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         THIS IS A MAPLE BUG SAMPLE


 BUG # 1         int: INVALID INDEFINITE INTEGRATION
 Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
 Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
 Maple 9.00, IBM INTEL NT, Jun 13 2003 Build ID 136194
 Maple 8.01, IBM INTEL NT, May  1 2002 Build ID 119670

 EXAMPLE 1:      int(sin(z)*exp(z)*sin(1/z), z);

 ACTUAL:         0

 EXPECTED:       int(sin(z)*exp(z)*sin(1/z), z);


 EXAMPLE 2:      diff(int(sin(z)*exp(z)*cos(1/z), z),z);

 ACTUAL:         exp(z)*sin(z)

 EXPECTED:       sin(z)*exp(z)*cos(1/z)


 The same problem with

 int(sin(z)*exp(-z)*sin(1/z), z);
 int(cos(z)*exp(z)*sin(1/z), z);
 int(cos(z)*exp(-z)*sin(1/z), z);
 diff(int(exp(z)*cos(z+1/z), z), z);
 diff(int(exp(z)*cos(z-1/z), z), z);
 diff(int(exp(-z)*cos(z+1/z), z), z);
 diff(int(exp(-z)*cos(z-1/z), z), z);


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Dear Mr. Cooper,

Maple bug analysis is going to be the death of me. You know that I have already thereby forfeited one eye, and from that I was in some considerable danger. One morning, while I was bent over to examine a portion of a novelty, a Maple bug genetic map which was sent to me by one of our promising computer scientists, I suddenly felt a blow of pain. This work, in which one must hang over and examine a large area at one time, attacks the sight far more violently than only simple reading or writing alone. On account of these things, I must ask you, if you have good will for me, to appeal to Mr. Bernardin if it would please him that I be excused from this work, which is only a small part of my responsibilities, but which easily make me unfit for all the rest. I am with all honor and respect your humble servant,

Leonhard Euler



HOT NEWS:     MAPLE 9  BUG  LISTS ARE  COMING  SOON

Maplesoft, Inc.announces the upcoming release of Maple 9 between late June and late July 2003.

The Cyber Tester, LLC announces Maple 9 extensive bug lists will be published within 30 days after we get access to Maple 9.



Produced by our GEMM, below is published for the first time a tiny random demo of Maple howlers in 10 functions:

limit, int, sum, product, simplify, series, asympt, coulditbe, is, testeq.

Apr 10, 2004: This page will be updated within several days.

Jul 12, 2004: The selected 100 Maple 9.5 bugs are coming....


BUG # 1int (1-D):   SPURIOUS DIVERGENCE
Regression:YES
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
ABSENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
ABSENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
ABSENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
ABSENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(1/z, z= I..2*I);
ACTUAL:
infinity
EXPECTED:
ln(2)

.6931471806
CHECKUP: 
evalf(Int(1/z, z= I..2*I));

.6931471806
COMMENT 1: 
Maple V, Release 3 returns  ln(2*I)-1/2*I*Pi = .6931471806+0.*I
COMMENT 2: 
Derive 6, Mathematica 5 and MuPAD 3 calculate this integral co
rrectly.
INTEGRATE ME: 
INT(1/z, z, #i, 2*#i)
Integrate[1/z, {z, I, 2 I}]
int(1/z, z= I..2*I);

LN(2)
Log[2]
ln(2*I) - 1/2*I*PI

0.6931471805
0.693147
0.6931471806

BUG # 2int (1-D):   INVALID MAGNITUDE OF THE REAL-VALUED INTEGRAL
Regression:YES
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
ABSENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
ABSENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
ABSENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
ABSENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(sqrt((z+1)^2), z= 0..1);
ACTUAL:
1/2
EXPECTED:
3/2

1.500000000
CHECKUP: 
evalf(Int(sqrt((z+1)^2), z= 0..1));

1.500000000

WORKAROUND 1:   f := int(sqrt((z+1)^2), z): simplify(subs(z=1,f)-subs(z=0,f));

3/2

WORKAROUND 2:   subs(a=1,b=1,int(sqrt((a*z+b)^2), z = 0..1)) assuming a>0, b>0;

3/2
COMMENT: 
Derive 6, Mathematica 5 and MuPAD 3 calculate this integral
correctly.
INTEGRATE ME: 
INT(SQRT((z+1)^2), z, 0, 1)
Integrate[Sqrt[(z+1)^2], {z, 0, 1}]
int(sqrt((z+1)^2), z= 0..1);

