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With the help of GEMM it should be possible to supplement present QA
mechanisms, by adding a component that automatically locates and list
bugs of a new nature.
This can be compared and contrasted against a test suite which is slow
to incorporate new material, and as a result is rather static in nature.
GEMM, on the other hand, is dynamical and continually searching various
branches of behavior.
It is anticipated that on a time scale of 12 months, that GEMM should be
able to locate examples of new bugs for hundreds system functions, many
thousands classified nice-formatted entries like the samples shown below.
Please completely realize that:
* the structure of an entry is under y o u r control
* the choice of the function is under y o u r control
Had you have any questions please don't hesitate to contact me at
vvb@mail.strace.net. Enjoy!
Sincerely,
VB
...............................................................................
TESTING ENVIRONMENT
CPU ID AuthenticAMD AMD Athlon(tm) XP 1600+
RAM size 512 Mb
Free HDD size 11 Gb
OS ID Microsoft Windows 98 4.10.2222 A
...............................................................................
MEANINGS OF THE MARKERS
ABSENT The result of the evaluation is correct
BUG-1 The bug differs from the bug in Maple 8
CANNOT The expression is returned unevaluated
CRASHED Invalid memory addressing occurred
ERROR An error message interrupted the computation
LOOPED The expression is running after 2 hours
PRESENT The quoted bug is present in the output
REGRESSION At least 1 Maple version can handle it correctly
REPRODUCIBLE The bug can can be reproduced
UNDONE Maple transformed the input without full success
...............................................................................
BUG # 1 (software protection)
****************************************
*** UNRELIABLE SOFTWARE PROTECTION ***
****************************************
ACTUAL: Can make Maple 8 Trial Version copy running forever.
HOW-TO-DO: Keep/reset the system date within 29 days after
the date of the installation.
EXPECTED: Cannot run Maple 8 Trial Version after 30 days.
FORMAL ADVICE: 1) Consider SciFace experience.
2) Consider WRI experience.
3) Consider TI experience.
4) Consider the ideas of Vladimir V. Bondarenko.
5) Consider using dongles.
TRUE ADVICE: Keep her steady! ;-)
...............................................................................
BUG # 2 (evalf)
**************************************
*** INVALID PAGE FAULT EXCEPTION ***
**************************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
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
evalf(Int(AiryAi(1/sqrt(z)), z=0..1));
ACTUAL: MSERVER caused an invalid page fault in module MAPLE.DLL
at 0167:1016d5af.
EXPECTED: .07316096643
...............................................................................
BUG # 3 (evalf)
**************************************
*** INVALID PAGE FAULT EXCEPTION ***
**************************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
ERROR 4 Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
ERROR 3 Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
ERROR 2 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ABSENT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ERROR 1 Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(Int(StruveH(1/3,1/z), z=0..1));
ACTUAL: MSERVER caused an invalid page fault in module MAPLE.DLL
at 0167:1016d5af.
EXPECTED: .5386098780
The same problem with
evalf(Int(StruveH(1/3,1/sqrt(z)), z=0..1));
...............................................................................
BUG # 4 (evalf)
**********************************
*** MEMORY ALLOCATION FAILED ***
**********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
LOOPED Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ERROR Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(Int(arccosh(1/tanh(z)), z=-1..1));
ACTUAL: Execution stopped: Memory allocation failed.
The kernel has been shut down.
Further computations cannot be performed.
EXPECTED: 3.439997633+3.141592654*I
CHECK-UP: evalf(Int(arccosh(1/tanh(z)), z=-1..0))+
evalf(Int(arccosh(1/tanh(z)), z=0..1));
3.439997634+3.141592654*I
The same problem with
evalf(Int(arccosh(1/tanh(z)), z=-1..0))+
evalf(Int(arccosh(1/tanh(z)), z=0..1));
...............................................................................
BUG # 5 (int)
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ABSENT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ABSENT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(exp(z)*ln(z), z=infinity..0);
ACTUAL: Error, (in limit) inconsistent direction with infinities
EXPECTED: -infinity
CHECK-UP: evalf(Int(exp(z)*ln(z), z=infinity..0));
Float(-infinity)
evalf(Int(exp(z)*ln(z), z=100..0));
-.1235208139e45
...............................................................................
BUG # 6 (int)
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
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
int(arctan(sqrt(3)*(2*z - 1)/3)/(z^2 + 1), z=0..infinity);
ACTUAL: Error, (in signum/main) numeric exception: division by zero
EXPECTED: 13/288*Pi^2+1/16*ln(7-4*3^(1/2))*ln(2-3^(1/2))+1/4*dilog(-2/(-\
2-I+3^(1/2)))+1/4*dilog(-2/(-2+I+3^(1/2)))+1/4*dilog((3*I+3^(1\
/2))/(3*I+(1+2*I)*3^(1/2)))+1/4*dilog((3+I*3^(1/2))/(3+(2+I)*3\
^(1/2)))
CHECK-UP: .8224670361+0.*I
evalf(Int(arctan(sqrt(3)*(2*z-1)/3)/(z^2+1), z=0..infinity));
.8224670334
...............................................................................
BUG # 7 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
CANNOT Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
LOOPED Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
CRASHED Maple V, Release 5, IBM INTEL NT, Nov 27 1997
LOOPED Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ERROR Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
a := 1/10^10:
evalf(Int(Int(Int(1/(3 - cos(x) - cos(y) - cos(z)), x=a..Pi-a),
y=a..Pi-a), z=a..Pi-a));
ACTUAL 1 (often): Error, (in property/OrProp/*) too many levels of recursion
ACTUAL 2 (seldom): Error, (in collect/series) too many levels of recursion
...............................................................................
BUG # 8 (evalf)
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ERROR 2 Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
ERROR 2 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ABSENT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ERROR 1 Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(Int(arcsec(1/arccsch(z)), z=-1..1));
ACTUAL: Error, (in evalf/int) cannot assume on a constant object
EXPECTED: 3.141592654
CHECK-UP: evalf(Int(arcsec(1/arccsch(z)), z=-1..0))+
evalf(Int(arcsec(1/arccsch(z)), z=0..1));
3.141592654+0.*I
The same problem with
evalf(Int(arcsec(1/arccsch(z)), z=-0.99..0.99));
evalf(Int(arccsc(1/arccsch(z)), z=-1..1));
...............................................................................
BUG # 9 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
UNDONE Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
UNDONE Maple V, Release 5, IBM INTEL NT, Nov 27 1997
UNDONE Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNDONE Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(I^z, z=0..infinity);
ACTUAL: Error, (in limit/range) invalid terms in sum
EXPECTED: undefined
...............................................................................
BUG # 10 (int)
******************************
*** INVALID Re MAGNITUDE ***
******************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ABSENT 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 1 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
BUG 1 Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(int(arctan((z - 1))/(z^2 + 1), z=0..infinity),30);
ACTUAL: .328636331315204260235482460675-.8e-30*I
EXPECTED: 1/8*ln(-1/5+2/5*I)^2+1/6*Pi^2+1/8*ln(-1/5-2/5*I)^2-1/8*I*ln(2-\
I)*Pi+1/8*I*ln(2+I)*Pi + 1/16*I*Pi*ln(2)-1/8*I*ln(1-I)*Pi+1/4*\
dilog(3/5+1/5*I)+1/4*dilog(3/5-1/5*I)
.31465653030289119628
CHECK-UP: evalf(Int(arctan((z - 1))/(z^2 + 1), z=0..infinity),30);
.314656530302891196278478318862
The same problem with
int(arctan((z + 1))/(z^2 + 1), z=0..infinity)
int(arctan((2*z - 1)/3)/(z^2 + 1), z=0..infinity);
int(arctan((2*z - 1))/(z^2 + 1), z=0..infinity);
...............................................................................
BUG # 11 (int)
******************************
*** INVALID Re MAGNITUDE ***
******************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ABSENT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ABSENT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int((sin(1)-sin(z/(1+z)))^2, z=0..infinity);
ACTUAL: -1+Si(2)*cos(2)-sin(2)*Ci(2)-I*sin(2)*Pi+cos(1)^2+2*sin(1)*cos\
(1)*Ci(1)+2*I*sin(1)*cos(1)*Pi+2*Si(1)*sin(1)^2
-.114183263+0.*I
EXPECTED: -1/2+(Ci(1)-Ci(2)+ln(2))*sin(2)+Si(1)+1/2*cos(2)*(1-2*Si(1)+2*\
Si(2))
.5160936848
CHECK-UP: evalf(Int((sin(1)-sin(z/(1+z)))^2, z=0..infinity));
.5160936847
...............................................................................
BUG # 12 (int)
******************************
*** INVALID Re MAGNITUDE ***
******************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ABSENT Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
ABSENT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(int(exp(-z^2)*arctan(z^3),z=0..infinity));
ACTUAL: .1084191096
EXPECTED: .2744301134
ANSWER: See Maple V Release 5
The same problem with
int(exp(-z^2)*arctan(z^5),z=0..infinity);
int(exp(-z^2)*arctan(z^7),z=0..infinity);
int(exp(-z^2)*arctan(z^9),z=0..infinity);
int(exp(-z^2)*arctan(z^11),z=0..infinity);
...............................................................................
