|
| Dear Mr. Cooper,
Maple bug analysis is going to be the
death of me. You know that I have already thereby forfeited
one eye, and from that I was in some considerable danger.
One morning, while I was bent over to examine a portion
of a novelty, a Maple bug genetic map which was sent
to me by one of our promising computer scientists, I
suddenly felt a blow of pain. This work, in which one
must hang over and examine a large area at one time,
attacks the sight far more violently than only simple
reading or writing alone. On account of these things,
I must ask you, if you have good will for me, to appeal
to Mr.
Bernardin if it would please him that I be excused
from this work, which is only a small part of my responsibilities,
but which easily make me unfit for all the rest. I am
with all honor and respect your humble servant,
Leonhard Euler
|
Produced by our GEMM, below
is published for the first time a tiny random demo of
Maple howlers in 10 functions: limit, int, sum,
product, simplify, series, asympt, coulditbe, is, testeq.
|
BUG # 1 int: INVALID INDEFINITE INTEGRATION
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: int(sin(z)*exp(z)*sin(1/z), z);
ACTUAL: 0
EXPECTED: int(sin(z)*exp(z)*sin(1/z), z);
EXAMPLE 2: diff(int(sin(z)*exp(z)*cos(1/z), z),z);
ACTUAL: exp(z)*sin(z)
EXPECTED: sin(z)*exp(z)*cos(1/z)
The same problem with
int(sin(z)*exp(-z)*sin(1/z), z);
int(cos(z)*exp(z)*sin(1/z), z);
int(cos(z)*exp(-z)*sin(1/z), z);
diff(int(exp(z)*cos(z+1/z), z), z);
diff(int(exp(z)*cos(z-1/z), z), z);
diff(int(exp(-z)*cos(z+1/z), z), z);
diff(int(exp(-z)*cos(z-1/z), z), z);
|
BUG # 2 int: INVALID INDEFINITE INTEGRATION
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
int(sqrt(sqrt(z)-1),z);
ACTUAL: -I/Pi^(1/2)*(-8/15*Pi^(1/2)-4/15*Pi^(1/2)*(-1+z^(1/2))*(3*z^(1/2)+2)*(1-z^(1/2\
))^(1/2))
HINT: func := sqrt(sqrt(z)-1): simplify(func-diff(int(func,z),z)); plot(%, z=0..2);
((z^(1/2)-1)^(1/2)*(1-z^(1/2))^(1/2)*z^(1/2)-I*z^(1/2)+I*z)/(1-z^(1/2))^(1/2)/\
z^(1/2)
while the above expression should be equal to 0 identically.
EXPECTED: 4/15*(z^(1/2)-1)^(1/2)*(-2-z^(1/2)+3*z)
CHECKUP: simplify(sqrt(sqrt(z)-1)-diff(4/15*(z^(1/2)-1)^(1/2)*(-2-z^(1/2)+3*z),z));
0
CHECKUP: plot(func-diff(4/15*(z^(1/2)-1)^(1/2)*(-2-z^(1/2)+3*z),z),z=-10..10,y=-1..1);
plot(func-diff(4/15*(z^(1/2)-1)^(1/2)*(-2-z^(1/2)+3*z),z),z=-999..999,y=-1..1);
IMPLICATIONS: Maple calculates incorrectly definite integrals involving sqrt(sqrt(z)-1)
EXAMPLE 1: INVALID OUTPUT SIGN:
evalf(int(sqrt(sqrt(z)-1), z=1..2));
ACTUAL: -.4437859441
EXPECTED: .4437859441
CHECKUP: evalf(Int(sqrt(sqrt(z)-1), z=1..2));
.4437859441
EXAMPLE 2: INVALID MAGNITUDE OF THE REALS AND IMAGINARY PARTS
evalf(int(sqrt(sqrt(I*z)-1), z=-1..1));
ACTUAL: 1.591279201*I
EXPECTED: .6108037585
CHECKUP: evalf(Int(sqrt(sqrt(I*z)-1), z=-1..1));
.6108037585
|
BUG # 3 int: INVALID MAGNITUDE OF THE REAL-VALUED INTEGRAL
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
int(exp(-z^2)/(1+z^2), z=1..infinity);
ACTUAL: 1/2*Pi*exp(1)-1/2*Pi*exp(1)*erf(1)
.671646711
EXPECTED: 1/2*Pi*exp(1)-1/2*Pi*exp(1)*erf(1)-sum(1/2*(-1)^n*(2/(n+1/2)/(3+2*n)*exp(-1/2)\
*WhittakerM(1/2*n+1/4,1/2*n+3/4,1)+1/(n+1/2)*exp(-1/2)*WhittakerM(1/2*n+5/4,1/\
2*n+3/4,1)),n = 0 .. infinity)
.528247477e-1
CHECKUP: evalf(Int(exp(-z^2)/(1+z^2), z=1..infinity));
.5282474752e-1
The same problem with
int(exp(-z^(3/2))/(1+z^(3/2)), z=1..infinity);
int(exp(-z^(2/3))/(1+z^(2/3)), z=1..infinity);
int(exp(-z^(4/3))/(1+z^(4/3)), z=1..infinity);
int(exp(-z^(3/4))/(1+z^(3/4)), z=1..infinity);
int(exp(-z^3)/(1+z^3), z=1..infinity);
int(exp(-z^4)/(1+z^4), z=1..infinity);
int(exp(-z^5)/(1+z^5), z=1..infinity);
int(exp(-z^6)/(1+z^6), z=1..infinity);
int(Ei(0, 1+z^2), z=1..infinity);
int(Ei(0, 1+z^3), z=1..infinity);
int(Ei(0, 1+z^4), z=1..infinity);
int(Ei(0, 1+z^5), z=1..infinity);
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BUG # 4 int: Error, (in limit/range) should not happen 33
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
int(arctan(tan(1/z)), z=0..1);
ACTUAL: Error, (in limit/range) should not happen 33
The same problem with
int(ln(z)*arctan(tan(1/z)), z=0..1);
int(sqrt(z)*arctan(tan(1/z)), z=0..1);
int(z^(1/3)*arctan(tan(1/z)), z=0..1);
int(exp(-z)*arctan(tan(z)), z=0..infinity);
int(exp(-z^2)*arctan(tan(z)), z=0..infinity);
int(exp(-z^3)*arctan(tan(z)), z=0..infinity);
int(exp(-2*z)*arctan(tan(z))*cosh(z), z=0..infinity);
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BUG # 5 int: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: int(arcsec(z*sqrt(1 - z^2)), z = -2..2);
ACTUAL: undefined
EXPECTED: 2*Pi
WORKAROUND: subs(a=2,int(arcsec(z*sqrt(1 - z^2)), z = -a..a));
EXAMPLE 2: int(arccsc(z*sqrt(1 - z^2)), z = -2..2);
ACTUAL: undefined
EXPECTED: 0
WORKAROUND: subs(a=2,int(arccsc(z*sqrt(1 - z^2)), z = -a..a));
COMMENT: Derive 5.06 calculates all these integrals correctly.