3/2
3/2
3/2

BUG # 3int (1-D):   Error, (in X) Limit uses a 3rd argument, dir, whichis missing
Regression:YES
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
ABSENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
ABSENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
ABSENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
ABSENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
DESCRIPTION: 
Only Maple 9 raises an exception. All other Maple versions ret
urn a correct answer.
EXPRESSION :int(cos(z), z= I..a);
ACTUAL:
Error, (in Limit) Limit uses a 3rd argument, dir, which is mis
sing
EXPECTED:
sin(a)-I*sinh(1)
COMMENT 1: 
Derive 6, Mathematica 5 and MuPAD 3 calculate this integral co
rrectly.
INTEGRATE ME: 
INT(COS(z), z, #i, a)
Integrate[Cos[z], {z, I, a}]
int(cos(z), z= I..a);

SIN(a) + #i*EXP(-1)*(1 - EXP(2))/2
Sin[a] - I Sinh[1]
sin(a) - I*sinh(1)
EXPRESSION 2:int(exp(I*z), z= I..I*infinity);
ACTUAL:
Error, (in Limit) Limit uses a 3rd argument, dir, which is mis
sing
EXPECTED:
I/exp(1)
CHECKUP: 
evalf(int(exp(I*z), z= I..I*100));

.6321205588*I
COMMENT 1: 
Derive 6 and Mathematica 5 calculate this integral correctly.
INTEGRATE ME: 
INT(EXP(#i*z), z, #i, #i*inf)
Integrate[Exp[I z],{z, I, I Infinity}]

#i*#e^(-1)
I/E

0.3678794411*#i
0.367879 I

BUG # 4int (1-D):   INVALID SIGN OF THE IMAGINARY PART
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:NO
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
PRESENT   Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(arccoth(z), z= 0..1);
ACTUAL:
ln(2)+1/2*I*Pi

.6931471806+1.570796327*I
EXPECTED:
ln(2)-1/2*I*Pi

.6931471806-1.570796327*I
CHECKUP: 
evalf(Int(arccoth(z), z= 0..1));

.6931471806-1.570796327*I
COMMENT: 
Derive 6, Mathematica 5 and MuPAD 3 calculate this integral
correctly.
INTEGRATE ME: 
INT(ACOTH(z), z, 0, 1)
Integrate[ArcCoth[z], {z, 0, 1}]
int(arccoth(z), z= 0..1);

LN(2) - pi*#I/2
-I Pi/2 + Log[2]
ln(2) - 1/2*I*PI

0.6931471805 - 1.570796326*#I
0.693147     - 1.5708 I
0.6931471806 - 1.570796327*I

BUG # 5int (1-D):   SIDE EFFECT
Regression:YES
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
ABSENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
ABSENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
ABSENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
ABSENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
DESCRIPTION: 
If the user starts Maple several times in line and calculates 
each time the same integral, s/he sees TWO distinct outputs, A
and B, both are invalid.
EXPRESSION :restart; int(z^(2/3), z= 1..10);
ACTUAL:
(output A)

-1/3*3^(1/2)*GAMMA(2/3)*(-6*75^(1/2)*3^(1/2)*Pi/GAMMA(2/3)+3/5
*Pi*3^(1/2)/GAMMA(2/3))/Pi

51.36152423

(output B)

-3*3^(1/2)*GAMMA(2/3)*(1/15*Pi*3^(1/2)/GAMMA(2/3)-2/3*25^(1/2)
*Pi/GAMMA(2/3))/Pi

16.72050808
EXPECTED:
Always the same answer, 

6*10^(2/3)-3/5

27.24953300
CHECKUP: 
evalf(Int(sqrt(z)*(z^(1/6)), z= 1..10));

27.24953300
COMMENT: 
Mathematica 5 calculates this integral correctly.
INTEGRATE ME: 
INT(z^(2/3), z, 1, 10)
Integrate[z^(2/3), {z, 1, 10}]
int(z^(2/3), z= 1..10);

6*10^(2/3) - 3/5
-(3/5) + 6*10^(2/3)
6*10^(2/3) - 3/5

27.24953300
27.2495
27.249533

BUG # 6int (1-D):   INVALID INDEFINITE INTEGRATION
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:NO
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
BUG-1     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
IMPLICATION:
Maple cannot calculate definite integrals derived from the
original indefinite one.
EXPRESSION :int(z^(1/3)*sqrt(-z), z= -2-I..2+1);
ACTUAL:
(-12/11-6*I)*((278+29*I)^(1/6)-(278+29*I)^(1/6))/(-278-29*I)^(
1/6)/(278+29*I)^(1/6)