BUG # 13 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
****************************
*** MEANINGLESS OUTPUT ***
****************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The answer depends on the integration variable.
type(int(BesselJ(1, 1/sqrt(z)), z=-1..1), freeof(z));
ACTUAL: false
EXPECTED: true
int(BesselJ(1, 1/sqrt(z)), z=-1..1);
ACTUAL: (-z^(1/2)*BesselJ(0,1)*StruveH(1,1)+z^(1/2)*BesselJ(1,1)*Struv\
eH(0,1)-(-z)^(1/2)*BesselI(0,1)*StruveL(1,1)+(-z)^(1/2)*Bessel\
I(1,1)*StruveL(0,1))*Pi/z^(1/2)
EXPECTED: -2/3+4/3*BesselJ(0,1)-1/3*Pi*(BesselJ(0,1)*StruveH(1,1)-
BesselJ(1,1)*StruveH(0,1))
CHECK-UP: .4566187310
evalf(Int(BesselJ(1, 1/sqrt(z)), z=0..1));
.4566187311
...............................................................................
BUG # 14 (int)
****************************
*** MEANINGLESS OUTPUT ***
****************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ABSENT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ABSENT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The answer involves trunc(`limit/mrv/Re`(-1))
EXAMPLE 1: int(sin(1/tanh(z)), z=-1..1);
ACTUAL: 1/2*I*sin(1)*Pi+1/2*I*trunc(`limit/mrv/Re`(-1))*Pi*sin(1)
EXPECTED: 0
CHECK-UP: evalf(Int(sin(1/tanh(z)), z=-1..0))+
evalf(Int(sin(1/tanh(z)), z=0..1));
0
EXAMPLE 2: int(cos(1/tanh(z)), z=-1..1);
ACTUAL: -Si(2/(exp(-1)-exp(1))*exp(-1))*sin(1)-
Ci(-2/(exp(-1)-exp(1))*exp(-1))*cos(1)-
Si(2/(exp(-1)-exp(1))*exp(1))*sin(1)+
Ci(-2/(exp(-1)-exp(1))*exp(1))*cos(1)-Pi*sin(1)-
1/2*I*trunc(`limit/mrv/Re`(-1))*Pi*cos(1)-1/2*I*Pi*cos(1)
-.8487048775*I*trunc(`limit/mrv/Re`(-1))-.414495363-
.8487048775*I
EXPECTED: -Si(2*exp(-2)/(exp(-2)-1))*sin(1)-Ci(-2*exp(-2)/(exp(-2)-1))*\
cos(1)-Si(2/(exp(-2)-1))*sin(1)+Ci(-2/(exp(-2)-1))*cos(1)-Pi*\
sin(1)
-.414495363
CHECK-UP: evalf(Int(cos(1/tanh(z)), z=-1..0))+
evalf(Int(cos(1/tanh(z)), z=0..1));
-.4144953636
The same problem with
int(sqrt(sinh(z)), z = -1..1);
...............................................................................
BUG # 15 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
****************************
*** MEANINGLESS OUTPUT ***
****************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The answer depends on the integration variable.
int(sqrt(z)*sqrt(1+z^2)/sqrt(1+z^6), z = -infinity..infinity):
evalf(%);
ACTUAL: 2.831474421*(z^(1/2)+(-1.*z)^(1/2))/z^(1/2)
EXPECTED: (1+I)*1/60*(5*GAMMA(3/4)^2*sin(5/12*Pi)*sin(1/12*Pi)* GAMMA(7/\
12)*GAMMA(11/12)*hypergeom([1/2,5/6, 7/6, 3/4],[5/4, 4/3, 5/3]\
,1) - 48*GAMMA(3/4)^2*sin(5/12*Pi) * sin(1/12*Pi)*GAMMA(7/12)*\
GAMMA(11/12)*hypergeom([1/2, 11/12, 7/12, 1/4],[17/12, 3/4, 13\
/12],1)+5*Pi^2*hypergeom([1/2, 1/6, 5/6, 5/12],[11/12, 2/3, 4/\
3],1)+10*Pi^2*hypergeom([1/2, 1/6, 1/12, -1/6],[2/3, 7/12, 1/3\
],1))/Pi^(1/2)*csc(5/12*Pi)*csc(1/12*Pi)/GAMMA(7/12)/GAMMA(11/\
12)
CHECK-UP: 2.831474419+2.831474419*I
evalf(Int(sqrt(z)*sqrt(1 + z^2)/sqrt(1 + z^6), z = -infinity..\
infinity));
2.831474417+2.831474417*I
...............................................................................
BUG # 16 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
****************************
*** SPURIOUS undefined ***
****************************
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
BUG 1 Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
CANNOT Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXAMPLE 1: int(abs(sqrt(z/(1+z^2))), z = -infinity..infinity);
ACTUAL: undefined
EXPECTED: infinity
CHECK-UP: evalf(Int(abs(sqrt(z/(1+z^2))), z = -infinity..infinity));
Float(infinity)
EXAMPLE 2: int(abs(sqrt(z))/sqrt(1+z^2), z = -infinity..infinity);
ACTUAL: undefined
EXPECTED: infinity
CHECK-UP: evalf(Int(abs(sqrt(z))/sqrt(1+z^2), z = -infinity..infinity));
Float(infinity)
...............................................................................
BUG # 17 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
************************************
*** TRIVIAL INTEGRAL IS UNDONE ***
************************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
This integral obviously diverges because the integrand is continuous, and it
asymptotically equals to 1/sqrt(z) + O((1/z)^(5/2)) at z = infinity, and
z^(1/2)+O(z^(5/2)) at z = 0.
I consider the Maple's 8 answer as a bug because the integral is TRIVIAL
that is can be immediately done in mind.
int(sqrt(z/(1+z^2)), z = 0..infinity);
ACTUAL: limit((2*(z/(1+z^2))^(1/2)*(-I*(z+I))^(1/2)*2^(1/2)*(I*(z-I))^\
(1/2)*(I*z)^(1/2)*EllipticE((-I*(z+I))^(1/2),1/2*2^(1/2))-(z/(\
1+z^2))^(1/2)*(-I*(z+I))^(1/2)*2^(1/2)*(I*(z-I))^(1/2)*(I*z)^(\
1/2)*EllipticF((-I*(z+I))^(1/2),1/2*2^(1/2))+2*(z/(1+z^2))^(1/\
2)*(-I*(z+I))^(1/2)*2^(1/2)*(I*(z - I))^(1/2)*(I*z)^(1/2)*z^2*\
EllipticE((-I*(z+I))^(1/2),1/2*2^(1/2))-(z/(1+z^2))^(1/2)*(-I*\
(z+I))^(1/2)*2^(1/2)*(I*(z-I))^(1/2)*(I*z)^(1/2)*z^2*EllipticF\
((-I*(z+I))^(1/2),1/2*2^(1/2))-2*(z*(1+z^2))^(1/2)*(z^3+z)^(1/\
2)*EllipticE(1/2*2^(1/2))+(z*(1 + z^2))^(1/2)*(z^3 + z)^(1/2)*\
EllipticK(1/2*2^(1/2)) -2*I*(z*(1 + z^2))^(1/2)*(z^3+z)^(1/2)*\
EllipticE(1/2*2^(1/2)) + I*(z*(1 + z^2))^(1/2)*(z^3 +z)^(1/2)*\
EllipticK(1/2*2^(1/2)))/(z*(1+z^2))^(1/2)/(z^3 + z)^(1/2),z = \
infinity)
EXPECTED: infinity
CHECK-UP: evalf(Int(sqrt(z/(1+z^2)), z = 0..infinity));
Float(infinity)
...............................................................................
BUG # 18 (int)
******************************
*** INVALID Im MAGNITUDE ***
******************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CRASHED Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
ABSENT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(sqrt(csc(z)), z = -1..1);
ACTUAL: 2.034805316-2.034805318*I
EXPECTED: 2.034805316+2.034805318*I
CHECK-UP: evalf(Int(sqrt(csc(z)), z = -1..1));
2.034805316+2.034805318*I
...............................................................................
BUG # 19 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************
*** INVALID Re MAGNITUDE ***
******************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
BUG 1 Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
BUG 2 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXAMPLE 1: evalf(int(arctan(z)/(1+z^3), z=0..1),30);
ACTUAL: .295402437233686437670241585805+.100e-29*I
EXPECTED: .332572518837625079597240253208
CHECK-UP: evalf(Int(arctan(z)/(1+z^3), z=0..1),30);
.332572518837625079597240253208
EXAMPLE 2: evalf(int(arccot(z)/(1+z^3), z=0..1),30);
ACTUAL: 1.01723170411092331267670505565-.10e-29*I
EXPECTED: .980061622506984670749706388244
CHECK-UP: evalf(Int(arccot(z)/(1+z^3), z=0..1),30);
.980061622506984670749706388244
...............................................................................
BUG # 20 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************
*** INVALID Re MAGNITUDE ***
******************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(int(ln(z^2 - z + 1)/(z^2 + 1), z=0..infinity));
ACTUAL: -2.600402544+0.*I
EXPECTED: 1/24*Pi*(-7*ln(2-3^(1/2))+13*ln(2+3^(1/2)))+
1/2*I*(polylog(2,(I+3^(1/2))/(2+I+3^(1/2)))+
polylog(2,1+2/(-2-I+3^(1/2)))-polylog(2,1+2/(-2+I+3^(1/2)))-
polylog(2,1-2/(2-I+3^(1/2))))
CHECK-UP: 1.536942713+.1000000000e-9*I
evalf(Int(ln(z^2 - z + 1)/(z^2 + 1), z=0..infinity));
1.536942710
...............................................................................
BUG # 21 (int)
****************************
*** SPURIOUS undefined ***
****************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT 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
This integral must be positive.
int(int(1/(1 + x + y)^3, x = 0..infinity), y = 0..infinity);
ACTUAL: undefined
EXPECTED: 1/2
CHECK-UP: evalf(Int(Int(1/(1 + x + y)^3,x=0..infinity), y=0..infinity));
0.5000000000
...............................................................................