The same problem with
int(arcsec(z*sqrt(1 + z^2)), z = -2..2);
int(arccsc(z*sqrt(1 + z^2)), z = -2..2);
int(arccsc(z*sqrt(1 - z^2)), z = -2..2);
int(arccsch(z*sqrt(1 - z^2)), z = -2..2);
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BUG # 6 int: INVALID INDEFINITE INTEGRATION
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
int(arctan(tan(1/z)), z);
ACTUAL: z*arctan(tan(1/z))+ln(z)
EXPECTED: -Pi*z*floor(1/(Pi*z)+1/2)+Psi(floor(1/(Pi*z)+1/2)+1/2)+ln(z)
CHECKUP: evalf(subs(z=1, %)-subs(z=1/20, %),15);
evalf(Int(arctan(tan(1/z)), z=1/20..1),14);
.18178871320958
.18178871320958
The same problem with
int(arctan(cot(1/z)), z);
int(arccot(cot(1/z)), z);
int(arccot(tan(1/z)), z);
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BUG # 7 sum: INVALID MAGNITUDE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
evalf(sum(sin(Pi/2^n), n=1..infinity));
ACTUAL: 1
EXPECTED: 2.481049919
CHECKUP: evalf(Sum(sin(Pi/2^n), n=1..infinity));
2.481049919
HINT: plot(sum(sin(Pi/2^n), n=1..k), k=1..100);
The same problem with
sum((-1)^n*sin(Pi/2^n), n=1..infinity);
sum(sin(Pi/3^n), n=1..infinity);
sum(sin(Pi/4^n), n=2..infinity);
sum((-1)^n*sin(Pi/3^n), n=1..infinity);
sum((-1)^n*sin(Pi/4^n), n=2..infinity);
sum(n^2*sin(Pi/(3^n))^2, n=1..infinity);
sum(4^n*sin(Pi/(5^n)), n=1..infinity);
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BUG # 8 int: Error, (in X) numeric exception: division by zero
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
int(arctan(z*sqrt(1 - z^2)), z = -2..2);
ACTUAL: Error, (in ln) numeric exception: division by zero
EXPECTED: 0
CHECKUP: evalf(Int(arctan(z*sqrt(1 - z^2)), z = -2..2, method = _CCquad));
0.+0.*I
HINT: plot(Re(arctan(z*sqrt(1 - z^2))), z = -2..2);
plot(Im(arctan(z*sqrt(1 - z^2))), z = -2..2);
COMMENT: Derive 5.06 calculates this integral correctly.
COMMENT: Maple cannot see that the integrand is an odd bounded function;
thus, the integral of it over any finite symmetric segment is
equal to zero.
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BUG # 9 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(arcsin(1/cos(z)),z = Pi/2-4);
ACTUAL: undefined
EXPECTED: arcsin(1/sin(4))
-1.570796327+.7816340727*I
CHECKUP: evalf(Limit(arcsin(1/cos(z)),z = Pi/2-4));
-1.570796327+.7816340724*I
COMMENT: Derive 5.06 and Mathematica 4.2.1 calculate all these limits correctly.
The same problem with
limit(arcsin(1/cos(z)),z = Pi/2-5);
limit(arccos(1/cos(z)),z = Pi/2-4);
limit(arccos(1/cos(z)),z = Pi/2-5);
limit(arcsin(1/cos(z)),z = 5-Pi/2);
limit(arccos(1/cos(z)),z = 4-Pi/2);
limit(arccos(1/cos(z)),z = 5-Pi/2);
limit(arcsin(1/cos(z)),z = 5+Pi/2);
limit(arccos(1/cos(z)),z = 4+Pi/2);
limit(arccos(1/cos(z)),z = 5+Pi/2);
limit(arcsin(1/cos(z)),z = 111+Pi/2);
limit(arccos(1/cos(z)),z = 111+Pi/2);
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BUG # 10 limit: BEYOND CLASSIFICATION
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(sin(z)^2+cos(z)^2, z = infinity);
ACTUAL: 0 .. 2
EXPECTED: 1
CHECKUP: seq(round(evalf(limit(sin(z)^2+cos(z)^2, z = 10^k))), k=1..20);
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
WORKAROUND: limit(simplify(sin(z)^2+cos(z)^2), z = infinity);
COMMENT: Derive 5.06 and MuPAD 2.5.2 calculate it correctly.
::::::::::::::::::::::::::::::::::::::::::::::::: 10%
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BUG # 11 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(sqrt(1-ln(1+1/z^2)), z=1);
ACTUAL: undefined
EXPECTED: (1-ln(2))^(1/2)
.5539429749
CHECKUP: evalf(Limit(sqrt(1-ln(1+1/z^2)), z=1));
.5539429749
EXAMPLE 2: limit(sqrt(1-ln(1+1/z^2)), z=1, left);
ACTUAL: -(1-ln(2))^(1/2)
EXPECTED: (1-ln(2))^(1/2)
.5539429749
CHECKUP: evalf(Limit(sqrt(1-ln(1+1/z^2)), z=1-1/10^100));
.5539429749
HINT: plot(sqrt(1-ln(1+1/z^2)), z=1..3);
plot(sqrt(1-ln(1+1/z^2)), z=9/10..11/10);
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BUG # 12 limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(sin(1/sqrt(z))*z,z = 0);
ACTUAL: 0
EXPECTED: undefined
CHECKUP: evalf(limit(sin(1/sqrt(z))*z,z = -1/10^10));
evalf(limit(sin(1/sqrt(z))*z,z = 1/10^10));
.1403331680e43420*I
.3574879797e-11
EXAMPLE 2: limit(sin(1/z)*z,z = 0,left);
ACTUAL: 0
EXPECTED: I*infinity
CHECKUP: evalf(limit(sin(1/sqrt(z))*z,z = -1/10^10));
.1403331680e43420*I
COMMENT: Derive 5.06 and Mathematica 4.2.1 calculate these limits correctly.
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BUG # 13 limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(sqrt(-sinh(z)), z = Pi/2+1, left);
ACTUAL: -1/2*I*2^(1/2)*(-1/exp(Pi)^(1/2)*exp(-1)+exp(Pi)^(1/2)*exp(1))^(1/2)
-2.549486088*I
EXPECTED: 1/2*I*2^(1/2)*(-exp(-1)+exp(Pi+1))^(1/2)*exp(-1/4*Pi)
2.549486087*I
CHECKUP: evalf(Limit(sqrt(-sinh(z)), z = Pi/2+1, left));
2.549486088*I
EXAMPLE 2: limit(sqrt(-sinh(z)), z = Pi/2+1, right);
ACTUAL: -1/2*I*2^(1/2)*(-1/exp(Pi)^(1/2)*exp(-1)+exp(Pi)^(1/2)*exp(1))^(1/2)
-2.549486088*I
EXPECTED: 1/2*I*2^(1/2)*(-exp(-1)+exp(1+Pi))^(1/2)*exp(-1/4*Pi)
2.549486087*I
CHECKUP: evalf(Limit(sqrt(-sinh(z)), z = Pi/2+1, right));
2.549486088*I
COMMENT: Derive 5.06 and Mathematica 4.2.1 calculate these limits
correctly.
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BUG # 14 limit: HISTORY-DEPENDENT OUTPUT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
The results of the INDEPENDENT computations depend on the previous inputs; in other words,
the outcomes of the INDEPENDENT computations are not the same for the a;b; and the b;a;
sequences.
