrag package.

The "classic" plot format along with textplot would allow one to place text markers in the eps file that psfrag could mark up according LaTeX code. That allowed something close to publication quality.

But now the bloated Maple eps file does not afford this technique--Maple's new eps format is not compatible with psfrag.

## Developers vs Founders...

I always cringe when we refer to the "Developers" as if they were the "Founders" referenced in Deep Space Nine.

The "Developers" are the ones who decided to orphan Classic Maple, give us that absurd Document Mode, and who believe that they can can do better than Knuth/LaTeX with their "ingenious" 2D input mode.

For math presentation, Knuth is the "Founder."

## numeric formatting-save change...

Yes, this seems to work. But how do I save the change so that the "fixed" format is the default when Maple is launched?

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