BUG # 22 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***************************************************
*** INVALID Re MAGNITUDE / SPURIOUS undefined ***
***************************************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ERROR 1 Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
ERROR 1 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ERROR 2 Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
This integral must be positive.
However, Maple 8 always returns one of these invalid answers:
either dilogarithms (almost always) or undefined (rarely).
int(arctan(z)/(1+z^3), z=0..infinity);
ACTUAL: dilogarithms (negative num value) OR undefined (wrong)
EXPECTED: (1/144)*(4*Pi*(sqrt(3)*Pi+ln(97/8+7*sqrt(3)))-Psi(1,5/12)+\
Psi(1,11/12))
CHECK-UP: .7190728728
evalf(Int(arctan(z)/(1+z^3), z=0..infinity));
.7190728725
The same problem with
int(arctan(z)/(1+z^4), z=0..infinity);
int(arctan(z)/(1+z^5), z=0..infinity);
...............................................................................
BUG # 23 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
ERROR 1 Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
ERROR 1 Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
UNDONE Maple V, Release 5, IBM INTEL NT, Nov 27 1997
UNDONE Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNDONE Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(int(int(1/(3 - cos(x) - cos(y) - cos(z)), x=0..Pi), y=0..Pi), z= 0..Pi);
ACTUAL: Error, (in gcd/doit) too many levels of recursion
EXPECTED: 4*Pi*(18 + 12*sqrt(2) - 10*sqrt(3) -
7*sqrt(6))*EllipticK((2 - sqrt(3))*(sqrt(3) - sqrt(2)))^2
CHECK-UP: 15.67249482
a := 1/10^7:
evalf(Int(Int(Int(1/(3 - cos(x) - cos(y) - cos(z)), x=a..Pi-a),
y=a..Pi-a), z=a..Pi-a));
15.67247795
...............................................................................
BUG # 24 (int)
************************************************************************
*** FEATURE REQUEST: TOO COMPLICATED - CAN BE EXPRESSED MUCH SIMPLER ***
************************************************************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(1/sqrt(sech(z)), z=0..infinity);
ACTUAL: 2^(1/2)*EllipticPi(1,1/2*2^(1/2))
EXPECTED: infinity
int(sqrt(cosh(z)), z=0..infinity);
ACTUAL: 2^(1/2)*EllipticPi(1,1/2*2^(1/2))
EXPECTED: infinity
int(1/sqrt(1/cosh(z)), z=0..infinity);
ACTUAL: 2^(1/2)*EllipticPi(1,1/2*2^(1/2))
EXPECTED: infinity
...............................................................................
BUG # 25 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************
*** SPURIOUS CONVERGENCE ***
******************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
LOOPED Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ERROR Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(sqrt(1-1/z^(3/2)), z=1..infinity);
ACTUAL: 1/12*I*Pi^(1/2)*2^(1/2)*(12/7/Pi^(1/2)*2^(1/2)*hypergeom([3/4,\
1/4, 7/12],[3/2, 19/12],1)-24/Pi^(1/2)*2^(1/2)*hypergeom([1/12\
,-1/4,1/4],[1/2,13/12],1)+3/2*sin(5/12*Pi)*sec(1/12*Pi)*csc(1/\
12*Pi)*2^(2/3)*Pi^(1/2)*GAMMA(7/12)/GAMMA(2/3)/GAMMA(11/12))
0.3389019737e-10+0.*I
EXPECTED: infinity
CHECK-UP: evalf(Int(sqrt(1-1/z^(3/2)), z=1..10^10));
9999999999.
The same problem with
int(sqrt(1-1/z^(5/3)), z=1..infinity);
int(sqrt(1-1/z^(7/4)), z=1..infinity);
int(sqrt(1-1/z^(6/5)), z=1..infinity);
...............................................................................
BUG # 26 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************
*** SPURIOUS CONVERGENCE ***
******************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(FresnelC(z)*ln(z), z=0..infinity);
ACTUAL: 1/4
EXPECTED: infinity
CHECK-UP: evalf(Int(FresnelC(z)*ln(z), z=0..infinity));
Float(infinity)
int(FresnelS(z)*ln(z), z=0..infinity);
ACTUAL: 1/2*(2-ln(2)+gamma+ln(Pi))/Pi
EXPECTED: infinity
CHECK-UP: evalf(Int(FresnelS(z)*ln(z), z=0..infinity));
Float(infinity)
...............................................................................
BUG # 27 (int)
*********************************
*** INVALID Re/Im MAGNITUDE ***
*********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
LOOPED 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
evalf(int(sqrt(sqrt(z))/(1+z^2),z=-infinity..infinity));
ACTUAL: 0. + 0.*I
EXPECTED: Pi*sqrt(sqrt(2)/4+1/2)+Pi*I*sqrt(1/2-sqrt(2)/4)
CHECK-UP: 2.902453152+1.202235460*I
evalf(Int(sqrt(sqrt(z))/(1+z^2),z=-infinity..infinity));
2.902453152+1.202235460*I
The same problem with
int(z^(1/5)/(1+z^2),z=-infinity..infinity);
...............................................................................
BUG # 28 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
*********************************
*** INVALID Re/Im MAGNITUDE ***
*********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
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
BUG 1 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(signum(ln(z)), z= -1..1);
ACTUAL: 0
EXPECTED: -1+Pi/2+Pi^2*(2*BesselY(1,Pi)+StruveH(-1,Pi)-StruveH(1,Pi))/4+\
I*(Pi^2*(-BesselY(0,Pi)+StruveH(0,Pi)))/2
-1.267639165+.9349432435*I
COMMENT: Alas, the Maple 8 numeric integrator cannot knock out this,
evalf(Int(signum(ln(z)), z= -1..1));
evalf(Int(signum(ln(z)), z= -1..1));
COMPARE: MuPAD 2.5 numerical integration yields
numeric::int(sign(ln(z)), z= -1..1);
-1.267639165 + 0.9349432437*I
HINT: plot(Re(signum(ln(z))), z= -1..1);
plot(Im(signum(ln(z))), z= -1..1);
...............................................................................
BUG # 29 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************
*** INVALID Re MAGNITUDE ***
******************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
BUG 1 Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
BUG 2 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
BUG 3 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNDONE Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(arccot(1/sin(z)), z=0..Pi/2);
ACTUAL: 1/2*dilog(1/(1+2^(1/2))*2^(1/2)+1/(1+2^(1/2))+I/(1+2^(1/2)))+1\
/4*I*Pi*ln(-1-I)-1/4*I*Pi*ln(2^(1/2)-1+I)-1/4*I*Pi*ln(2^(1/2)+\
1-I)+1/6*Pi^2-1/4*I*Pi*ln(-1+I)-1/2*dilog(1/(2^(1/2)-1)*2^(1/2\
)-1/(2^(1/2)-1)+I/(2^(1/2)-1))+1/4*I*Pi*ln(2^(1/2)-1-I)-1/2*di\
log(1/(1+2^(1/2))*2^(1/2)+1/(1+2^(1/2))-I/(1+2^(1/2)))+1/4*I*P\
i*ln(2^(1/2)+1+I)+1/2*dilog(1/(2^(1/2)-1)*2^(1/2)-1/(2^(1/2)-1\
)-I/(2^(1/2)-1))+1/2*dilog(1/(2^(1/2)-1)*2^(1/2))+1/2*dilog(1+\
2/(2^(1/2)-1)-1/(2^(1/2)-1)*2^(1/2))+1/2*ln(1+2^(1/2))*ln(2-2^\
(1/2))-1/2*ln(1+2^(1/2))*ln(2^(1/2)-1)-1/2*I*ln(1+2^(1/2))*Pi-\
1/2*dilog(2/(1+2^(1/2))+1/(1+2^(1/2))*2^(1/2))+1/2*dilog(1/(1+\
2^(1/2))*2^(1/2))
5.780093050+.2e-8*I
EXPECTED: -1/2*polylog(2,3-2*2^(1/2))+2*polylog(2,2^(1/2)-1)
CHECK-UP:
evalf(Int(arccot(1/sin(z)), z=0..Pi/2));
.8452908502
HINT: plot(arccot(1/sin(z)), z=0..Pi/2);
The same problem with
int(arccot(csc(z)), z=0..Pi/2);
...............................................................................
BUG # 30 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************
*** SPURIOUS CONVERGENCE ***
******************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXAMPLE 1: simplify(int(a^(log[2](z)), z=0..infinity));
ACTUAL: 0
EXPECTED: undefined or int(a^(log[2](z)), z=0..infinity);
COMMENT: int(1^(log[2](z)), z=0..infinity);
infinity
EXAMPLE 2: int(I^(log[2](z)), z=0..infinity);
ACTUAL: 0
EXPECTED: undefined
...............................................................................
BUG # 31 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************
*** SPURIOUS CONVERGENCE ***
******************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(ln(z)*arctan(sqrt(z)), z=0..infinity);
ACTUAL: -1/2*Pi
EXPECTED: infinity
CHECK-UP: evalf(Int(ln(z)*arctan(sqrt(z)), z=0..infinity));
Float(infinity)
...............................................................................