limit((csch(z)^2-1)^(1/3),z = 1);
limit((csch(z)^2-1)^(1/3),z = 11);
restart;
limit((csch(z)^2-1)^(1/3),z = 11);
limit((csch(z)^2-1)^(1/3),z = 1);
ACTUAL: 1/2*(-6/(exp(1)-exp(-1))^2+1/(exp(1)-exp(-1))^2*exp(-2)+1/(exp(\
1)-exp(-1))^2*exp(2))^(1/3)+1/2*I*(-6/(exp(1)-exp(-1))^2+1/(exp\
(1)-exp(-1))^2*exp(-2)+1/(exp(1)-exp(-1))^2*exp(2))^(1/3)*3^(1/\
2)
1/2*(-6/(exp(11)-exp(-11))^2+1/(exp(11)-exp(-11))^2*exp(-22)+1/\
(exp(11)-exp(-11))^2*exp(22))^(1/3)+1/2*I*(-6/(exp(11)-exp(-11)\
)^2+1/(exp(11)-exp(-11))^2*exp(-22)+1/(exp(11)-exp(-11))^2*exp(\
22))^(1/3)*3^(1/2)
undefined
undefined
EXPECTED: 1/2*(-6/(exp(1)-exp(-1))^2+1/(exp(1)-exp(-1))^2*exp(-2)+1/(exp(\
1)-exp(-1))^2*exp(2))^(1/3)+1/2*I*(-6/(exp(1)-exp(-1))^2+1/(exp\
(1)-exp(-1))^2*exp(-2)+1/(exp(1)-exp(-1))^2*exp(2))^(1/3)*3^(1/\
2)
1/2*(-6/(exp(11)-exp(-11))^2+1/(exp(11)-exp(-11))^2*exp(-22)+1/\
(exp(11)-exp(-11))^2*exp(22))^(1/3)+1/2*I*(-6/(exp(11)-exp(-11)\
)^2+1/(exp(11)-exp(-11))^2*exp(-22)+1/(exp(11)-exp(-11))^2*exp(\
22))^(1/3)*3^(1/2)
1/2*(-6/(exp(1)-exp(-1))^2+1/(exp(1)-exp(-1))^2*exp(-2)+1/(exp(\
1)-exp(-1))^2*exp(2))^(1/3)+1/2*I*(-6/(exp(1)-exp(-1))^2+1/(exp\
(1)-exp(-1))^2*exp(-2)+1/(exp(1)-exp(-1))^2*exp(2))^(1/3)*3^(1/\
2)
1/2*(-6/(exp(11)-exp(-11))^2+1/(exp(11)-exp(-11))^2*exp(-22)+1/\
(exp(11)-exp(-11))^2*exp(22))^(1/3)+1/2*I*(-6/(exp(11)-exp(-11)\
)^2+1/(exp(11)-exp(-11))^2*exp(-22)+1/(exp(11)-exp(-11))^2*exp(\
22))^(1/3)*3^(1/2)
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BUG # 15 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
restart;
limit((csch(z)^2-1)^(1/3),z = 11);
ACTUAL: undefined
EXPECTED: (1/sinh(11)^2*(sinh(11)^2 - 1))^(1/3)*(1/2*I*3^(1/2) + 1/2)
.4999999998+.8660254037*I
CHECKUP: evalf(Limit((csch(z)^2-1)^(1/3),z = 11));
.4999999998+.8660254035*I
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BUG # 16 evalf: INVALID MAGNITUDE OF THE REAL AND IMAGINARY PARTS
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
1) The values of approximations are not correct.
2) What is even worse, Maple is NOT consistent with itself. Compare with Mathematica.
restart;
func := EllipticF(I,2*I):
evalf(evalf(func, 10), 10);
evalf(evalf(func, 20), 10);
evalf(evalf(func, 100), 10);
ACTUAL: .5328240547+.7423732236*I # <---------------------------------.
.5604418122+.7421443374*I # <-- These values must be identical.
.5499902134+.7397678082*I # <---------------------------------.
EXPECTED: .5499964467+.7422062367*I
.5499964467+.7422062367*I
.5499964467+.7422062367*I
COMMENT: Mathematica 4.2.1 approximates these inputs correctly.
N[N[EllipticF[ArcSin[I], -4], 10], 10]
N[N[EllipticF[ArcSin[I], -4], 20], 10]
N[N[EllipticF[ArcSin[I], -4], 100], 10]
0.549996 + 0.742206 I
0.549996 + 0.742206 I
0.549996 + 0.742206 I
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BUG # 17 limit: INVALID TYPE OF DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
This is like 2 + 2 = sin(z).
limit(cos(sqrt(-z)),z = infinity);
ACTUAL: -1 .. 1
EXPECTED: infinity
CHECKUP: seq(evalf(limit(cos(sqrt(-z)),z = 10^k)), k=15..20);
.1198972659e13733598,
.7749883733e43429448,
.3143132997e137335974,
.4001490885e434294482,
.4818341088e1373359738,
Float(infinity)
The same problem with
limit(sin(sqrt(-z)), z = infinity);
limit(cos(sqrt(-z))+sin(z),z = infinity);
limit(cos(sqrt(-z))+cos(z),z = infinity);
limit(sin(sqrt(-z))+sin(z),z = infinity);
limit(sin(sqrt(-z))+cos(z),z = infinity);
COMMENT: Mathematica 4.2.1 calculates all these limits correctly.
Derive 5.06 does 4 first of them, too.
|
BUG # 18 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(tan(z)*cot(z),z = infinity);
ACTUAL: undefined
EXPECTED: 1
CHECKUP: evalf(Limit(tan(z)*cot(z),z = infinity));
1.000000000
The same problem with
limit(tan(z)*cot(z),z = -infinity);
COMMENT: Derive 5.06, Mathematica 4.2.1 and MuPAD 2.5.2 calculate
it correctly.
LIM(COT(z)*TAN(z), z, inf)
1
Limit[Tan[z]*Cot[z], z -> Infinity]
1
limit(cot(z)*tan(z),z = infinity);
1
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BUG # 19 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit((1/z-(1-1/z^2))^(1/3),z = 2);
ACTUAL: undefined
EXPECTED: 1/4*2^(1/3)+1/4*I*2^(1/3)*3^(1/2)
.3149802625+.5455618182*I
CHECKUP: evalf(Limit((1/z-(1-1/z^2))^(1/3),z = 2));
.3149802625+.5455618180*I
EXAMPLE 2: limit((1/z-(1-1/z^2))^(1/3),z = 2, left);
ACTUAL: 1/8*4^(2/3)-1/8*I*4^(2/3)*3^(1/2)
EXPECTED: 1/8*4^(2/3)+1/8*I*4^(2/3)*3^(1/2)
.3149802625+.5455618181*I
CHECKUP: evalf(Limit((1/z-(1-1/z^2))^(1/3),z = 1.999999999));
.3149802623+.5455618176*I
COMMENT: Derive 5.06 and Mathematica 4.2.1 calculate these limits
correctly.
The same problem with
limit((1/z-(1+1/z^2))^(1/3),z = 2);
limit((1/z^2-(1-1/z^2))^(1/3),z = 2);
limit((1/z^4-(1-1/z^2))^(1/3),z = 2);
limit((1/z^4-(1-1/z^3))^(1/3),z = 2);
limit((1/z^4-(1-1/z^4))^(1/3),z = 2);
limit((1/z^4-(1-1/z^4))^(1/3),z = 2);
limit(1/(1/z^4-(1-1/z^4))^(1/3),z = 2);
limit(1/(1/z^4-(1-1/z^4)^(1/1))^(1/3),z = 2);
limit(1/(1/z^4-(1-1/z^4)^(1/2))^(1/3),z = 2);
limit(1/(-1/z^4-(1-1/z^4)^(1/2))^(1/3),z = 2);
limit((1/z-(1+1/z^2))^(1/3),z = 2, left);
limit((1/z^2-(1-1/z^2))^(1/3),z = 2, left);
limit((1/z^4-(1-1/z^2))^(1/3),z = 2, left);
limit((1/z^4-(1-1/z^3))^(1/3),z = 2, left);
limit((1/z^4-(1-1/z^4))^(1/3),z = 2, left);
limit((1/z^4-(1-1/z^4))^(1/3),z = 2, left);
limit(1/(1/z^4-(1-1/z^4))^(1/3),z = 2, left);
limit(1/(1/z^4-(1-1/z^4)^(1/1))^(1/3),z = 2, left);
limit(1/(1/z^4-(1-1/z^4)^(1/2))^(1/3),z = 2, left);
limit(1/(-1/z^4-(1-1/z^4)^(1/2))^(1/3),z = 2, left);
|
BUG # 20 limit: Error, (in X) should not happen 33
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(arctan(tan(z)),z = infinity);
ACTUAL: Error, (in limit/range) should not happen 33
EXPECTED: -Pi/2..Pi/2
HINT: plot(arctan(tan(z)),z = 1000..1020);
COMMENT: Mathematica 4.2.1 calculates it correctly.