.2975335661 - 4.597771575*I
EXPECTED:
-6/11*(-2-I)^(4/3)*(2+I)^(1/3)*((-2-I)^(1/6)+(2+I)^(1/6))

4.130553767 - 2.041214157*I
CHECKUP: 
evalf(Int(z^(1/3)*sqrt(-z), z= -2-I..2+I, _Gquad));

4.130553767 - 2.041214160*I
COMMENT 1: 
BUG-1  =  Maple returns  2/5*I*z^(5/2)
COMMENT 2: 
Derive 6, Mathematica 5 and MuPAD 3 calculate this integral co
rrectly.
INTEGRATE ME: 
INT(z^(1/3)*SQRT(-z), z)
Integrate[z^(1/3) Sqrt[-z], z]
int(z^(1/3)*sqrt(-z), z)

6*z^(4/3)*SQRT(-z)/11
(6/11)*Sqrt[-z]*z^(4/3)
-3/11*(-z)^(11/6)*(I*3^(1/2) + 1)

BUG # 7int (1-D):   KERNEL FAILURE
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:YES
Reproducible:ALWAYS
BUG HISTORY:
LOOPED-1  Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
PRESENT*  Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
LOOPED-2  Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
LOOPED-2  Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
UNEVAL    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
UNEVAL    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNEVAL    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(sqrt(exp(z)+sinh(z)), z= 0..infinity);
ACTUAL:
Kernel Failure
Worksheet lost contact with kernel.
You should save this worksheet and restart Maple.
EXPECTED:
infinity
COMMENT 1: 
LOOPED-1  Maple keeps running after 3000 seconds.

PRESENT*  =  Execution stopped: Memory allocation failed.
The kernel has been shut down.
Further computations cannot be performed.
COMMENT 2: 
A typical time before the kernel failure is some 6000 seconds.
COMMENT 3: 
LOOPED-2  =  Maple keeps running after 8000 seconds.

BUG # 8int (1-D):   SPURIOUS CONVERGENCE
Regression:YES
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
ABSENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
ABSENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
ABSENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
ABSENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ERROR     Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(sqrt((z+1)^2)/z, z= 0..1);
ACTUAL:
1
EXPECTED:
infinity
CHECKUP: 
evalf(Int(sqrt((z+1)^2)/z, z= 0..1));

Float(infinity)
COMMENT 1: 
Derive 6, Mathematica 5 and MuPAD 3 calculate this integral
correctly.
COMMENT 2: 
ERROR  =   Error, (in arctanh) singularity encountered
INTEGRATE ME: 
INT(SQRT((z+1)^2), z, 0, inf)
Integrate[Sqrt[(z+1)^2], {z, 0, Infinity}]
int(sqrt((z+1)^2), z = 0..infinity);

inf
Integral of Sqrt[(z+1)^2] does not converge on {0, Infinity}
infinity

BUG # 9int (1-D):   INVALID INDEFINITE INTEGRATION
Regression:YES
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
ABSENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
ABSENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
ABSENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(ln(z)*abs(exp(z)/z), z);
ACTUAL:
0
EXPECTED:
int(ln(z)*exp(Re(z))/abs(z), z)
HINT: 
f := ln(z)*abs(exp(z)/z):
int1 := int(f, z):
s := simplify(f - diff(int1, z));
plot(abs(s), z= -3..3, 0..10);

s := ln(z)*exp(Re(z))/abs(z)         #  <--- This must = 0

BUG # 10int (1-D):   KERNEL FAILURE
Regression:YES
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
ABSENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
ABSENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
UNEVAL    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
BUG-1     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
BUG-2     Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNEVAL    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
DESCRIPTION: 
Regression to Maple 8.
EXPRESSION :int(ln(abs(z^2-1))/(1+z)^2, z= 0..infinity);
ACTUAL:
Kernel Failure
Execution stopped: Stack limit reached.
Worksheet lost contact with kernel.
You should save this worksheet and restart Maple.
EXPECTED:
1
CHECKUP: 
evalf(Int(ln(abs(z^2-1))/(1+z)^2, z= 0..infinity));