BUG # 32 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
*****************************
*** SPURIOUS DIVERGENCE ***
*****************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ERROR Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXAMPLE 1: int(ln(1+z^(1/2))/(1+z^2), z = 0..infinity);
ACTUAL: infinity*signum(1/2*sum(_R1*(ln(_R1)+ln(1/_R1))/(_R1^3-3*_R1^2\
+3*_R1-1),_R1 = RootOf(2+_Z^4-4*_Z^3+6*_Z^2-4*_Z))-1/2*sum((ln\
(_R1)+ln(1/_R1))/(_R1^3-3*_R1^2+3*_R1-1),_R1 = RootOf(2+_Z^4-4\
*_Z^3+6*_Z^2-4*_Z)))
evalf(%);
Float(undefined)+Float(undefined)*I
EXPECTED: 1/2*Pi*ln(2^(3/4)+2^(1/4))-1/2*Catalan
CHECK-UP: 1.198673857
evalf(Int(ln(1+z^(1/2))/(1+z^2),z = 0 .. infinity));
1.198673857
EXAMPLE 2: int(ln(1+1/z^(1/2))/(1+z^2),z = 0 .. infinity);
ACTUAL: infinity*signum(1/2*sum(_R1*(ln(_R1)+ln(1/_R1))/(_R1^3-3*_R1^2\
+3*_R1-1),_R1 = RootOf(2+_Z^4-4*_Z^3+6*_Z^2-4*_Z))-1/2*sum((ln\
(_R1)+ln(1/_R1))/(_R1^3-3*_R1^2+3*_R1-1),_R1 = RootOf(2+_Z^4-4\
*_Z^3+6*_Z^2-4*_Z)))
evalf(%);
Float(undefined)+Float(undefined)*I
EXPECTED: 1/2*Pi*ln(2^(3/4)+2^(1/4))-1/2*Catalan
CHECK-UP: 1.198673857
evalf(Int(ln(1+1/z^(1/2))/(1+z^2),z = 0 .. infinity));
1.198673857
EXAMPLE 3: int(ln(z^(3/2)+1)/(1+z^3),z = 0 .. infinity);
ACTUAL: signum(1/2*Sum(1,_alpha = RootOf(_Z^2+1))-1/2*Sum(_alpha^2,_al\
pha = RootOf(_Z^4-_Z^2+1)))*infinity
evalf(%);
Float(undefined)+Float(undefined)*I
EXPECTED: -(Pi*(Pi - 6*sqrt(3)*ln(2)))/18
CHECK-UP: .7089185601
evalf(Int(ln(z^(3/2)+1)/(1+z^3),z = 0 .. infinity));
.7089185598
...............................................................................
BUG # 33 (int)
****************************
*** SPURIOUS undefined ***
****************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
BUG-2 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
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXAMPLE 1: int(1/abs(1-tan(z)), z=0..Pi/5);
ACTUAL: undefined
EXPECTED: Pi/10 - ln(- sqrt(5/8 - sqrt(5)/8) + sqrt(5)/4 + 1/4)/2
CHECK-UP: 1.068431525
evalf(Int(1/abs(1-tan(z)), z=0..Pi/5));
1.068431525
EXAMPLE 2: int(1/abs(1+tan(z)), z=0..Pi/5);
ACTUAL: undefined
EXPECTED: 1/2*ln(1+cot(3/10*Pi))+1/10*Pi-1/4*ln(1+cot(3/10*Pi)^2)
CHECK-UP: .4812520226
evalf(Int(1/abs(1+tan(z)), z=0..Pi/5));
.4812520226
...............................................................................
BUG # 34 (int)
***********************************
*** BAD NUMERICAL INTEGRATION ***
***********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
CANNOT Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
ERROR 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
ERROR Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(Int(sqrt(1+1/z^(3/2)), z=-1..1));
ACTUAL: 5.859030449+1.1610594455*I
EXPECTED: 7.303152458+2.657766004*I
7.241889406 + 2.646626173*I (Derive)
...............................................................................
BUG # 35 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************************
*** SPURIOUS NON-ZERO IMAGINARY PART ***
******************************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
BUG 2 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
BUG 2 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNDONE Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(ln(sin(z)/(1+z)), z=0..Pi);
ACTUAL: -Pi*ln(2)-I*Pi^2-ln(1+Pi)-Pi*ln(1+Pi)+Pi
-4.921529636-9.869604404*I
EXPECTED: -Pi*ln(2)-ln(1+Pi)-Pi*ln(1+Pi)+Pi
CHECK-UP: -4.921529636
evalf(Int(ln(sin(z)/(1+z)), z=0..Pi));
-4.921529635
...............................................................................
BUG # 36 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************
*** SYSTEM ERROR ***
**********************
REPRODUCIBLE INTERMITTENTLY
BUG HISTORY: 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
CRASHED Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(arcsin(1/arccos(z)), z=0..infinity);
ACTUAL: unevaluated or `System error, `, "ran out of memory"
EXPECTED: int(Re(arcsin(1/arccos(z))), z=0..1)-Infinity*I
...............................................................................
BUG # 37 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
UNDONE Maple V, Release 5, IBM INTEL NT, Nov 27 1997
UNDONE Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(ln(sin(z)/(1+z)), z=0..infinity);
ACTUAL: Error, (in limit/range) numeric exception: division by zero
EXPECTED: -infinity+I*infinity
...............................................................................
BUG # 38 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
********************
*** WRONG SIGN ***
********************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(ln(z)*arctan(z), z=0..infinity);
ACTUAL: -infinity
EXPECTED: infinity
CHECK-UP: evalf(Int(ln(z)*arctan(sqrt(z)), z=0..infinity));
Float(infinity)
..............................................................................
BUG # 39 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************
*** INVALID Im MAGNITUDE ***
******************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(int(ln(z)*arctan(z)/(1+z^2)^2,z=-infinity..infinity));
ACTUAL: -1.937892292*I
EXPECTED: -1.152494129*I
ANSWER: -1/16*I*Pi*(-4+Pi^2)
-1.152494130*I
CHECK-UP: evalf(Int(ln(z)*arctan(z)/(1+z^2)^2,z=-infinity..infinity));
0.-1.152494129*I
...............................................................................
BUG # 40 (evalf)
*********************************
*** SLOWDOWN OF 14240 TIMES ***
*********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ERROR 1 Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
It takes 213.6 seconds to calculate the following approximation. In Maple 7 it
takes only 0.015 seconds.
time(evalf(hypergeom([1, 1, 5/4],[2, 7/4],1)));
ACTUAL: 213.6
EXPECTED: 0.015
...............................................................................
BUG # 41 (int)
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
UNDONE Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(ln(1+sin(z)), z=0..infinity);
ACTUAL: Error, (in limit/range) invalid terms in sum
EXPECTED: infinity
The same problem with
int(ln(1+sin(z)^2), z=0..infinity);
int(ln(1-sin(z)), z=0..infinity);
int(ln(1+cos(z)), z=0..infinity);
int(ln(1-cos(z)), z=0..infinity);
int(ln(1-sin(z)^2), z=0..infinity);
int(ln(1+cos(z)^2), z=0..infinity);
int(ln(1-cos(z)^2), z=0..infinity);
int(ln(1+sin(z)^2), z=0..infinity);
...............................................................................
BUG # 42 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
****************************
*** SPURIOUS undefined ***
****************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(abs(sin(z)), z=-infinity..infinity);
ACTUAL: undefined
EXPECTED: infinity
...............................................................................
BUG # 43 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
LOOPED Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
ERROR 2 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ERROR 2 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ERROR 1 Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(Int(arcsin(1/arccos(z)), z=0..1));
ACTUAL: Error, (in simpl/simpl/ReIm/sum) too many levels of recursion
EXPECTED: 1.224555967 - 0.4729516698*I
CHECK-UP: evalf(Int(arcsin(z)/z^2*sin(1/z),z=2/Pi..infinity));
1.224555970-.4729517363*I
...............................................................................
BUG # 44 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***********************************
*** SIMPLE INTEGRAL IS UNDONE ***
***********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ERROR 1 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ERROR 1 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
PRESENT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
This integral is TOO simple to be left unprocessed.
I definitely feel, it is a BUG.
int(Ci(z), z=0..infinity);
ACTUAL: limit(z*Ci(z)-sin(z),z = infinity)
EXPECTED: 0
CHECK-UP: evalf(Int(Ci(z), z=0..infinity));
-.2e-12
...............................................................................
BUG # 45 (int)
*********************************
*** INVALID Re/Im MAGNITUDE ***
*********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
BUG 1 Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
ABSENT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(int(sqrt(abs(z^3+1)),z=0..2));
ACTUAL: 2.144908076+.9220552755*I
EXPECTED: 12/5+2/5*3^(3/4)*EllipticK(1/4*2^(1/2)*3^(1/2)+1/4*2^(1/2))-1/\
5*3^(3/4)*EllipticF(2*3^(1/4)/(1+3^(1/2)),1/4*2^(1/2)*3^(1/2)+\
1/4*2^(1/2))-1/5*3^(3/4)*EllipticF(2*3^(3/4)/(3+3^(1/2)),1/4*2\
^(1/2)*3^(1/2)+1/4*2^(1/2))
CHECK-UP: 3.241309265
evalf(Int(sqrt(abs(z^3+1)),z=0..2));
3.241309263
...............................................................................
BUG # 46 (int)
******************************
*** INVALID Re MAGNITUDE ***
******************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ABSENT Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
BUG 2 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
BUG 2 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
BUG 1 Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(int(1/(1+(-1+z)^2)*arctan(z), z=0..infinity));
ACTUAL: .7101324486+0.*I
EXPECTED: -1/4*arctan(1/3)^2-1/2*Pi*arctan(1/3)+1/16*ln(5)^2 -1/8*ln(2)*\
ln(5)+1/4*dilog(2/5-1/5*I)+1/4*dilog(2/5+1/5*I)+15/64*Pi^2
CHECK-UP: 2.152744571+0.*I
evalf(Int(1/(1+(-1+z)^2)*arctan(z), z=0..infinity));
2.152744570
...............................................................................