The same problem with
limit(arccot(tan(z)),z = infinity);
limit(arctanh(tan(z)),z = infinity);
::::::::::::::::::::::::::::::::::::::::::::::::: 20%
|
BUG # 21 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit((ln(z)/(1+z^3)^2-1)^(1/3),z = 2);
ACTUAL: undefined
EXPECTED: 1/18*(-ln(2)+162)^(1/3)*(3^(2/3)+3*I*3^(1/6))
.6290607728+1.089565219*I
CHECKUP: evalf(Limit((ln(z)^2/(1+z^3)^2-2)^(1/3),z = 2));
.6290607726+1.089565219*I
EXAMPLE 2: limit((ln(z)/(1+z^3)^2-1)^(1/3),z = 2, left);
ACTUAL: 1/162*81^(2/3)*(-ln(2)+81)^(1/3)-1/162*I*81^(2/3)*(-ln(2)+81)\
^(1/3)*3^(1/2)
.4985696836-.8635480234*I
EXPECTED: 1/162*81^(2/3)*(-ln(2)+81)^(1/3)+1/162*I*81^(2/3)*(-ln(2)+81)\
^(1/3)*3^(1/2)
.4985696836+.8635480234*I
CHECKUP: evalf(Limit((ln(z)/(1+z^3)^2-1)^(1/3),z = 2));
.4985696835+.8635480230*I
The same problem with
limit((ln(z)/(1+z^3)^2-2)^(1/3),z = 2);
limit((ln(z)^2/(1+z^3)^2-2)^(1/3),z = 2);
limit((ln(z)^2/(1+z^3)^2-2)^(1/4),z = 2);
limit((ln(z)^2/(1+z^3)^2-2)^(1/4),z = 10);
limit((ln(z)/(1+z^3)^2-2)^(1/3),z = 2, left);
limit((ln(z)^2/(1+z^3)^2-2)^(1/3),z = 2, left);
limit((ln(z)^2/(1+z^3)^2-2)^(1/4),z = 2, left);
limit((ln(z)^2/(1+z^3)^2-2)^(1/4),z = 10, left);
|
BUG # 22 limit: INVALID MAGNITUDE OF THE REAL-VALUED LIMIT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(Fresnelf(z),z = -infinity);
ACTUAL: 0
EXPECTED: 1
CHECKUP: evalf(limit(Fresnelf(z),z = -10^10));
1.000000000
EXAMPLE 2: limit(Fresnelg(z),z = -infinity);
ACTUAL: 0
EXPECTED: 1
CHECKUP: evalf(Limit(Fresnelg(z),z = -infinity));
1.000000000
|
BUG # 23 limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(arccot(1/sqrt(z)),z = -infinity);
ACTUAL: -1/2*Pi
EXPECTED: 1/2*Pi
1.570796327
CHECKUP: fnormal(evalf(Limit(arccot(1/sqrt(z)),z = -infinity)));
1.570796327+0.*I
|
BUG # 24 limit: SPURIOUS DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(BesselJ(0, sqrt(z)),z = -infinity);
ACTUAL: 0
EXPECTED: infinity
CHECKUP: seq(evalf(Limit(BesselJ(0, sqrt(z)),z = -10^k)), k=8..10);
.3513456066e4341, .8877534180e13731, .3540796227e43427
EXAMPLE 2: limit(BesselJ(1, sqrt(z)),z = -infinity);
ACTUAL: 0
EXPECTED: I*infinity
CHECKUP: seq(evalf(Limit(BesselJ(1, sqrt(z)),z = -10^k)), k=8..10);
.3513280389e4341*I, .8877393813e13731*I, .3540778523e43427*I
|
BUG # 25 limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(arctanh(sqrt(z))*BesselK(0,z),z = -infinity);
ACTUAL: 0
EXPECTED: infinity
CHECKUP: evalf(limit(arctanh(sqrt(z))*BesselK(0,z),z = -10^5));
evalf(limit(arctanh(sqrt(z))*BesselK(0,z),z = -10^10));
.1743795279e43428
Float(infinity)
|
BUG # 26 limit: SPURIOUS DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
evalf(Limit(sqrt(z)*EllipticPi(1/2,z), z= infinity));
ACTUAL: Float(infinity)
EXPECTED: 0
CHECKUP: evalf(Limit(sqrt(z)*EllipticPi(1/2,z), z= 1000000000000));
.1570796327e-5-.2980271364e-4*I
evalf(Limit(sqrt(z)*EllipticPi(1/2,z), z= 10^20), 50);
.15707963267948966192313216916397514420986632395039e-9-
.48223394384398252608809954182423513009224676425905e-8*I
|
BUG # 27 limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(KelvinKei(0,z),z = -infinity);
ACTUAL: 0
EXPECTED: undefined
CHECKUP: seq(evalf(limit(KelvinKei(0,z),z = -10^k)), k=5..9);
-.4518269280e30707+0.*I,
.6756894672e307089+0.*I,
.1853952270e3070923+0.*I,
-.1675955604e30709254+0.*I,
.2220299636e307092569+0.*I
The same problem with
limit(KelvinKer(0,z),z = -infinity);
limit(KelvinKer(1,z),z = -infinity);
limit(KelvinKer(2,z),z = -infinity);
limit(KelvinKer(3,z),z = -infinity);
limit(KelvinKer(4,z),z = -infinity);
limit(KelvinKei(1,z),z = -infinity);
limit(KelvinKei(2,z),z = -infinity);
limit(KelvinKei(3,z),z = -infinity);
limit(KelvinKei(4,z),z = -infinity);
limit(KelvinBer(0,z),z = -infinity);
limit(KelvinBer(1,z),z = -infinity);
limit(KelvinBer(2,z),z = -infinity);
limit(KelvinBer(3,z),z = -infinity);
limit(KelvinBer(4,z),z = -infinity);
limit(KelvinBei(0,z),z = -infinity);
limit(KelvinBei(1,z),z = -infinity);
limit(KelvinBei(2,z),z = -infinity);
limit(KelvinBei(3,z),z = -infinity);
limit(KelvinBei(4,z),z = -infinity);
limit(KelvinHer(0,z),z = -infinity);
limit(KelvinHer(1,z),z = -infinity);
limit(KelvinHer(2,z),z = -infinity);
limit(KelvinHer(3,z),z = -infinity);
limit(KelvinHer(4,z),z = -infinity);
limit(KelvinHei(0,z),z = -infinity);
limit(KelvinHei(1,z),z = -infinity);
limit(KelvinHei(2,z),z = -infinity);
limit(KelvinHei(3,z),z = -infinity);
limit(KelvinHei(4,z),z = -infinity);
limit(KelvinKer(0,z),z = -infinity);
limit(KelvinKei(0,z),z = -infinity);
limit(KelvinBer(0,z),z = -infinity);
limit(KelvinBei(0,z),z = -infinity);
limit(ln(z)*KelvinHer(0,z),z = -infinity);
limit(ln(z)*KelvinHei(0,z),z = -infinity);
limit(KelvinKei(2,z)*HankelH1(1/3,z),z = -infinity);
limit(arccot(z)-KelvinKei(0,z),z = -infinity);
limit(Chi(z)-KelvinKer(1,z),z = -infinity);
|
BUG # 28 limit: Error, (in X) too many levels of recursion
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(EllipticPi(1,z),z = 0);
ACTUAL: Error, (in depends/internal) too many levels of recursion
EXPECTED: limit(EllipticPi(1,z),z = 0) or complex_infinity
|
BUG # 29 evalf: MEANINGLESS OUTPUT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
evalf(EllipticPi(1,0));
ACTUAL: answer
EXPECTED: EllipticPi(1,0)
|
BUG # 30 limit: MEANINGLESS OUTPUT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(z/BesselY(0,I*sqrt(z)),z = infinity);
ACTUAL: signum(O(1))*infinity
EXPECTED: 0
CHECKUP: evalf(Limit(z/BesselY(0,I*sqrt(z)),z = 10^19));
-.4854522468e-1373359757-.1236050411e-1373359713*I
int(polylog(2,1-I/z^(3/2)),z = 1..infinity);