1.000000000
COMMENT 1: 
BUG-1  =  Maple returns   infinity .
BUG-2  =  Maple returns   I*Pi+1 .
COMMENT 2: 
Mathematica 5 and MuPAD 3 calculate this integral correctly.
INTEGRATE ME: 
Integrate[Log[Abs[z^2 - 1]]/(1 + z)^2, {z, 0, Infinity}]
int(ln(abs(z^2-1))/(1+z)^2, z=0..infinity);

1
1

BUG # 11int (1-D):   INVALID MAGNITUDE OF THE REAL AND IMAGINARY PARTS
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:YES
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
ABSENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
ABSENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
ABSENT    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
ABSENT    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
DESCRIPTION: 
Only Maple 9 cannot calculate this trivial integral; all other
Maple versions solve it correctly.
EXPRESSION :int(sqrt(z), z= -I..I);
ACTUAL:
-1/3*2^(1/2)+1/3*I*2^(1/2)

-.4714045206+.4714045206*I
EXPECTED:
2*sqrt(2)*I/3

.9428090414*I
CHECKUP: 
evalf(Int(sqrt(z), z= -I..I));

0.+.9428090416*I
COMMENT 1: 
Derive 6, Mathematica 5 and MuPAD 3 calculate this integral
correctly.
INTEGRATE ME: 
INT(SQRT(z), z, -#I, #I)
Integrate[Sqrt[z], {z, -I, I}]
int(sqrt(z), z= -I..I);

2*sqrt(2)*#i/3
2 I Sqrt[2]/3
2/3*(I)^(3/2) - 2/3*((-I))^(3/2)

0.9428090415*#i
0.942809 I
0.9428090416*I
EXPRESSION 2:int(1/(1+z), z= -I..I);
ACTUAL:
1/2*ln(2)+1/4*I*Pi

.3465735903+.7853981635*I
EXPECTED:
I*Pi/2

1.570796327*I
CHECKUP: 
fnormal(evalf(Int(1/(1+z),z = -I .. I)));

-0.+1.570796327*I
COMMENT 1: 
Derive 6, Mathematica 5 and MuPAD 3 calculate this integral
correctly.
INTEGRATE ME: 
INT(1/(1 + z), z, -#I, #I)
Integrate[1/(1 + z), {z, -I, I}]
int(1/(1+z), z= -I..I);

pi*#I/2
I Pi/2
ln(1 + I) - ln(1 - I)

1.570796326*#I
1.5708 I
1.570796327*I

BUG # 12int (1-D):   INVALID MAGNITUDE OF THE REAL-VALUED INTEGRAL
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:YES
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
ABSENT    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
ABSENT    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
BUG-1     Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
BUG-1     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ABSENT    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ABSENT    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(ln(exp(z)), z= -I..I);
ACTUAL:
(-1)/2

-.5000000000
EXPECTED:
0
CHECKUP: 
evalf(Int(ln(exp(z)), z= -I..I));

0.
COMMENT 1: 
ABSENT  =  Maple returns  1/2*ln(exp(I))^2-1/2*ln(exp(-I))^2

BUG-1   =  Maple returns  -1/2*I*Pi^2  =  -4.934802202*I
COMMENT 2: 
Derive 6, Mathematica 5 and MuPAD 3 calculate this integral co
rrectly.
INTEGRATE ME: 
INT(LN(EXP(z)), z, -#i, #i)
Integrate[Log[Exp[z]], {z, -I, I}]
int(ln(exp(z)), z= -I..I);

0
0
0

BUG # 13int (1-D):   INVALID MAGNITUDE OF THE REAL AND IMAGINARY PARTS
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:NO
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
PRESENT   Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(cos(z)/sqrt(z), z= -infinity..infinity);
ACTUAL:
0
EXPECTED:
(1-I)*sqrt(1/2*Pi)

1.253314137 - 1.253314137*I
CHECKUP: 
evalf(int(cos(z)/sqrt(z), z= -10^10..10^10));

1.253304440 - 1.253304440*I
EXPRESSION 2:int(BesselY(1/2, z), z= -infinity..infinity);
ACTUAL:
0
EXPECTED:
-1 + I
CHECKUP: 
evalf(int(BesselY(1/2, z), z= -10^100..10^100));

-1.000000000 + 1.000000000*I
COMMENT: 
Mathematica 5 calculates these integrals correctly.
INTEGRATE ME: 
Integrate[Cos[z]/Sqrt[z], {z, -Infinity, Infinity}]