BUG # 47 (fourier/invfourier)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this expression correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
********************************
*** BAD fourier/invfourier ***
********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
UNDONE Maple V, Release 5, IBM INTEL NT, Nov 27 1997
UNDONE Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNDONE Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
with(inttrans):
invfourier(fourier(ln(1+1/z),z,p),p,z);
ACTUAL: 0
EXPECTED: ln(1+1/z)
...............................................................................
BUG # 48 (fourier/invfourier)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this expression correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
********************************
*** BAD fourier/invfourier ***
********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
UNDONE Maple V, Release 5, IBM INTEL NT, Nov 27 1997
UNDONE Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNDONE Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
with(inttrans):
invfourier(fourier(ln(z),z,p),p,z);
ACTUAL: -infinity/Pi
EXPECTED: ln(z)
The same problem with
fourier(ln(1+z),z,p);
fourier(ln(1-z),z,p);
fourier(ln(z)/(1-z^2),z,p);
fourier(ln(1+1/z),z,p);
fourier(ln(1-1/z),z,p);
fourier(ln(1-1/z^2),z,p);
fourier(ln(z)*Heaviside(z),z,p);
...............................................................................
BUG # 49 (fourier)
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
UNDONE Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
UNDONE Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
UNDONE Maple V, Release 5, IBM INTEL NT, Nov 27 1997
UNDONE Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
with(inttrans):
fourier(ln(z)*ln(1/z), z, p);
ACTUAL: Error, (in inttrans/normalize/distributional) unable to
evaluate sign
The same problem with
fourier(ln(z)*ln(-z), z, p);
fourier(ln(1+z)*ln(1-z), z, p);
fourier(ln(z)/(1+z), z, p);
fourier(ln(z)/(1-z), z, p);
fourier(ln(z)/(1+z^2), z, p);
fourier(ln(z)/(1-z^2), z, p);
fourier(ln(z)/(1+z^3), z, p);
fourier(ln(z)/(1-z^3), z, p);
...............................................................................
BUG # 50 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
****************************
*** SPURIOUS undefined ***
****************************
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
BUG 2 Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
BUG 2 Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
BUG 1 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(int(sqrt(abs(z-1)*(z^2+1)),z=0..2));
ACTUAL: undefined
EXPECTED:
...............................................................................
BUG # 51 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
*********************************
*** INVALID Re/Im MAGNITUDE ***
*********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
BUG 2 Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
BUG 2 Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
BUG 1 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNDONE Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(sqrt(-z^3+z^2-z+1),z=0..1):
evalf(%,25);
ACTUAL: .7282824328479719343655894-.30452847612989774120152e-2*I
EXPECTED: .7356418194982207194404737
ANSWER: 2/15+8/15*(2+2*I)^(1/2)*EllipticF(1/2*(2-2*I)^(1/2),1/2*2^(1/2\
)+1/2*I*2^(1/2))-4/15*(2+2*I)^(1/2)*EllipticE(1/2*(2-2*I)^(1/2\
),1/2*2^(1/2)+1/2*I*2^(1/2))+4/15*I*(2+2*I)^(1/2)*EllipticE(1/\
2*(2-2*I)^(1/2),1/2*2^(1/2)+1/2*I*2^(1/2))-4/15*I*(2+2*I)^(1/2\
)*EllipticF(1/2*(2-2*I)^(1/2),1/2*2^(1/2)+1/2*I*2^(1/2))
CHECK-UP: evalf(%,25);
.7356418194982207194404731+0.*I
evalf(Int(sqrt(-z^3+z^2-z+1),z=0..1),25);
.7356418194982207194404737
...............................................................................
BUG # 52 (laplace)
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ABSENT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ABSENT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
with(inttrans):
laplace(ln(z)^2/(1+z),z,p);
ACTUAL: Error, (in int/cook/ngritty) wrong number (or type) of
parameters in function diff
EXPECTED: 1/6*Pi^2*exp(p)*Ei(1,p)+gamma^2*exp(p)*Ei(1,p)+2*exp(p)*gamma*\
ln(p)*Ei(1,p)+2*exp(p)*gamma*MeijerG(3,0,p)*p+exp(p)*ln(p)^2*\
Ei(1,p)+2*exp(p)*ln(p)*MeijerG(3,0,p)*p+2*exp(p)*MeijerG(4,0,p\
)*p
...............................................................................
BUG # 53 (plot)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can draw this graph correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***********************
*** INVALID GRAPH ***
***********************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
plot((1 - signum(z*(z + 1)))/sqrt(z + 1),z=0..10);
ACTUAL: A vertical line from y = 0 to y = 0.55
EXPECTED: The vertical line is absent.
COMMENT: Mathematica 4.2, MuPAD 2.5 and Derive 5.06 handle it.
DRAW ME: Plot[(1 - Sign[z*(z + 1)])/Sqrt[z + 1], {z, 0, 10}]
plotfunc2d((1 - sign(z*(z + 1)))/sqrt(z + 1), z=0..10);
(1 - SIGN(z*(z + 1)))/SQRT(z + 1)
...............................................................................
BUG # 54 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
*************************
*** INVALID Re SIGN ***
*************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
The sign of the output must be opposite.
The value of the integral must be negative as the integrand is negative
everywhere over the integration region.
evalf(int(1/(sqrt(z-1)*sqrt(z-2)*sqrt(3-z)), z=0..1));
ACTUAL: 1.168165683
EXPECTED: -1.168165683
CHECK-UP: evalf(Int(1/(sqrt(z-1)*sqrt(z-2)*sqrt(3-z)), z=0..1));
-1.168165683
HINT: plot(1/(sqrt(z-1)*sqrt(z-2)*sqrt(3-z)), z=0..1)
...............................................................................
BUG # 55 (invlaplace)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this expression correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
*************************
*** INVALID Re SIGN ***
*************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
UNDONE Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
UNDONE Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The output of the Laplace transform is correct.
with(inttrans):
laplace(1/sqrt(1+z), z, p), p, z);
(Pi/p)^(1/2)*exp(p)*erfc(p^(1/2)) # OK
However, the output of the inverse Laplace transform has the wrong sign.
The easiest way to see it is to draw
original := 1/sqrt(1+z):
plot(original + invlaplace(laplace(original,z,p),p,z),z=0..10);
which yields the straight line y = 0 (in fact, Maple 8 explodes it into
a picket fence of vertical lines) instead of the curve y = 2/sqrt(1+z).
...............................................................................
BUG # 56 (invlaplace)
*************************
*** INVALID Re SIGN ***
*************************
REGRESSION YES
REPRODUCIBLE INTERMITTENTLY
BUG HISTORY: 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
ABSENT Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
ABSENT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The output of the Laplace transform is correct.
with(inttrans):
laplace(arccosh(1-z), z, p);
1/p*exp(-p)*BesselK(0,-p) # OK
However, the output of the inverse Laplace transform has the wrong sign.
The easiest way to see it is to draw
original := arccosh(1-z):
plot(original + invlaplace(laplace(original,z,p),p,z),z=0..10);
which yields the straight line y = 0 (in fact, Maple 8 explodes it into
a picket fence of vertical lines) instead of the curve y = 2*arccosh(1-z).
invlaplace(laplace(original,z,p),p,z);
EXPECTED: 2*ln(-1/2*I*2^(1/2)*(z^(1/2)+(z-2)^(1/2)))
...............................................................................
BUG # 57 (int)
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
BUG 1 Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223
BUG 2 Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
BUG 2 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(sqrt(abs(z^2-1)*(z^2+1)),z=0..2);
ACTUAL: Error, (in signum/main) too many levels of recursion
EXPECTED: 1/4*Beta(1/4,3/2)+2/3*5^(1/2)*3^(1/2)-1/3*2^(1/2)*EllipticF(1/\
2*3^(1/2),1/2*2^(1/2))
CHECK-UP: 2.917461861
evalf(Int(sqrt(abs(z^2-1)*(z^2+1)),z=0..2));
2.917461860
The same problem with
int(sqrt(abs(z^2-1)*(z^2+1)),z=-2..2);
int(sqrt(abs(z^2-1)*(z^2+1)),z=-infinity..infinity);
...............................................................................
BUG # 58 (evalf)
**************************************
*** NUMERIC VALUE IS UNAVAILABLE ***
**************************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ABSENT Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
ABSENT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
BUG 1 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ABSENT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(Int(sqrt(1-1/z^(4/3)), z=0..1));
ACTUAL: Int((1.-1./z^(4/3))^(1/2),z = 0. .. 1.)
EXPECTED: 2.622057554*I
...............................................................................
BUG # 59 (fourier/invfourier)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this expression correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
BUG 1 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
BUG 1 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
with(inttrans);
invfourier(fourier(ln(z)*ln(1/z), z, p), p, z);
ACTUAL: Error, (in inttrans/normalize/distributional) unable to
evaluate sign
EXPECTED: ln(z)*ln(1/z)
The same problem with
invfourier(fourier(ln(1+z)*ln(1-z), z, p), p, z);
...............................................................................
BUG # 60 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
****************************
*** SPURIOUS undefined ***
****************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(erf(1+z/exp(z)), z=-infinity..infinity);
ACTUAL: undefined
int(erf(1+z/exp(z)), z=-infinity..infinity,
'CauchyPrincipalValue');
ACTUAL: undefined
EXPECTED: -infinity
CHECK-UP: evalf(Int(erf(1+z/exp(z)), z=-10^6..10^6));
-157298.1589
HINT: plot(evalf(Int(erf(1+z/exp(z)), z=-a..a)),a=0..20);
...............................................................................