int(polylog(2,1+I/z^(3/2)),z = 1..infinity);
int(polylog(2,1+1/z^(3/2)),z = 1..infinity);
int(polylog(2,1-1/z^(3/2)),z = 1..infinity);
int(polylog(2,1-I/z^(3/2)),z = 2..infinity);
int(polylog(2,1+I/z^(3/2)),z = 2..infinity);
int(polylog(2,1-1/z^(3/2)),z = 2..infinity);
int(polylog(2,1+1/z^(3/2)),z = 2..infinity);
::::::::::::::::::::::::::::::::::::::::::::::::: 30%
|
BUG # 31 limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(arccoth(1/(1-sqrt(1-z))),z = infinity);
ACTUAL: 1/2*I*Pi
1.570796327*I
EXPECTED: -1/2*I*Pi
CHECKUP: fnormal(evalf(limit(arccoth(1/(1-sqrt(1-z))),z = 10^(10^2)),30));
0.-1.570796327*I
The same problem with
limit(arccoth(1/ln(z-sqrt(1-z))),z = infinity);
limit(arccoth(1/tanh(z^(1/3)-(1-z^(1/3))^(1/2))),z = infinity);
limit(arccoth(1/cosh(z^(1/4)-(1-z^(1/5))^(1/9))),z = infinity);
|
BUG # 32 limit: INVALID MAGNITUDE OF THE IMAGINARY PART
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(arccoth(I/sqrt(z)),z = -infinity);
ACTUAL: 3/2*I*Pi
4.712388981*I
EXPECTED: I*Pi/2
1.570796327*I
CHECKUP: fnormal(evalf(Limit(arccoth(I/sqrt(z)),z = -infinity)));
0.+1.570796327*I
EXAMPLE 2: limit(arccoth(I/(-z)^(1/3)),z = infinity);
ACTUAL: 1/2*I*Pi
1.570796327*I
EXPECTED: -1/2*I*Pi
-1.570796327*I
CHECKUP: fnormal(evalf(limit(func,z = 10^50)));
0.-1.570796327*I
The same problem with
limit(arccoth(HankelH1(1,z)),z = -infinity);
|
BUG # 33 limit: Error, (in X) too many levels of recursion
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(erf(sqrt(-sqrt(1+I/z))), z=infinity);
ACTUAL: Error, (in int) too many levels of recursion
EXPECTED: -erf(I)
-1.650425759*I
CHECKUP: evalf(Limit(erf(sqrt(-sqrt(1+I/z))), z=infinity));
-.9855680608e-13-1.650425759*I
EXAMPLE 2: limit(erfc(sqrt(-sqrt(1+I/z))), z=infinity);
ACTUAL: Error, (in int) too many levels of recursion
EXPECTED: erf(I) + 1
1.+1.650425759*I
CHECKUP: evalf(Limit(erfc(sqrt(-sqrt(1+I/z))), z=infinity));
1.000000000+1.650425759*I
EXAMPLE 3: limit(erfi(sqrt(-sqrt(1+I/z))), z=infinity);
ACTUAL: Error, (in int) too many levels of recursion
EXPECTED: Limit[Erfi[Sqrt[-Sqrt[1+I/z]]], z->Infinity]
The same problem with
limit(erf(sqrt(-sqrt(1+I/z))), z=-infinity);
limit(erf(sqrt(-sqrt(1-I/z))), z=-infinity);
limit(erf(1/sqrt(-sqrt(1-I/z))), z=-infinity);
limit(erfi(1/sqrt(-sqrt(1-I/z))), z=-infinity);
limit(erfi(1/sqrt(-sqrt(1-I/z^2))), z=-infinity);
limit(erfi(1/sqrt(-sqrt(1-I/z^3))), z=-infinity);
COMMENT: Only Derive 5.06 calculates it correctly.
|
BUG # 34 limit: INVALID MAGNITUDE OF THE REAL-VALUED LIMIT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(StruveH(0,EllipticPi(1/2,z)),z = 0);
ACTUAL: StruveH(0,EllipticPi(1/2,0))
.6148427355
EXPECTED: StruveH(0, Pi/sqrt(2))
.77733468418002546656412161004184905579430164572297
CHECKUP: evalf(Limit(StruveH(0,EllipticPi(1/2,z)),z = 0),50);
.77733468418002546656412161004184905579430164572296
EXAMPLE 2: limit(StruveL(0,EllipticPi(1/2,z)),z = 0);
ACTUAL: StruveL(0,EllipticPi(1/2,0))
.8089409725
EXPECTED: StruveL(0, Pi/sqrt(2))
2.3591001975827913005960695139630449059412292612616
CHECKUP: evalf(Limit(StruveL(0,EllipticPi(1/2,z)),z = 0),50);
2.3591001975827913005960695139630449059412292612617
COMMENT: Mathematica 4.2.1 calculates these limits correctly.
|
BUG # 35 limit: Error, (in X) too many levels of recursion
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(sqrt(z)*EllipticPi(1/2,z), z= infinity);
ACTUAL: Error, (in depends/internal) too many levels of recursion
EXPECTED: 0
CHECKUP: evalf(Limit(sqrt(z)*EllipticPi(1/2,z), z= 10^20), 50);
.15707963267948966192313216916397514420986632395039e-9-
.48223394384398252608809954182423513009224676425905e-8*I
The same problem with
limit(sqrt(z)*EllipticPi(1/3,z), z= infinity);
limit(sqrt(z-1)*EllipticPi(1/2,z), z= infinity);
limit(sqrt(z^2-1)*EllipticPi(1/2,z), z= infinity);
limit(sqrt(z^2-z-1)*EllipticPi(1/2,z), z= infinity);
limit(sqrt(z^2-z-3)*EllipticPi(1/2,z), z= infinity);
limit(sqrt(z^2-I*z-3)*EllipticPi(1/2,z), z= infinity);
|
BUG # 36 limit: TOO TIME CONSUMING
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
Maple cannot do quickly a REGULAR limit at a FINITE point.
limit(cot(1/(arccos(-z))),z = 2);
ACTUAL: It takes 709 seconds to show the answer.
EXPECTED: It takes less than 0.1 second to show the answer.
HINT: plot(Re(cot(1/(arccos(-z)))),z = 1..3)
plot(Im(cot(1/(arccos(-z)))),z = 1..3)
COMMENT: Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2
calculate it correctly in some 0.001-0.03 second.
|
BUG # 37 limit: TRIVIAL LIMIT CANNOT BE DONE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
The following is trivial and correct.
limit(cos(1/arcsin(z)),z = -1);
2*cos(1/Pi)^2-1
However, here Maple fails to yield the answer.
limit(cos(1/arcsin(z)),z = -2);
ACTUAL: limit(cos(1/arcsin(z)),z = -2);
EXPECTED: cos(1/arcsin(-2))
.9770333572-.1163454356*I
CHECKUP: evalf(Limit(cos(1/arcsin(z)),z = -2));
.9770333572-.1163454356*I
The same problem with
limit(cosh(1/arccsch(z)),z = -2);
limit(cosh(1/arcsin(z)),z = -2);
limit(cot(1/arcsin(z)),z = -2);
limit(coth(1/(Pi-arccos(z))),z = -2);
limit(coth(1/arcsin(z)),z = -2);
limit(csc(1/arcsin(z)),z = -2);
limit(csch(1/(Pi-arccos(z))),z = -2);
limit(csch(1/arcsin(z)),z = -2);
limit(sec(1/arcsin(z)),z = -2);
limit(sech(1/(Pi-arccos(z))),z = -2);
limit(sech(1/arcsin(z)),z = -2);
limit(sin(1/arcsin(z)),z = -2);
limit(sinh(1/arcsin(z)),z = -2);
limit(tan(1/arcsin(z)),z = -2);
limit(tanh(1/(Pi-arccos(z))),z = -2);
limit(tanh(1/arcsin(z)),z = -2);
COMMENT: Derive 5.06 and Mathematica 4.2.1 calculate all these limits correctly.