(1 - I)*Sqrt[Pi/2]

1.25331 - 1.25331 I

Integrate[BesselY[1/2, z], {z, -Infinity, Infinity}]

-1 + I

BUG # 14int (1-D):   INVALID MAGNITUDE OF THE REAL AND IMAGINARY PARTS
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:NO
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
PRESENT   Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int((2-z)^(1/3)*sqrt(z-2), z= 0..1);
ACTUAL:
-6/11*2^(5/6)*3^(1/2)+6/11*I*2^(5/6)+3/11*3^(1/2)-3/11*I

-1.210984519+.6991622379*I
EXPECTED:
6/11*I*(-1+2*2^(5/6))

1.398324476*I
CHECKUP: 
evalf(Int((2-z)^(1/3)*sqrt(z-2), z= 0..1));

1.398324476*I
COMMENT: 
Derive 6, Mathematica 5 and MuPAD 3 calculate this integral co
rrectly.
INTEGRATE ME: 
INT((2-z)^(1/3)*SQRT(z-2), z, 0, 1)
Integrate[(2-z)^(1/3) Sqrt[z-2], {z, 0, 1}]
int((2-z)^(1/3)*sqrt(z-2), z= 0..1)

#i*(12*2^(5/6)/11 - 6/11)
(6/11)*I*(-1 + 2*2^(5/6))
12/11*I*2^(5/6) - 6/11*I

1.398324475*#i
1.39832 I
1.398324476*I

BUG # 15int (1-D):   INVALID INDEFINITE INTEGRATION
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:NO
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNEVAL    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
IMPLICATION:
Maple calculates incorrectly definite integrals involving
BesselJ(0, z^2+z)  e.g.

evalf(int(BesselJ(0, z^2+z), z= 0..1));
evalf(Int(BesselJ(0, z^2+z), z= 0..1));

1.425770294
.7754594832

evalf(int(BesselJ(0, z^2+z), z= 0..2));
evalf(Int(BesselJ(0, z^2+z), z= 0..2));

.7062212242
.5987388649

evalf(int(BesselJ(0, z^2+z), z= 2..3));
evalf(Int(BesselJ(0, z^2+z), z= 2..3));

0.679009659e-1
0.2707675940e-1
DESCRIPTION: 
Maple's indefinite integrator yields invalid expressions for
BesselJ, BesselY, and BesselK of simple nonlinear arguments.
EXPRESSION :int(BesselJ(0, z^2+z), z);
ACTUAL:
(z^2+z)*BesselJ(0, z^2+z)+1/2*Pi*(z^2+z)*(StruveH(0, z^2+z)*Be
sselJ(1, z^2+z)-StruveH(1, z^2+z)*BesselJ(0, z^2+z))
EXPECTED:
int(BesselJ(0, z^2+z), z);
CHECKUP: 
f := BesselJ(0, z^2+z): simplify(f- diff(int(f,z),z));

-2*z*BesselJ(0, z^2+z)  # This must be = 0
COMMENT 1: 
int(BesselJ(0, z^2+z), z= 0..infinity);

undefined  # INVALID, the integral obviously converges as

op(1,series(BesselJ(0, z^2+z), z= infinity,2));

2^(1/2)*sin(z^2+z+1/4*Pi)/(Pi^(1/2)*z)
COMMENT 2: 
Plot[NIntegrate[BesselJ[0, z^2 + z], {z, 0, k}], {k, 0, 10}]
shows nice damping oscillations near y = 0.56;  Maple is too
sluggish here to draw the graph...
HINT: 
f := BesselJ(0, z^2+z):
plot(f-simplify(diff(int(f,z),z)), z=0..1);
Compare: 
f := BesselJ(0, z^2+1): simplify(f- diff(int(f,z),z));

0   #  Okey-dokey.

BUG # 16int (1-D):   SPURIOUS DIVERGENCE
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:NO
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNEVAL    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(cos(z)^2*polylog(1,exp(I*z)), z= 0..2*Pi);
ACTUAL:
infinity
EXPECTED:
Pi/4

.7853981635
CHECKUP: 
fnormal(evalf(Int(cos(z)^2*polylog(1,exp(I*z)), z=0..2*Pi, met
hod=_Sinc)));