BUG # 61 (invlaplace)
******************************
*** INVALID Re MAGNITUDE ***
******************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
BUG 1 Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
UNDONE Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The output for the inverse Laplace transform is invalid.
with(inttrans):
laplace(sqrt(1+z), z, p):
invlaplace(%,p,z);
ACTUAL: 1+sqrt(Pi)/2*int(2*Heaviside(_U1-1)*Heaviside(1+z-_U1)*sqrt(1+\
z-_U1)/(Pi^(3/2)*_U1*(_U1-1)), _U1=0..z)
evalf(subs(z=1, %));
1. # it should be 1.414213562, evalf(sqrt(2))
EXPECTED: 1-1/(1+z)+1/(1+z)/z^(1/2)/(1/(-1-z))^(1/2)/(1+1/z*(-1-z))^(1/2\
)-1/(1+z)*z+1/(1+z)*z^(1/2)/(1/(-1-z))^(1/2)/(1+1/z*(-1-z))^(1\
/2)
...............................................................................
BUG # 62 (invlaplace)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this expression correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
****************************
*** SPURIOUS undefined ***
****************************
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
BUG 1 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
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The output for the inverse Fourier transform is invalid.
with(inttrans):
invfourier(fourier(abs(z)*sin(z)*ln(z), z, p), p, z);
ACTUAL: undefined/Pi
EXPECTED: abs(z)*sin(z)*ln(z)
...............................................................................
BUG # 63 (invfourier)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this expression correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
BUG 1 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
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
with(inttrans):
fourier(sin(5*z)*cos(2*z)*ln(z), z, p);
invfourier(%, p, z);
ACTUAL: Error, (in inttrans/normalize/exp/classsimp) unable to
compute coeff
EXPECTED: sin(5*z)*cos(2*z)*ln(z)
...............................................................................
BUG # 64 (evalf)
****************
*** LOOPED ***
****************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
CRASHED 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
ERROR 1 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ERROR 1 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
LOOPED Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(Int(ln(1+z)*ln(1-z^3), z=-infinity..infinity));
ACTUAL: Being the single task, after 2 hours the input keeps running
EXPECTED: a large number like .3178376964e^1008 + .2892257128e1005*I
...............................................................................
BUG # 65 (interface)
**************************************
*** INDICATORS ARE NOT REFRESHED ***
**************************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
evalf(Int(ln(1+z)*ln(1-z^3), z=-infinity..infinity));
ACTUAL: The same report 'Timer: 3.3s' is shown for 2 hours
EXPECTED: The reading of the indicator is changed
...............................................................................
BUG # 66 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************************
*** SPURIOUS NON-ZERO IMAGINARY PART ***
******************************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
evalf(int(ln(1+z)*ln(1-z^2), z=-1..1));
ACTUAL: 4*ln(2)^2-8*ln(2)+4*I*Pi*ln(2)-4*I*Pi+8-1/3*Pi^2
1.086766477-3.856026256*I
EXPECTED: 4*ln(2)^2-8*ln(2)+8-1/3*Pi^2
CHECK-UP: 1.086766477
evalf(Int(ln(1+z)*ln(1-z^2), z=-1..1));
1.086766477
...............................................................................
BUG # 67 (invlaplace)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this expression correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************
*** INVALID Re MAGNITUDE ***
******************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The value of the inverse Laplace transformation of laplace(BesselK(1, sqrt(z)\
), z, p); is incorrect. Spurious factor 1/64*Pi is present in the answer.
with(inttrans):
laplace(BesselK(1, sqrt(z)), z, p);
1/8*Pi^(1/2)/p^(3/2)*exp(1/8/p)*(BesselK(1,1/8/p)- # VALID
BesselK(0,1/8/p)) # VALID
invlaplace(%, p, z);
ACTUAL: 1/64*Pi*BesselK(1,z^(1/2)) # INVALID
EXPECTED: BesselK(1,z^(1/2))
...............................................................................
BUG # 68 (laplace)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this expression correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************************
*** SPURIOUS NON-ZERO IMAGINARY PART ***
******************************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
with(inttrans):
laplace(1/(z^2-1), z, p);
ACTUAL: -I*(I*Ci(I*p)*sinh(p)-Ssi(I*p)*cosh(p))
evalf(subs(p=1/2,%));
-.5992044654-.9527361321*I
EXPECTED: The imaginary part of the answer = 0
...............................................................................
BUG # 69 (fourier)
****************
*** LOOPED ***
****************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
BUG 1 Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
with(inttrans):
fourier(sin(z)/(1+z^3),z,p);
ACTUAL: Being the single task, after 7.4 hours the input keeps running
EXPECTED: -1/2*I*(1/3*I*exp(I*(-1+p))*Pi*(Heaviside(1-p)-Heaviside(-1+p)\
)+exp(-1/2*I*(-1+p))*(1/3*I*(-1-I*3^(1/2))*exp(1/2*3^(1/2)*(-1\
+p))*Pi*Heaviside(1-p)-1/3*I*(-1+I*3^(1/2))*exp(-1/2*3^(1/2)*(\
-1+p))*Pi*Heaviside(-1+p))) + 1/2*I*(1/3*I*exp(I*(1 + p))*Pi*(\
Heaviside(-1-p)-Heaviside(1+p))+exp(-1/2*I*(1+p))*(1/3*I*(-1-I\
*3^(1/2))*exp(1/2*(1+p)*3^(1/2))*Pi*Heaviside(-1-p)-1/3*I*(-1+\
I*3^(1/2))*exp(-1/2*(1+p)*3^(1/2))*Pi*Heaviside(1+p)))
...............................................................................
BUG # 70 (laplace)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this expression correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************************
*** SPURIOUS NON-ZERO IMAGINARY PART ***
******************************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The imaginary part of the output must be equal to zero.
with(inttrans):
laplace(exp(-z)/(1-z^2), z,p);
ACTUAL: I*(I*Ci(I*(1+p))*sinh(1+p)-Ssi(I*(1+p))*cosh(1+p))
evalf(subs(p=1,%));
.515905660+.212584166*I
...............................................................................
BUG # 71 (laplace)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this expression correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************************
*** SPURIOUS NON-ZERO IMAGINARY PART ***
******************************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The imaginary part of the output must be equal to zero.
with(inttrans):
laplace(sqrt(z)/(1-z), z,p);
ACTUAL: -(Pi/p)^(1/2)+I*Pi*exp(-p)*erfc((-p)^(1/2))
evalf(subs(p=1,%));
.134988344+1.155727338*I
...............................................................................
BUG # 72 (laplace)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this expression correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************************
*** SPURIOUS NON-ZERO IMAGINARY PART ***
******************************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The imaginary part of the output must be equal to zero.
with(inttrans):
laplace(sec(z), z, p);
ACTUAL: -I*p*Sum(2*n/(p^2+n^2)*exp(-1/2*I*n*Pi),n=0..infinity)-1/p^2
evalf(subs(p=1,%));
-1.626020143+.5161277204*I
...............................................................................
+++
BUG # 73 (laplace)
**********************************
*** FAILURE AFTER 266 minutes ***
**********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
with(inttrans):
laplace(exp(-z^3)/z^10, z, p);
ACTUAL: int(int(int(int(int(int(int(int(int(int(laplace(exp(-z^3), z, \
_U1),_U1=_U2..infinity),_U2=_U3..infinity),_U3=_U4..infinity),\
_U4=_U5..infinity),_U5=_U6..infinity),_U6=_U7..infinity), _U7=\
_U8..infinity),_U8=_U9..infinity),_U9=_U10..infinity), _U10= \
p..infinity)
EXPECTED: If Maple cannot return an answer, it should be recognized
faster.
...............................................................................
BUG # 74 (invlaplace)
******************************
*** INVALID Re MAGNITUDE ***
******************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
BUG 1 Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
UNDONE Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The Laplace transform is v a l i d.
with(inttrans):
laplace(sqrt(1+z), z, p);
1/p^(3/2)*exp(p)*(p^(1/2)*exp(-p)+1/2*Pi^(1/2)*erfc(p^(1/2)))
However, the inverse Laplace transform is i n v a l i d.
invlaplace(%,p,z);
ACTUAL: 1+sqrt(Pi)/2*int(2*Heaviside(_U1-1)*Heaviside(1+z-_U1)*sqrt(1+\
z-_U1)/(Pi^(3/2)*_U1*(_U1-1)), _U1=0..z)
evalf(subs(z=1,%));
1.
EXPECTED: 1-1/(1+z)-1/(1+z)*z+1/(1+z)/(1+1/(-1-z)*z)^(1/2)+1/(1+z)*z/(1+\
1/(-1-z)*z)^(1/2)
CHECK-UP: evalf(subs(z=1,%));
1.414213562
evalf(sqrt(1+1));
1.414213562
...............................................................................
BUG # 75 (laplace)
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
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
with(inttrans):
laplace(sin(z)*sqrt(z),z,p);
ACTUAL: Error, (in tablelook) wrong number (or type) of parameters
in function iquo
EXPECTED: 1/2*Pi^(1/2)/(p^2+1)^(3/4)*sin(3/2*arctan(1/p))
COMMENT: Mathematica 4.2 handles it.
The same problem with
laplace(sqrt(z)*cos(z),z,p);
laplace(sqrt(z)*sin(2*z),z,p);
laplace(sqrt(z)*cos(2*z),z,p);
laplace(sqrt(z)*sin(z+1),z,p);
laplace(sqrt(z)*sin(z+c),z,p);
laplace(sqrt(z)*sin(c*z),z,p);
laplace(z^(1/3)*sin(z),z,p);
laplace(z^(1/3)*cos(z),z,p);
laplace(z^(1/4)*sin(z),z,p);
laplace(z^(1/4)*cos(z),z,p);
laplace(z^(1/3)*sin(c*z),z,p);
...............................................................................