|
BUG # 38 limit: LINEARITY PROPERTY IS NOT USED
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
Maple calculates these limits correctly.
limit(arcsech(sqrt(z)),z = -infinity);
-1/2*I*Pi
limit(StruveL(0,1/z),z = -infinity);
0
However, for the sum of these function, Maple yields an invalid result.
limit(arcsech(sqrt(z))+StruveL(0,1/z),z = -infinity);
ACTUAL: 1/2*I*Pi
1.570796327*I
EXPECTED: -1/2*I*Pi
-1.570796327*I
CHECKUP: fnormal(evalf(Limit(arcsech(sqrt(z))+StruveL(0,1/z),z = -10^20)));
0.-1.570796327*I
|
BUG # 39 limit: DIVEGENT + CONVERGENT = CONVERGENT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
Maple calculates the following limits correctly.
limit(BesselI(0,z),z = -infinity);
infinity
limit(EllipticPi(1/2,1/z),z = -infinity);
1/2*2^(1/2)*Pi
However, for the sum, Maple produces a finite output.
limit(BesselI(0,z)+EllipticPi(1/2,1/z),z = -infinity);
ACTUAL: 1/2*2^(1/2)*Pi
EXPECTED: infinity
CHECKUP: evalf(limit(BesselI(0,z)+EllipticPi(1/2,1/z),z = -10^10));
Float(infinity)
The same problem with
limit(KelvinHer(0,z)-Chi(z),z = infinity);
limit(KelvinHer(0,z)-Chi(z),z = -infinity);
limit(KelvinKer(0,z)+arctan(z),z = -infinity);
|
BUG # 40 limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(sqrt(1/sqrt(z^2+I*z)-1),z = infinity);
ACTUAL: I
EXPECTED: -I
CHECKUP: fnormal(evalf(Limit(sqrt(1/sqrt(z^2+I*z)-1),z = infinity)));
0.-1.000000000*I
HINT: plot(Im(func),z = 10^10..10^11);
::::::::::::::::::::::::::::::::::::::::::::::::: 40%
|
BUG # 41 limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(arccoth(1-sqrt(1-1/z)),z = infinity);
ACTUAL: 1/2*I*Pi
1.570796327*I
EXPECTED: -1/2*I*Pi
CHECKUP: fnormal(evalf(Limit(arccoth(1-sqrt(1-1/z)),z = infinity)));
0.-1.570796327*I
The same problem with
limit(arccoth(1-1/sqrt(1-I*z^3)),z = 0, left);
|
BUG # 42 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(coth(1/arcsinh(z)),z = 2);
ACTUAL: undefined
EXPECTED: coth(1/arcsinh(2))
1.667470009
CHECKUP: evalf(Limit(coth(1/arcsinh(z)),z = 2));
1.667470009
COMMENT: Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2
calculate this limit correctly.
|
BUG # 43 limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(arccot(1/(-arcsinh(z^(1/2)-1))^(1/2)),z = infinity);
ACTUAL: -1/2*Pi
-1.570796327
EXPECTED: 1.570796327
CHECKUP: evalf(limit(arccot(1/sqrt((-arcsinh(sqrt(z)-1)))),z = 10^200));
1.570796327+.6589727518e-1*I
|
BUG # 44 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(ln(1-1/arcsech(z)^2),z = 10^10);
ACTUAL: undefined
EXPECTED: ln(1 - 1/(1/2*I*Pi + arcsinh(-1/10000000000*I))^2)
.3402399399
CHECKUP: plot(ln(1-1/arcsech(z)^2),z = 10^10-1000..10^10+1000);
COMMENT: Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2 calculate
it correctly.
|
BUG # 45 limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
This answer is correct.
evalf(limit(arcsinh(1/(I*z)^(1/3)),z = infinity));
fnormal(evalf(Limit(arcsinh(1/(I*z)^(1/3)),z = 10^50),30));
0.
0.-0.*I
However, below, the sign of the answer is invalid.
evalf(limit(arccosh(1/(I*z)^(1/3)),z = infinity));
ACTUAL: 1/2*I*Pi
1.570796327*I
EXPECTED: -1/2*I*Pi
-1.570796327*I
fnormal(evalf(Limit(arccosh(1/(I*z)^(1/3)),z = 10^50),30));
CHECKUP: 0.-1.570796327*I
HINT: plot(Im(arccosh(1/(I*z)^(1/3))),z = 100000..100010);
The same problem with
limit(arccosh(1/(I*z)^(1/4)),z = infinity);
limit(arccosh(1/(I*z)^(1/6)),z = infinity);
|
BUG # 46 limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(arccoth(z),z = 0);
ACTUAL: 1/2*I*Pi
EXPECTED: -1/2*I*Pi
-1.570796327*I
CHECKUP: fnormal(evalf(Limit(arccoth(z),z = 0)));
0.-1.570796327*I
HINT: plot(Im(arccoth(z)),z = -1..1);
The same problem with
limit(arccot(1/(1-z^3)^(1/2)),z = infinity);
limit(arccoth(1/(1+z)^(1/2)),z = infinity);
limit(arccoth(1-(1-I/z^3)^(1/2)),z = infinity);
limit(arccot((-csch(z^(1/2)-1))^(1/2)),z = infinity);
limit(arctanh((z^2+I*z+1)^(1/4)),z = infinity);
limit(-arctanh(-1+(1-ln(1-z^3))^(1/2)),z = infinity);
limit(ln(1+z^(1/3)-z^(2/3))-arccoth(z^(1/2)),z = 0);
|
BUG # 47 evalf: INVALID MAGNITUDE OF THE REAL PART
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(arccot(sqrt(-csch(z-1))), z = 4);
ACTUAL: -1/2*Pi-I*Re(arccoth(2^(1/2)/(exp(3)-exp(-3))^(1/2)))
-1.570796327-.3271365711*I
EXPECTED: arccot(sqrt(-csch(3))))
1.570796327-.3271365712*I
CHECKUP: evalf(Limit(arccot(sqrt(-csch(z-1))), z = 4));
1.570796327-.3271365711*I
HINT: plot(Re(arccot(sqrt(-csch(z-1)))), z = 3..5);
COMMENT: Derive 5.06 and Mathematica 4.2.1 calculate the limit correctly.
COMMENT: Mathematica 4.2.1 produces the negative value of the real part; this is due to
Mathematica's branch cut defaults. Please note the ideal agreement of the three
following numbers.
N[ArcCot[Sqrt[-Csch[3]]]]
N[Limit[ArcCot[Sqrt[-Csch[z - 1]]], z -> 4]]
<< NumericalMath`NLimit`
NLimit[ArcCot[Sqrt[-Csch[z - 1]]], z -> 4]
-1.5708 - 0.327137 I
-1.5708 - 0.327137 I
-1.5708 - 0.327137 I
|
BUG # 48 Maple language: UNDOCUMENTED FEATURE or BUG
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: 1.......................................................2;
ACTUAL: 1 .. 2
EXPECTED: The behavior is described in the Help or an "Error, `.`
unexpected" message is generated.
EXAMPLE 2: sum(n, n=1.........................................2);
ACTUAL: 3
EXPECTED: The behavior is described in the Help or an "Error, `.`
unexpected" message is generated.
