f

#### A Maplesoft's customer

```A word to you guys and gals from a Maplesoft's customer.

..................................................................

http://www.maplesoft.com/support/

"Maplesoft is committed to providing the lowest
level of support for the products it sells."

..................................................................

DESCRIPTION:    Regression bug.  1 of many 1000s.

TEST CASE:      int(1/(1+z^2+z^5), z= 0..1);

EXPECTED:       sum(ln(1-1/z)/(2*z+5*z^4),z= RootOf(1+_Z^2+_Z^5))

.7398318370+0.*I

CHECKUP:        evalf(Int(1/(1+z^2+z^5), z= 0..1));

.7398318370

--------------- (2005)  Maple 10.00 -----------------------------
int(1/(1+z^2+z^5),z = 0 .. 1)
--------------- (2004)  Maple 9.5.1 -----------------------------
int(1/(1+z^2+z^5),z = 0 .. 1)
--------------- (2004)  Maple 9.5 -------------------------------
int(1/(1+z^2+z^5),z = 0 .. 1)
--------------- (2003)  Maple 9 ---------------------------------
int(1/(1+z^2+z^5),z = 0 .. 1)
--------------- (2002)  Maple 8 ---------------------------------
sum(_R*ln(-109507419/7363759*_R^2+14455759/7363759-2224698426/736
3759*_R^4+797015325/7363759*_R^3+18837605/7363759*_R),_R = RootOf
(3233*_Z^5+27*_Z^3+50*_Z^2-1))-sum(_R*ln(-2224698426/7363759*_R^4
+797015325/7363759*_R^3-109507419/7363759*_R^2+18837605/7363759*_
R+7092000/7363759),_R = RootOf(3233*_Z^5+27*_Z^3+50*_Z^2-1))

..7398318370+0.*I
--------------- (2001)  Maple 7 ---------------------------------
sum(_R*ln(-109507419/7363759*_R^2+14455759/7363759-2224698426/736
3759*_R^4+797015325/7363759*_R^3+18837605/7363759*_R),_R = RootOf
(3233*_Z^5+27*_Z^3+50*_Z^2-1))-sum(_R*ln(-2224698426/7363759*_R^4
+797015325/7363759*_R^3-109507419/7363759*_R^2+18837605/7363759*_
R+7092000/7363759),_R = RootOf(3233*_Z^5+27*_Z^3+50*_Z^2-1))

..7398318370+0.*I
--------------- (2000)  Maple 6 ---------------------------------
sum(_R*ln(-109507419/7363759*_R^2+14455759/7363759-2224698426/736
3759*_R^4+797015325/7363759*_R^3+18837605/7363759*_R),_R = RootOf
(3233*_Z^5+27*_Z^3+50*_Z^2-1))-sum(_R*ln(-2224698426/7363759*_R^4
+797015325/7363759*_R^3-109507419/7363759*_R^2+18837605/7363759*_
R+7092000/7363759),_R = RootOf(3233*_Z^5+27*_Z^3+50*_Z^2-1))

..7398318370+0.*I
--------------- (1997)  Maple V Rel 5 ---------------------------
sum(_R*ln(14455759/7363759+18837605/7363759*_R-2224698426/7363759
*_R^4+797015325/7363759*_R^3-109507419/7363759*_R^2),_R = RootOf(
3233*_Z^5+27*_Z^3+50*_Z^2-1))-sum(_R*ln(18837605/7363759*_R-22246
98426/7363759*_R^4+797015325/7363759*_R^3-109507419/7363759*_R^2+
7092000/7363759),_R = RootOf(3233*_Z^5+27*_Z^3+50*_Z^2-1))

..7398318370
--------------- (1995)  Maple V Rel 4 ---------------------------
sum(_R*ln(14455759/7363759+18837605/7363759*_R-2224698426/7363759
*_R^4+797015325/7363759*_R^3-109507419/7363759*_R^2),_R = RootOf(
3233*_Z^5+27*_Z^3+50*_Z^2-1))-sum(_R*ln(18837605/7363759*_R-22246
98426/7363759*_R^4+797015325/7363759*_R^3-109507419/7363759*_R^2+
7092000/7363759),_R = RootOf(3233*_Z^5+27*_Z^3+50*_Z^2-1))

..7398318370
--------------- (1994)  Maple V Rel 3 ---------------------------
sum(_R*ln(14455759/7363759+18837605/7363759*_R-2224698426/7363759
*_R^4+797015325/7363759*_R^3-109507419/7363759*_R^2),_R = RootOf(
3233*_Z^5+27*_Z^3+50*_Z^2-1))-sum(_R*ln(-2224698426/7363759*_R^4+
797015325/7363759*_R^3-109507419/7363759*_R^2+18837605/7363759*_R
+7092000/7363759),_R = RootOf(3233*_Z^5+27*_Z^3+50*_Z^2-1))

..7398318370
-----------------------------------------------------------------

..................................................................

Maple: Unsafe at any evaluation

http://maple.bug-list.org/maple-crisis.php

Teach, learn, and crash your career using Maple.

..................................................................

```
 0
5/3/2006 6:17:43 PM
comp.soft-sys.math.maple 4344 articles. 3 followers.