+++
BUG # 76 (laplace)
****************************
*** MEANINGLESS OUTPUT ***
****************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
The answer does NOT depend on p though it must depend.
with(inttrans):
laplace(frac(z), z, p);
ACTUAL: (exp(-1/N*t)*t+exp(-1/N*t)*N-N)/t^2/(exp(-1/N*t)-1)
EXPECTED: The output depends on p only.
...............................................................................
BUG # 77 (invlaplace)
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ABSENT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
with(inttrans);
invlaplace(exp(-p*Pi)/(p*(-1+exp(-p*Pi))),p,z);
ACTUAL: Error, (in inttrans/simpfloor) unable to evaluate sign
EXPECTED: Heaviside(z-Pi)*floor(-(z-Pi)/Pi)
The same problem with
invlaplace(1/(p*(1+exp(-p*Pi))),p,z);
invlaplace(1/(p*(1-exp(-p*Pi))),p,z);
invlaplace(1/(p*(1-exp(p*Pi))),p,z);
invlaplace(exp(-p*Pi)/(p*(1+exp(-p*Pi))),p,z);
invlaplace(exp(-p*Pi/2)/(p*(1+exp(-p*Pi))),p,z);
invlaplace(exp(-p*Pi/2)/(p*(-1+exp(-p*Pi))),p,z);
...............................................................................
BUG # 78 (laplace)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this expression correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
BUG 1 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
BUG 2 Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
with(inttrans):
laplace(BesselY(0, sqrt(z)), z, p);
ACTUAL: Error, (in cot) numeric exception: division by zero
EXPECTED: 1/p/Pi*exp(-1/4/p)*Ei(1/4/p)
The same problem with
laplace(BesselY(k, sqrt(z)), z, p);
where k = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
...............................................................................
BUG # 79 (laplace)
*****************************
*** STRANGE LIMITATIONS ***
*****************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
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
These 3 examples work fine.
with(inttrans):
laplace(z*sin(z),z,p):
invlaplace(%, p, z);
z*sin(z)
laplace(z^2*sin(z),z,p):
invlaplace(%, p, z);
z^2*sin(z)
laplace(z^3*sin(z),z,p):
invlaplace(%, p, z);
z^3*sin(z)
However, the next example does not work.
laplace(z^4*sin(z),z,p):
invlaplace(%, p, z);
ACTUAL: 24*invlaplace(1/(p^2+1)^(5/2)*sin(5*arctan(1/p)),p,z)
EXPECTED: z^4*sin(z)
The same problem with
laplace(z^k*sin(z),z,p):
invlaplace(%, p, z);
where k = 5, 6, 7, 8, 9, 10.
...............................................................................
BUG # 80 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
****************************
*** SPURIOUS undefined ***
****************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT 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
EXAMPLE 1: int(sqrt(1+cos(z)), z=0..infinity);
ACTUAL: undefined
EXPECTED: infinity
CHECK-UP: evalf(Int(sqrt(1+cos(z)), z=0..1000));
900.7628495
EXAMPLE 2: int(sqrt(1+sin(z)), z=0..infinity);
ACTUAL: undefined
EXPECTED: infinity
CHECK-UP: evalf(Int(sqrt(1+sin(z)), z=0..1000));
900.6076621
...............................................................................
BUG # 81 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CRASHED Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
CRASHED Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
EXAMPLE 1: int(sqrt(1+sin(z)^2), z=0..infinity);
ACTUAL: Error, (in gcd/doit) too many levels of recursion
EXPECTED: infinity
CHECK-UP: evalf(Int(sqrt(1+sin(z)^2), z=0..1000));
1215.912321
EXAMPLE 2: int(sqrt(1+cos(z)^2), z=0..infinity);
ACTUAL: Error, (in gcd/doit) too many levels of recursion
EXPECTED: infinity
CHECK-UP: evalf(Int(sqrt(1+cos(z)^2), z=0..1000));
1216.104119
...............................................................................
BUG # 82 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(ln(Ci(z)), z=1..infinity);
ACTUAL: Error, (in limit/range) numeric exception: division by zero
EXPECTED: -infinity+infinity*I
...............................................................................
BUG # 83 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
*********************************
*** INVALID Re/Im MAGNITUDE ***
*********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
BUG 1 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
BUG 1 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
PRESENT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(sqrt(abs(sqrt(z) - 1)), z= -1..1);
ACTUAL: 4/3*(1-I)^(1/2)+4/15*I*(1-I)^(1/2)
1.586269446-.3138040504*I
EXPECTED: 8*2^(1/4)/5 - 4/15
1.636064717
CHECK-UP: evalf(Int(sqrt(abs(sqrt(z) - 1)), z= -1..1));
...............................................................................
BUG # 84 (plot)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can draw this graph correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***********************
*** INVALID GRAPH ***
***********************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
EXAMPLE 1: plot(sin(z),z=10^10..infinity);
ACTUAL: A vertical line at infinity
EXPECTED: A warning message like 'Unable show the graph. Try THIS or
THAT' is shown where THIS and THAT are actions proposed to
the user.
EXAMPLE 2: plot(sin(z),z=10^7..infinity);
ACTUAL: 4 vertical lines connected by 3 obliques.
EXPECTED: A warning message like 'Unable show the graph. Try THIS or
THAT' is shown where THIS and THAT are actions proposed to
the user.
EXAMPLE 3: plot(sin(z),z=10^10..10^45);
ACTUAL: Only the axes are shown.
EXPECTED: A warning message like 'Unable show the graph. Try THIS or
THAT' is shown where THIS and THAT are actions proposed to
the user.
...............................................................................
BUG # 85 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculute this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
****************************
*** STRANGE LIMITATION ***
****************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
Consider int(Pi/2-arctan(z^k), z=0..infinity);
Maple 8 can calculate correctly the integral at k = 0, 1, 2, 3, 4, 5, 6, 8, 10.
However, for k = 7 and k = 9 it, unexpectedly, cannot do it.
EXAMPLE 1: int(Pi/2-arctan(z^7), z=0..infinity);
ACTUAL: int(Pi/2-arctan(z^7), z=0..infinity);
EXPECTED: (sin(3*Pi/14)*(4*Pi*sin(Pi/14)/7+2*Pi/7)-2*Pi*cos(Pi/7)*sin(3*\
Pi/14)/7)/cos(3*Pi/14) - cos(Pi/7)*(4*Pi/(7*cos(Pi/14))-12*Pi*\
sin(3*Pi/14)/(7*sin(Pi/7))+(6*Pi/7-6*Pi*sin(Pi/14)/7)/sin(Pi/7\
))+(Pi/7-2*Pi*sin(Pi/14)/7)/cos(Pi/14)
CHECK-UP: 1.611192283
evalf(Int(Pi/2-arctan(z^7), z=0..infinity));
1.611192281
EXAMPLE 2: int(Pi/2-arctan(z^9), z=0..infinity);
ACTUAL: int(Pi/2-arctan(z^9), z=0..infinity);
EXPECTED: -1/18*(-1)^(5/9)*(9*I-2*(-1)^(1/18) +8*(-1)^(7/18)+4*(-1)^(13/\
18)+3*3^(1/2)-6*(-1)^(4/9)*3^(1/2))*Pi
CHECK-UP: 1.595028393+.3418939372e-9*I
evalf(Int(Pi/2-arctan(z^9), z=0..infinity));
1.595028392
...............................................................................
BUG # 86 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculute this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************
*** SPURIOUS CONVERGENCE ***
******************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(ln(z)^2*sin(z), z = -infinity..infinity);
ACTUAL: Pi^2+2*I*Pi*gamma
EXPECTED: undefined
...............................................................................
BUG # 87 (evalf)
**************************************
*** NUMERIC VALUE IS UNAVAILABLE ***
**************************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
UNDONE 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
The answer involves terms like D[1,1](LommelS1)(1/2,1/2,1) .
evalf(subs(a=1,int(ln(z)^2*sin(z), z = 0..a)));
ACTUAL: .3011686789*D[1,1](LommelS1)(1/2,1/2,1)+
.4207354923*D[1](LommelS1)(3/2,3/2,1)-
.4207354924*D[1,1](LommelS1)(3/2,3/2,1)+.1606255735
EXPECTED: .2448680576
CHECK-UP: evalf(Int(ln(z)^2*sin(z), z = 0..1));
.2448680576
...............................................................................
BUG # 88 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(abs(1+sin(z)), z=-I*infinity..I*infinity);
ACTUAL: Error, (in limit) invalid limiting point
EXPECTED: I*infinity
CHECK-UP: evalf(Int(abs(1+sin(z)), z=-I*10..I*10));
22026.46575*I
...............................................................................
BUG # 89 (evalf)
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
ABSENT Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
ERROR 1 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
ERROR 1 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ABSENT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
evalf(Int(ln(Ci(z)), z=1..4));
ACTUAL: Error, (in evalf/int) cannot assume on a constant object
EXPECTED: -5.110609401+1.934654260*I
...............................................................................
