## 13426 Reputation

19 years, 96 days

## Maple 12...

@acer I executed your worksheet in Maple 12 and I got this dreaded result from NLPSolve:

sol := NLPSolve(bandpeak(Zstub), Zstub=Z[1]..Z[N],
method=sqp, initialpoint = [Zstub=Z[2]]);
Warning, no iterations performed as initial point satisfies first-order conditions
[0.375277160248564, [Zstub = 5.02596984406875]]

whereas in Maple 2022 I get

sol := NLPSolve(bandpeak(Zstub), Zstub=Z[1]..Z[N],
method=sqp, initialpoint = [Zstub=Z[2]]);
Warning, limiting number of evaluations reached
...................................many of these Warnings
Warning, limiting number of evaluations reached
[0.111740781972696004, [Zstub = HFloat(43.9058440724061)]]

## Cannot reproduce...

I tried your worksheet and didn't get any errors.
`Maple 2022.0, X86 64 WINDOWS, Mar 8 2022, Build ID 1599809`

## Plural or singular...

@Carl Love I'm always being put off (to use a polite expression) by the use of plural pronouns for a situation, where it is quite obvious a singular version should have been used.
" The member @nm has a long-standing habit of deleting their own Questions"
I would simply have said: The member @nm has a long-standing habit of deleting his own Questions.
By this I'm not implying that nm is a male (I don't know), but just using the time honored usage in such cases.

## Example...

@Mac Dude Could you give us an example?

I have an old one of my own:

```restart;
Digits:=15:
sys := {6*exp(x+y)/(1+exp(x+y))+exp(2*y)/(1+exp(2*y)) = 2,
5*exp(2*x)/(1+exp(2*x))+2*exp(x+y)/(1+exp(x+y)) = 1}:
plots:-implicitplot(sys,x=-10..10,y=-10..10);
S:=solve(sys);
evalf(S[1]);
fsolve(sys,S[1]); # returns unevaluated
fsolve(sys,{x=-1.2..-1, y=-.1..0.1}); #OK
```

But that one is not new, even Maple 12 has that behavior.

## The help page...

@opus64 In the help page for isolate you also find this statement:

"For direct solutions of equations, solve may be more efficient than isolate, which is intended, primarily, for use in an interactive Maple session." (my emphasis).
The code for isolate can easily be seen:

```restart;
showstat(isolate,1..6); # we need only look at the lines 1 through 6.
eq:=P=A+(z+x1/2/z); # Using x1 instead of x
## In the code expr and x will be:
expr:=eq; x:=z+x1/2/z;
has(expr,x); # Line 3, answer false
type(x,`^`);   # Line 4, answer false
```

'has' is builtin, so you cannot see its code:
op(3,eval(has)); # option builtin
but the help page for has states:

"The has(f, x) function returns true if f contains the expression x;  otherwise false is returned.
The expression f contains x if and only if a subexpression of f (as defined by Maple's op function) is equal to x." (my emphasis)

## The poster himself?...

Could it be the poster himself?

## Greek...

I cannot check Maple V Release 5 right now since I don't have it on this machine.
I checked Maple 12, however, and that behaves like all the versions I remember. I have had all Maple releases since Maple V Release 2.
I would really be surprised if Maple V Release 5 (or 5.1) really displays alpha and beta as they are written in Greek.
Could you show us a screenshot from Maple V Release 5?

## The data...

The output from sparsematrixplot makes suggests that what you ask for isn't readily available:

```restart;
with(plots):
with(LinearAlgebra):

A := Matrix([[2, 1, 0, 0, 3], [0, 2, 1, 0, 0], [0, 0, 2, 1, 0], [0, 0, 0, 2, 1], [0, 0, 0, 0, 2]]);

sparsematrixplot(A, matrixview, color = "DarkGreen"); p:=%:
pd:=plottools:-getdata(p);
pd[1];
plot(pd[1,3],thickness=4);
plot(pd[1,3],style=point,symbol=solidcircle,symbolsize=50);
```

## Change of variables...

@vv Maybe I misunderstand you when you say " Unfortunately, Maple cannot compute it."
In Maple 2021.2 I get (using your suggested change of variables):

```A:=Int(2/(1-x^p)^(1/p), x=0..1);
IntegrationTools:-Change(A,x^p=t) assuming p>1;
value(%) assuming p>1;
```

The answer given is 2*Beta(1/p, -1/p + 1)/p, i.e. the same as the result by cook.

So what is the correct answer?

## Make everything concrete...

@escorpsy I don't see any way of getting a symbolic answer with parameters. But you can certainly find exact answers with concrete values for the parameters. As an example:

```M := Int((x*(1 - x)*(-I*epsilon + p^2) + m^2)^((d - 4)/2), x = 0 .. 1);
value(eval(M,[epsilon=1/100,d=3,m=1,p=1])); # Exact integration
evalc(%)=evalf(%);
evalf(eval(M,[epsilon=1/100,d=3,m=1,p=1])); # Numerical integration
```

## D and i...

The use of D is unfortunate since it means the differentiation operator in Maple:

`D(sin); # Answer cos`

So use another name, e.g. D1.
Secondly, by default the imaginary unit is  'I', not 'i'.

## An observation...

@acer Just an observation: So the following two versions of dividing are not quite the same:

```1/4/(x-2);
1/(4*(x-2));
```

## Correction...

@tomleslie In order to be fair you must divide by 2000 000 in ans2:

```ans1:=(654321.987*123456.789)/2;
ans2:=(654321987*123456789)/2000000;```

## Floats and syntax...

@nm Normally you cannot put a number first followed by a letter; that would produre a syntax error. Example 1w would produce an error.
There are exceptions:  1d and  1e are examples.

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