EXAMPLE 3: int(z, z=1.........................................2);
ACTUAL: 3/2
EXPECTED: The behavior is described in the Help or an "Error, `.`
unexpected" message is generated.
|
BUG # 49 limit: TOO TIME-CONSUMING AND HUMAN UNREADABLE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
1) It takes some 4000 seconds to see the answer
2) The answer is too long, 71 screens, at the 1024x760 resolution.
limit(cot(1/(1-I*z)^(1/2)), z=-1/1000000);
ACTUAL: (1-354075436047184534392672953650763356584937159685161625650526649066203899209\
446192633986001095957111771950538774577147252118263203561387850635045190773465\
1522014893284877499675393132859815232516435452266000*cot(1/(1000000+I)^(1/2))^\
818+31076448318817750367832764892781363565235901257346067250059286473155861411\
835104258463507202002931295522457479169706881326876129001673276366061687212907\
859233049210665125304376265629268535388568868056954214915954536635717417719875\
*cot(1/(1000000+I)^(1/2))^776+380605941849653864811161109499867660798166907228\
217004407285922402013505041378805479840928013766981918167908777459375015918401\
5793571434561310338018210990177370260786687241197277355967000*cot(1/(1000000+I\
)^(1/2))^844-36753935140485732686754424398266887016977130808589822702429999773\
757984371834083974513182362408186590220660625314968964464077293965794116827039\
328790251300969037945514270123995842968421036740777418386336804032359996721180\
8358244500*cot(1/(1000000+I)^(1/2))^774-82106999666491760131994830553077735291\
308346086335846952596215698228023390582870804106891798253671025530455502742902\
478151756589109497159416984080315730316529980616745470296577025323611958500*co\
t(1/(1000000+I)^(1/2))^838-109166364096788650964372587325759832990651200982672\
971418103956906253887256672050741136411172446624808079142849267163447885920896\
758837665036515964575222680935157687158013327982474423594000*cot(1/(1000000+I)\
^(1/2))^842+950220356319270753294980984079236890999858643259206760034793059650\
247281413740131519663097956052254937063084461430635124739824646132076532859598\
092478745940018090438278341618930326740753536223504156355391524356184404498112\
19231102187491268621588692883969052837959995486141968208069973335000*cot(1/(10\
00000+I)^(1/2))^604-4054045444602469280484437321814205997605157487892565294837\
910983566311533664381839246807456626181537715282646577120801522292321172516690\
158194864949009231103227496559351340480404814357490334562925023514451688072289\
8985788044928481041287903984368173201621360076681402214609624600022652890000*c\
ot(1/(1000000+I)^(1/2))^606+17009248047264793102639470535212956436995409795268\
484874471403053124046499600608383352503690467332915950690289855592082212856249\
322455923693835333348719093104730773168383125126453499326457729569291286174042\
104300960083991026979146420584143405736627164672718061739957301099517396592136\
745625*cot(1/(1000000+I)^(1/2))^608+215435965165626662827854130326619938649317\
005068952869473412768472360186197423197213921137769885958324604274548694030583\
5347560307531646139384600323130896992220095184384757550535127343010974250*cot(\
1/(1000000+I)^(1/2))^836-70177971592784983941095505339932710409732710170943799\
662978300593782574365037671219499985077533959210035107327431325462998436109885\
904447936728558319870597818199549518544734834902170953856877077294517065540967\
735787073500570328884496911702282270433087935525660421726976611085908381651815\
00*cot(1/(1000000+I)^(1/2))^610+2427391512439247360308999651851182455144214737\
218666849453734946080973100097044304232714527393833530834418099060812383914937\
484965346712290473605440152422846108567090437492112315144433706579696088890173\
172281625000362925629463430712731520023322071021078012852977870853574330198988\
352822627500*cot(1/(1000000+I)^(1/2))^596+303864402818184642681578008185108901\
167476060307595714884161203507744949496733985514602978585908997061110922927314\
3172761158572219129781644692915010492760820328841656670861392987647554411575*c\
ot(1/(1000000+I)^(1/2))^840+49652723862542288611507356288962313262134135365982\
760466293218401264590573209645738216496413657550741717233904208977875190488785\
709241191057907741240853994820497412977839043739395425167680052468065347826666\
236435261924418093115402070111198232800077698030595552564950136994320207999678\
9539150*cot(1/(1000000+I)^(1/2))^600-13582050502974873233640581153002408621675\
243178694563751094136731273798872746092431799363899929896375971993521984773356\
424029798967483669293783508306409821668763182742099539488768012018940112979305\
59268692000*cot(1/(1000000+I)^(1/2))^814-2190307054262206749104917624479241462\
633320988941699761311545446637063547322640411003629838314808955831662216104873\
071149524328278780906156638734861067738037200288309977034781678241097827468165\
986708064946001220299446420176688138310564824748883337405709665245131139695707\
67809608480571170000*cot(1/(1000000+I)^(1/2))^602-9598511503532512443405345830\
273286420302873110520719745135666976663560400039290173574380250706440725981402\
763634981191088611821315594319284783550596692936528917072601959567777390923952\
604684426688861434308171085202267780483217850327735110835417381510961368133458\
2249614268937976403547105090000*cot(1/(1000000+I)^(1/2))^586+47548722719494838\
351305868672478156506513745963652774497988927064976094412947128615990876126339\
644920260757667021183291459891365996330583850515739205569414223924802339471161\
379603859103253431858177603917094870391650562344058383875254574879789467218460\
846592445009045775089905877578345128355000*cot(1/(1000000+I)^(1/2))^588-231691\
758957655893865020441254872412234496435541919703355110960771388795117641598308\
047740675817811102920624363961641653750577675085340002433758198358535870891935\
041574266372154213710962910711156770453411110718919138241283534121560950984821\
86153097857362594434399792061199746603154143297386000*cot(1/(1000000+I)^(1/2))\
^590+1110474432352669457465166626481386187165669366969192020385128190073918091\
567125109190690470627197624955662628035187945560588854504934966645176433446595\
980249630395891114142542030802613280585389910562643838579722171259537226066585\
6243389195127921105374826031979422477736836858930931650116438750*cot(1/(100000\
0+I)^(1/2))^592-52350640281043963930716867757675991135634703528096067515251686\
832040058429508839698777913136556665249924061685151449710145054486310968260806\
893508556033095523141766199047829037839598557503332228123957502302165654541671\
26964181243078202588521987914769170375952824986694000662745029797956335000*cot\
(1/(1000000+I)^(1/2))^594-1352174756047738536965732563594024997657263993095977\
594463124595472949439582756397782101654348412776609179735291350714403392493584\
549588732331544589527040533322470990719945790249999519709396475018059305000910\
370897152823983294206171303014085716166595296312128715459066090673792478765425\
619892500*cot(1/(1000000+I)^(1/2))^578+715353676103130617456988799694007709885\
607871899879612255099880533962072941312807881495277573842268828360699575165120\
071274841269782172096252417589376907495774929549024140935582739010989848122639\
087762030467924228247171146804881355506033257389391905346713731796336991840275\
407418743443054259250*cot(1/(1000000+I)^(1/2))^580+180487401413966384686434836\
763987305663867370047079159806946385380722780736266139783954512647940638422552\
0079389994275197942368824364111633398784129265292392148998455615125*cot(1/(100\
0000+I)^(1/2))^136-32718467279501535853152782595305511539109510344855478934822\
019578345603118092997314241231969888303513579468542936280630841669653327239293\
222697936341414457168675864940487771805828457685108596925600*cot(1/(1000000+I)\
^(1/2))^830-372293119223961903756649244903476872987293129208855493149778723070\
090806809601374366347685136554354290253550021108167072244638544328319597975112\
371070580351173388996449031240851034213892369101211995742504988275061030387169\
930748090867007744188492371556667561324885355336076755320399332554632500*cot(1\
/(1000000+I)^(1/2))^582+255670626520642779562667285146098531757580093903824262\
951603709019679063761624034068183144852184738977229998207023759283223554682566\
25547936564562788805622379102959954011029246660235891222624438704100977174000*\