BUG # 90 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
This works fine.
int(1/(1 + I)^2, z = -I*infinity..I*infinity);
infinity
However, this invokes an error.
int(1/sqrt(z + I), z = -I*infinity..I*infinity);
ACTUAL: Error, (in limit) invalid limiting point
EXPECTED: undefined
evalf(Int(1/sqrt(z + I), z = -I*infinity..I*infinity));
Float(undefined)+0.*I
The same problem with
int(1/z^2, z = 1..I*infinity);
int(1/z, z = 1..I*infinity);
int(z^sqrt(2), z=0..I*infinity);
int(z^sqrt(2), z=-I*infinity..infinity);
...............................................................................
BUG # 91 (limit)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this limit correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
****************************
*** SPURIOUS undefined ***
****************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
expr := z*(sin(z)*BesselJ(0,z)-cos(z)*BesselJ(1,z));
limit(expr, z=infinity);
ACTUAL: undefined
EXPECTED: infinity
CHECK-UP: evalf(limit(z*(sin(z)*BesselJ(0,z)-cos(z)*BesselJ(1,z)),
z=10^10));
56418.95836
HINT: plot(expr, z=0..100);
...............................................................................
BUG # 92 (limit)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this limit correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************
*** INVALID Im MAGNITUDE ***
******************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
limit(exp(-1 + I*z) + exp(1 - I*z), z = infinity);
ACTUAL: -exp(-1)-I*exp(-1)-exp(1)-I*exp(1) .. exp(-1)+I*exp(-1)+exp(1)\
+I*exp(1)
-3.086161269-3.086161269*I .. 3.086161269+3.086161269*I
EXPECTED: -2*cosh(1) - I*2*sinh(1) .. 2*cosh(1) + I*2*sinh(1)
-3.086161270-2.350402388*I .. 3.086161270+2.350402388*I
HINT: plot(Im(exp(-1 + I*z) + exp(1 - I*z)), z = 1000000..1000200);
...............................................................................
BUG # 93 (plot)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can draw this graph correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***********************
*** INVALID GRAPH ***
***********************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
plot(abs(cos(z) + I*sin(z)) - 1, z= -1..1);
ACTUAL: Spurious vertical lines near z = 0.4 .
EXPECTED: The straight line y = 0.
COMPARE 1: Derive 5.05 (You may wish to use a free trial version at
http://www.derive.com)
ABS(COS(z) + #I*SIN(z)) - 1
COMPARE 2: MuPAD 2.5 (You may wish to use a free trial version at
http://www.mupad.com)
plotfunc2d(abs(cos(z) + I*sin(z)) - 1, z= -1..1);
...............................................................................
BUG # 94 (plot)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can draw this graph correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***********************
*** INVALID GRAPH ***
***********************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
plot(-3 + abs((-1 + (1 + 6*(cos(z) + I*sin(z)))/(1 +3*(cos(z)+\
I*sin(z))))/(-2 + (1 + 6*(cos(z) + I*sin(z)))/(1 + 3*(cos(z) +\
I*sin(z))))), z= -2..2);
ACTUAL: A complex-looking shape filled with hundreds vertical lines.
EXPECTED: The straight line y = 0.
COMPARE 1: Derive 5.05 (You may wish to use a free trial version at
http://www.derive.com)
-3+ABS((-1+(1+6*(COS(z)+#i*SIN(z)))/(1+3*(COS(z)+#i*SIN(z))))/~
(-2+(1+6*(COS(z)+#i*SIN(z)))/(1+3*(COS(z)+#i*SIN(z)))))
COMPARE 2: MuPAD 2.5 (You may wish to use a free trial version at
http://www.mupad.com)
plotfunc2d(-3+abs((-1 + (1 +6*(cos(z)+I*sin(z)))/(1+3*(cos(z)+\
I*sin(z))))/(-2 + (1 + 6*(cos(z) + I*sin(z)))/(1 + 3*(cos(z) +\
I*sin(z))))), z= -2..2);
...............................................................................
BUG # 95 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**********************************
*** ERROR MESSAGE IS INVOKED ***
**********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT 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
int(Beta(1/z,-1/2), z=0..infinity);
ACTUAL: Error, (in expand/Psi) too many levels of recursion
EXPECTED: infinity
CHECK-UP: evalf(Int(Beta(1/z,-1/2), z=0..10^100));
.5000000000e200
The same problem with
int(Beta(1/z^(1/2),-1/2), z=0..infinity);
...............................................................................
BUG # 96 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***********************************
*** SIMPLE INTEGRAL IS UNDONE ***
***********************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple 6.01, IBM INTEL NT, Jun 9 2000 Build ID 79514
PRESENT Maple V, Release 5, IBM INTEL NT, Nov 27 1997
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
ERROR Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
This integral is TOO simple to be left unprocessed.
int(1/(z + sqrt(1-z)), z=0..1);
ACTUAL: 2/5*5^(1/2)*Re(arctanh(3/5*5^(1/2)))-1/2*I*Pi-1/2*ln(5+5^(1/2)\
)+1/2*ln(-5-5^(1/2))+limit(1/2*ln(z^2-1+z)+1/5*5^(1/2)*arctanh\
(1/5*(2*z+1)*5^(1/2))-1/2*ln(- z + (1-z)^(1/2)) - 1/5*5^(1/2)*\
arctanh(1/5*(2*(1-z)^(1/2)+1)*5^(1/2))+1/2*ln(-z-(1-z)^(1/2))-\
1/5*5^(1/2)*arctanh(1/5*(2*(1-z)^(1/2)-1)*5^(1/2)),z = RootOf(\
_Z^2-1+_Z,.6180339887),left)+limit(-1/2*ln(z^2-1+z)-1/5*5^(1/2\
)*arctanh(1/5*(2*z+1)*5^(1/2))+1/2*ln(-z+(1-z)^(1/2))+1/5*5^(1\
/2)*arctanh(1/5*(2*(1-z)^(1/2)+1)*5^(1/2))-1/2*ln(-z-(1-z)^(1/\
2))+1/5*5^(1/2)*arctanh(1/5*(2*(1-z)^(1/2) - 1)*5^(1/2)), z = \
RootOf(_Z^2-1+_Z,.6180339887),right)
evalf(%);
.9779728648+3.844074127*I+limit(-1/2*ln(z^2-1+z)-1/5*5^(1/2)*a\
rctanh(1/5*(2*z+1)*5^(1/2))+1/2*ln(-z+(1-z)^(1/2))+1/5*5^(1/2)\
*arctanh(1/5*(2*(1-z)^(1/2)+1)*5^(1/2))-1/2*ln(-z-(1-z)^(1/2))\
+1/5*5^(1/2)*arctanh(1/5*(2*(1-z)^(1/2)-1)*5^(1/2)),z = RootOf\
(_Z^2-1+_Z,.6180339887),right)
EXPECTED: sqrt(5)*ln(3*sqrt(5)/2+7/2)/5
CHECK-UP: .8608178820
evalf(Int(1/(z + sqrt(1-z)), z=0..1));
.8608178819
...............................................................................
BUG # 97 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
****************************
*** SPURIOUS undefined ***
****************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
BUG 1 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
BUG 2 Maple V, Release 5, IBM INTEL NT, Nov 27 1997
BUG 2 Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(abs(1,tan(z)-1)*(1+tan(z)^2)/(tan(z)-1)^2,z=0..Pi/5);
ACTUAL: undefined
EXPECTED: (5-2*5^(1/2))^(1/2)/((5-2*5^(1/2))^(1/2)-1)
-2.656875748
CHECK-UP: evalf(Int(abs(1,tan(z)-1)*(1+tan(z)^2)/(tan(z)-1)^2,z=0..Pi/5))
-2.656875757
...............................................................................
BUG # 98 (int)
******************************
*** SPURIOUS CONVERGENCE ***
******************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: PRESENT Maple 8.00, IBM INTEL NT, May 10 2002 Build ID 111221
BUG 1 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
int(ln(z)^2/sqrt(1+z), z=0..infinity);
ACTUAL: -16-4/3*Pi^2+16*ln(2)-8*ln(2)^2
-21.91274176
EXPECTED: infinity
CHECK-UP: evalf(Int(ln(z)^2/sqrt(1+z), z=0..infinity));
Float(infinity)
The same problem with
int(ln(z)^(2*k)/sqrt(1+z), z=0..infinity);
where k = 2, 3, 4, 5, and with
int(ln(z)^(2*k)/(1+z)^(1/3), z=0..infinity);
where k = 1, 2, 3, 4, 5.
...............................................................................
BUG # 99 (int)
****************************
*** SPURIOUS undefined ***
****************************
REGRESSION YES
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
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
int(ln(z)^2/sqrt(1+z^2), z=0..infinity);
ACTUAL: undefined
EXPECTED: infinity
CHECK-UP: evalf(Int(ln(z)^2/sqrt(1+z^2), z=0..infinity));
Float(infinity)
The same problem with
int(ln(z)^(2*k)/sqrt(1+z^2), z=0..infinity);
where k = 2, 3, 4, 5.
...............................................................................
BUG # 100 (int)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! NONE Maple version can calculate this integral correctly !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
******************************
*** SPURIOUS CONVERGENCE ***
******************************
REPRODUCIBLE ALWAYS
BUG HISTORY: 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
CANNOT Maple V, Release 4, IBM INTEL NT, Dec 15, 1995
CANNOT Maple V, Release 3, IBM INTEL NT, Jan 10, 1994
int(Si(z)*ln(z), z=0..infinity);
ACTUAL: 1+gamma
EXPECTED: infinity
CHECK-UP: evalf(Int(Si(z)*ln(z), z=0..100));
567.9000385
HINT: plot(Si(z)*ln(z), z=0..100);
...............................................................................
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© 2002-2008 Cyber Tester Ltd. All rights reserved. All logos and trademarks are property of their respective owners.
E-mail: vb@cybertester.com