.7853981633-0.*I
COMMENT: 
Mathematica 5 calculates all these integrals correctly.
HINT: 
plot(Re(cos(z)^2*polylog(1,exp(I*z))), z=0..2*Pi);
plot(Im(cos(z)^2*polylog(1,exp(I*z))), z=0..2*Pi);
INTEGRATE ME: 
Integrate[Cos[z]^2 PolyLog[1, Exp[I z]], {z, 0, 2 Pi}]

Pi/4

BUG # 17int (1-D):   INVALID MAGNITUDE OF THE REAL PART
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:NO
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
UNEVAL    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNEVAL    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(erf(z)*sqrt(1+z), z = 0..1);
ACTUAL:
8/15/Pi^(1/2)*hypergeom([1/2, 1],[7/4, 9/4],-1)

.2682236328
EXPECTED:
4/3*sqrt(2)*erf(1)-4/3*sum((-1)^n*hypergeom([(-3)/2, 1+2*n], [
2+2*n], -1)/(n!+2*n*n!), n = 0..infinity)/sqrt(Pi)

.6220539248
CHECKUP: 
evalf(Int(erf(z)*sqrt(1+z), z = 0..1));

.6220539253

BUG # 18int (1-D):   Error, (in X) numeric exceptiondivision by zero
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:NO
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
PRESENT*  Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
UNEVAL    Maple V, Release 5, IBM INTEL NT, Nov 27 1997
UNEVAL    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNEVAL    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(z/sec(exp(z)), z= 0..infinity);
ACTUAL:
Error, (in int/definite/contour/polypow) numeric exception: di
vision by zero
EXPECTED:
1/2*gamma^2-1/24*Pi^2-1/8*hypergeom([1,1,1],[3/2,2,2,2], -1/4)

-.3670785838
CHECKUP: 
evalf(Int(z/sec(exp(z)), z= 0..10)) + evalf(Int(z/sec(exp(z)),
z= 10..12, _Gquad));

-.3670054599

BUG # 19int (1-D):   Error, (in X) numeric exceptiondivision by zero
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:NO
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
UNEVAL    Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
UNEVAL    Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
UNEVAL    Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
ERROR     Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ERROR*    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNEVAL    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(sin(Dirac(a*z)), z= 0..1);
ACTUAL:
Error, (in assuming) when calling `Ci`. Received: 'numeric exc
eption: division by zero'
EXPECTED:
PIECEWISE([0, a <> 0], [sin(Dirac(0)), a = 0])
COMMENT: 
ERROR   =  Error, (in depends) too many levels of recursion

ERROR*  =  Error, (in signum) too many levels of recursion

BUG # 20int (1-D):   Error, (in X) must be 3 or 1 real roots for a real cubic
 
******************************************************************
***  NONE Maple version can calculate this integral correctly  ***
******************************************************************
Regression:NO
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
UNEVAL    Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNEVAL    Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :int(sqrt(1+I*z^3), z= 0..1);
ACTUAL:
Error, (in int/ellalg/trxstandard) must be 3 or 1 real roots f
or a real cubic
EXPECTED:
2/5*(1+I)^(1/2)+3/5*hypergeom([1/3, 1/2],[4/3],-I)

1.015593344+.1199726421*I
CHECKUP: 
evalf(Int(sqrt(1+I*z^3), z=0..1));

1.015593344+.1199726421*I

BUG # 21product (1-D):   INVALID MAGNITUDE
 
*****************************************************************
***  NONE Maple version can calculate this product correctly  ***
*****************************************************************
Regression:NO
Reproducible:ALWAYS
BUG HISTORY:
PRESENT   Maple 9.03, IBM INTEL NT, Oct  1 2003 Build ID 141050
PRESENT   Maple 9.01, IBM INTEL NT, Jul  9 2003 Build ID 137227
PRESENT   Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
PRESENT   Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
PRESENT   Maple 6.01, IBM INTEL NT,  Jun 9 2000 Build ID 79514
PRESENT   Maple V, Release 5, IBM INTEL NT, Nov 27 1997
PRESENT   Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
PRESENT   Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXPRESSION :product(i/(n-i), i= 1..n-1);
ACTUAL:
0
EXPECTED:
1
CHECKUP: 
product(i/(2-i), i= 1..2-1);
product(i/(3-i), i= 1..3-1);
product(i/(4-i), i= 1..4-1);
product(i/(5-i), i= 1..5-1);

1
1
1
1
COMMENT: 
Mathematica 5 calculates this product correctly.
HINT: 
plot(Product(i/(n-i), i= 1..n-1), n= 0..10);
INTEGRATE ME: 
Product[i/(n - i), {i, 1, n - 1}]

1


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