3 Replies
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Similar Articles

[PageSpeed] 43

```In article <1146680263.908226.205180@i40g2000cwc.googlegroups.com>,

>TEST CASE:      int(1/(1+z^2+z^5), z= 0..1);
>
>EXPECTED:       sum(ln(1-1/z)/(2*z+5*z^4),z= RootOf(1+_Z^2+_Z^5))
>
>                .7398318370+0.*I
>
>CHECKUP:        evalf(Int(1/(1+z^2+z^5), z= 0..1));
>
>                .7398318370
>
>
>--------------- (2005)  Maple 10.00 -----------------------------
>int(1/(1+z^2+z^5),z = 0 .. 1)

Evidently Maple is unsure about whether the denominator has
roots in the interval [0,1].  This works:

int(1/(1+z^2+z^5),z = 0 .. 1, continuous);

Robert Israel                                israel@math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada
```
 0
israel
5/3/2006 7:16:19 PM
```Robert Israel writes

RI>  Evidently Maple is unsure about whether
RI>  the denominator has roots in the interval [0,1]

Maple is _sure_ that the denominator has no roots in the [0,1].

readlib(iscont): # for compatibility with Maple V Rel 5/4/3
iscont(1/(1+z^2+z^5), z= 0..1);

--------------- (2005)  Maple 10.00 ---------------------------
true
--------------- (2004)  Maple 9.5.1 ---------------------------
true
--------------- (2004)  Maple 9.5 -----------------------------
true
--------------- (2003)  Maple 9 -------------------------------
true
--------------- (2002)  Maple 8 -------------------------------
true
--------------- (2001)  Maple 7 -------------------------------
true
--------------- (2000)  Maple 6 -------------------------------
true
--------------- (1997)  Maple V Rel 5 -------------------------
true
--------------- (1995)  Maple V Rel 4 -------------------------
true
--------------- (1994)  Maple V Rel 3 -------------------------
true
---------------------------------------------------------------

readlib(discont): # for compatibility with Maple V Rel 5/4/3
s := discont(1/(1+z^2+z^5), z);
evalf(s);

--------------- (2005)  Maple 10.00 ---------------------------
s := {RootOf(1+_Z^2+_Z^5,-1.193859111)}
{-1.193859111}
--------------- (2004)  Maple 9.5.1 ---------------------------
s := {RootOf(1+_Z^2+_Z^5,-1.193859111)}
{-1.193859111}
--------------- (2004)  Maple 9.5 -----------------------------
s := {RootOf(1+_Z^2+_Z^5,-1.193859111)}
{-1.193859111}
--------------- (2003)  Maple 9 -------------------------------
s := {RootOf(1+_Z^2+_Z^5,-1.193859111)}
{-1.193859111}
--------------- (2002)  Maple 8 -------------------------------
s := {RootOf(1+_Z^2+_Z^5,-1.193859111)}
{-1.193859111}
--------------- (2001)  Maple 7 -------------------------------
s := {RootOf(1+_Z^2+_Z^5,-1.193859111)}
{-1.193859111}
--------------- (2000)  Maple 6 -------------------------------
s := {RootOf(1+_Z^2+_Z^5,-1.193859111)}
{-1.193859111}
--------------- (1997)  Maple V Rel 5 -------------------------
s := {RootOf(1+_Z^2+_Z^5,-1.193859111)}
{-1.193859111}
--------------- (1995)  Maple V Rel 4 -------------------------
s := {RootOf(1+_Z^2+_Z^5,-1.193859111)}
{-1.193859111}
--------------- (1994)  Maple V Rel 3 -------------------------
s := {RootOf(1+_Z^2+_Z^5,-1.193859111)}
{-1.193859111}
---------------------------------------------------------------

VM and GEMM architect
Co-founder, CEO, Mathematical Director

http://www.cybertester.com/  Cyber Tester, LLC
http://maple.bug-list.org/   Maple Bugs Encyclopaedia
http://www.CAS-testing.org/  CAS Testing

```
 0
5/4/2006 1:01:35 AM
```In article <1146704495.900898.208170@e56g2000cwe.googlegroups.com>,
>Robert Israel writes
>
>
>RI>  Evidently Maple is unsure about whether
>RI>  the denominator has roots in the interval [0,1]
>

>
>Maple is _sure_ that the denominator has no roots in the [0,1].

>readlib(iscont): # for compatibility with Maple V Rel 5/4/3
>iscont(1/(1+z^2+z^5), z= 0..1);

My statement was not intended to be taken quite literally.
Maple is a computer program, so it can't be "sure" about
anything.  More to the point, if one Maple command "knows"
something, there's no guarantee that a different command
also "knows" it.  Apparently int does not use iscont to check
for singularities.

Actually it would have been more accurate to say that Maple isn't
sure that the antiderivative doesn't have discontinuities on the
interval.  The antiderivative is a linear combination of logarithms,
and logarithms have branch cuts.  If the path of integration crossed
a branch cut, int(f(x),x=a..b) = F(b) - F(a) would probably be wrong,
even though f itself has no singularities on that path.  So you really
should do

> iscont(int(1/(1+x^2+x^5),x), x=0..1);

This also returns true (correctly).  But, as I said, int does not
seem to use iscont.  What it does use is discont: the idea is,
rather than just checking whether F is continuous on the interval,
you want to know where any possible discontinuities are, and
then you can get a correct answer by taking into account the
one-sided limits of F at those points.  Unfortunately, discont
does not seem to work properly for a sum over RootOf's.

Robert Israel                                israel@math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada
```
 0
israel
5/4/2006 3:59:12 AM

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