13 years, 1 days

## Order of limits...

@Preben Alsholm Thanks, and glad to hear it got resolved in Maple 2023.

@mmcdara I was under the impression that an improper integral with infinity as one of the limits is meant to be read as the limit of a finite number going to infinite, so

limit(int(0,x=0..L),L=infinity)
limit(int(0,x=0..L,y=0..1),L=infinity)
0
0

and hence I was also expecting 0 for the 2D integrals.

I agree that the following is undefined

0*infinity;
undefined

However, when either one of them is fixed and one takes a variable to approach the other number in the limit, the result does not change. This is illustrated by the following limits

limit(infinity*x,x=0, right);
limit(infinity/x,x=infinity);
infinity
infinity
limit(0*x,x=infinity);
limit(0/x,x=0, right);
0
0

In the first two the result stays infinite, and in the last two the result stays zero.

However, it is indeed a bit odd that then

subs(c = 0, limit(int(c, x = 0 .. L), L = infinity))
subs(c = 0, int(c, x = 0 .. infinity))
subs(c = 0, int(c, x = 0 .. infinity, AllSolutions=true))
signum(0)*infinity
signum(0)*infinity
signum(0)*infinity

which Maple therefore considers to be undefined.

## Discontinuity in initial condition...

pdsolve using a system of 1st order PDEs doesn't seem to work out-of-the-box for a slight modification of example 2 (a discontinuous initial condition):

bc:={ u(0,t)=0, u(1,t)=1, u(x,0)=2*Heaviside(x-0.5) }:

while Rouben's solution does.

## THICKNESS(0.1)...

As @acer indicated, for Maple 2016 one cannot use stylesheet. The following command, using a thickness of 0.1 instead of 0, makes the edges even thinner than given in acer's solution:

P:=DrawGraph(G):
subsindets(P, specfunc(THICKNESS), ()->THICKNESS(0.1));

## Physics[Assume]...

From Maple 2015 onwards one can use Physics[Assume] instead of assume. This will resolve it:

with(Physics):

expr1:=sqrt(a);
Assume(a>0)
;
expr2:=sqrt(a);
subs(a=2, expr1); #gives correct answer: sqrt(2)
subs(a=2, expr2); #now also gives correct answer: sqrt(2)

## @ecterrab  Thank you very much aga...

Thank you very much again for the really quick fix.

## bug...

This still seems to be wrong (also in Maple 2018), because multi-dimensional indexing works differently in Python (https://scipy-cookbook.readthedocs.io/items/Indexing.html#Elements).

The correct output would need to be

import numpy
def QLoc():
Q = numpy.mat([[0,0],[0,0]])
Q[0, 0] = 0.1e6
Q[1, 1] = 0.1e5
Q[0, 1] = 0.1e4
Q[1, 0] = 0.1e4
return(Q)

## @Mac Dude  Thanks. This is a valid...

Thanks. This is a valid workaround, but the quality is less and available options are much more restricted. For example, a table of contents is not possible with this. I prefer to have the eBookTools working properly.

## Looks like it is fixed in Maple 2017....

Looks like it is fixed in Maple 2017.

## @pake Did you try it out?...

@pake Did you try it out?

## It is working in Maple 2017, thanks for ...

It is working in Maple 2017, thanks for the fix.

## The problem is still present in Maple 20...

The problem is still present in Maple 2017. Some of the integrals can be calculated correctly using the piecewise representation of the Heaviside function (similar to using the aforementioned option method=ftoc).

convert(Heaviside(z),piecewise)
H(z):= piecewise(z < 0, 0, z = 0, undefined, 0 < z, 1)
int(Heaviside(-x^2-y^2+1), x = 0 .. 1, y = 0 .. 1) # Gives incorrect -pi/4
int(H(-x^2-y^2+1), x = 0 .. 1, y = 0 .. 1) # Gives correct pi/4
int(H(-x^2-y^2+1), x = 0 .. infinity, y = 0 .. 1) # Gives correct pi/4
int(H(-x^2-y^2+1), x = 0 .. infinity, y = 0 .. 2) # Gives undefined

## @DJ Clayworth  Not sure what kind ...

Not sure what kind of problems the OP had exactly in mind, but in Maple 2016

loglogplot(exp(-t))

shows an upshoot near 1e-5 and

loglogplot(exp(-t),t=1e-5..1e5)

shows a flat region near t=1e3..1e5

## @ecterrab Thanks a lot for the really qu...

@ecterrab Thanks a lot for the really quick bug fix.

## @Preben Alsholm Thank you for confirming...

@Preben Alsholm Thank you for confirming this and submitting the bug report.

## @vv and @acer Thanks for simplifying and...

@vv and @acer Thanks for simplifying and filing the bug! I should have done so myself.

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