cot(1/(1000000+I)^(1/2))^812-4801444962415665669159245088581755290717934571976\
316684382350161984467362636573152427017908918531406287694151536666324511960809\
991241780663859477568952614305230258936720633266794467393758288596999894878178\
0286316587422513931487910900*cot(1/(1000000+I)^(1/2))^770+82778379580683978116\
916427800405049752814046412158263763650621689502916419352746031827293732962522\
731641689820385636359470766556115789987679701814178930112021587615101708531899\
271983333006584206847743037715858551205850970054450139424550725875865543691832\
33910534587050189385786654723962227270000*cot(1/(1000000+I)^(1/2))^572-4688590\
616092785600416664233412157012402749495925179602618922130552695439071840668420\
740260256165985189452107470558904157609966923411900677739274481324907857576004\
01682951576492945097797789398965989669303824800*cot(1/(1000000+I)^(1/2))^810-4\
599621023480392671596760943712967775393668590066462244799281554227944796059382\
567996737293619770875319672323310407768426899019382520420972931628494835711413\
313773155994139426267809434423308858963054686989072564284855823279661142127646\
895567120200942209080809948431420132475293023060767161060000*cot(1/(1000000+I)\
^(1/2))^574+251437616636813132002594676587932613446565126277636772168149132063\
094627212122951067575267816986569135454913688209337703408836793238321925467775\
162738528246189752001779208618093534691456020552208714085470824754759593341426\
5648097168509874524236450424477518359423802864175678296503095265381974375*cot(\
1/(1000000+I)^(1/2))^576-14590397202856894311383171157581186686377345403857115\
493563442693236707932790317968782383252319838046923565422845723785114783072309\
712630479452256612735963543122075356775472324487221372738232303457295888751338\
5500*cot(1/(1000000+I)^(1/2))^806+53050447932437455453785337257462210036811662\
153014188653592345898937577613039148767476677758022279474644206932926672464794\
509524184840938656723250725927591964397544861180560088576802094829366826047689\
0994095404848501837833524629360375*cot(1/(1000000+I)^(1/2))^768+83780174106114\
787197235926742818836405360976144873771318721462776229161056647755006801562094\
875191111332789907951094685466847601037374138173968400274525492746263625441432\
52033160503739526434752629345833281614125*cot(1/(1000000+I)^(1/2))^808-1465626\
503583582992395636597644380880894785131824569569272697828983136907765904433617\
779371209972107899764492633804600349079308636964839781863867779726173456258186\
921645754161689435735911527428902637558900333495588791966012436931150741657813\
1819914867608144381132555676459346617611929868005492000*cot(1/(1000000+I)^(1/2\
))^570+19975895067014008772036208278251239663233725963657008494001943577835068\
666222594171298956157076175832664584613618462423799983909556311948077075762570\
901051084837455759425829129974426910716833921379600104969711778325842729074483\
4015406349642854061817399878670398476919885270953376210520966007286500*cot(1/(\
1000000+I)^(1/2))^560-12238389413745237388771049381274571505351483773700965360\
221691760058049186339709498569871960025736083371366471814255814734760918701027\
067484245704791885508933422152087625342248354997437449850103252591509429493364\
992038180257760398124818574169692713395931440416569865024022601148860012379328\
3370000*cot(1/(1000000+I)^(1/2))^562-57315734304115545577537463085601517911015\
976048578419558215936513415820619981638267808851277336803232119177504644095916\
184282679062077077072328181614049381189575144319261171643624035682425089881303\
59772228052213756632159254331904048000*cot(1/(1000000+I)^(1/2))^766+7377212892\
329972751203379432221762321760660667866567702589323699739462361464477395296426\
540886228917947733680082887546688590908648226909032442504602357046606044746490\
067194041509632539437052041567985369833155735546861607429855531925850068678193\
7048872606643877592544524270624551185377520304085000*cot(1/(1000000+I)^(1/2))^\
564-43752531259867495293574938025428545043469992878688302650898750207717140356\
964032108318592130600774776508557796195017108257236052854145394386723957061916\
803505501942503084649986325929748573479164570002352873958435342498904441864979\
675934958113331188245969467706382945040411415780286496452362090000*cot(1/(1000\
000+I)^(1/2))^566-181510606348072736196081374721357174941930701885513122132454\
228533266355132472846606495370690828333990271015951474479552104593072387997293\
470419064971207308141437443325956916309833011512132928579234504510644376907309\
516321681910513931761137144175315861329456668556852081223528779295217291540632\
4300*cot(1/(1000000+I)^(1/2))^550+12057858574866545789085142219170091663713241\
509497858415155046448863222025341322318065437560194200558514906616755904479833\
350768785342477822173838106417987259652225013812039684237407604101389509006789\
906486130735330324236827582925425416350298528572085595891764605168456236097079\
70245096325382860625*cot(1/(1000000+I)^(1/2))^552+6055976766114076551204684095\
479919488041156113362147146938145805534896632726837397863921521818714988458261\
237999710379719586694393001541001372807635055318586959815870833727726550171054\
7321093435890903767182046821840044698908149160712000*cot(1/(1000000+I)^(1/2))^\
764-78817168146456642584231537861814646601359140223852930023478400769793688182\
827891256961119984014003924963315928381144120795251746426695975308858282810493\
483417294441620238274296637516962512578502414258932677244453760891049482130496\
4059568956131027259116042753739945755143267068628907638707593860000*cot(1/(100\
0000+I)^(1/2))^554+50692991645690744227404346747794260519060692722237640228659\
531404436299480348213033148854375614943803835210682175791281529047942553977413\
375944984734586303888231343017592489142697673185397211275436379448987143388223\
229135364308897600914722510637429553684945665554162299333791921310292000225599\
0000*cot(1/(1000000+I)^(1/2))^556-32080802535260592985903154284399749972700288\
195602291885792103598390586466762709593495989346564913568798399192739267384627\
425139530211531925835958563912052162390685253232890852993477391627408351795436\
209661908738301073290390393511344437104174508527164126173023845032885402991578\
6257792774540180000*cot(1/(1000000+I)^(1/2))^558+11015187296775979294455155403\
978240784495963807394182197540604838252145377140912411909445168925497610486470\
004680561977591900367627421371270952160514814435224286044792549420679835027158\
196812558385109192234383331503826235388526396776083888582876725552469938609200\
708498628544080357516688561721881000*cot(1/(1000000+I)^(1/2))^540-704992638138\
103624089681196721554636483767000*cot(1/(1000000+I)^(1/2))^978-793169218490181\
592183145027315810464166562467445555800447689227120938393070619614711911197988\
871764559996615802447925445141852801240612344963488132233570418746122561574126\
321469865028606883181881793301610509339890498622661305585329648645816271832206\
7063531515188620200395709725486785008024370470000*cot(1/(1000000+I)^(1/2))^542\
+56201615631197171329448784356842103040314742380010122944597024080467694216511\
993918891264897579756240180726514985905333665387228637359037304641915490358469\
446049970504561424764912918994960016272258770984620188730609056682221328554262\
62033542566897947706097414006030426226926998032231823778399163125*cot(1/(10000\
00+I)^(1/2))^544-3918644759606408276181750101944953973453138000808045269531535\
623959215376564139025537372598363359150691500197375164041613366448969210354894\
635583098410315300825502530593273653333377838180698382285932655808380131675493\
860411762357911889124304909029761703333976738149654983912402297702923001452627\
500*cot(1/(1000000+I)^(1/2))^546+268857443570828653603627980579605787403194353\
915245801993085936393166493005956164437097880717852243040844991790846884508162\
695868608381486389110907266330704105463944490476869884789346320313451840059742\
543556450793527208236033263738799203713285539198164984544871135635097646550021\
1339151010571098750*cot(1/(1000000+I)^(1/2))^548-26789758712846476679258848180\
728459312377886923715793685086814793529493932561461195540349035310611054901786\
505649498184128403900321049673933509919256739318217952443377629998152705617458\
217205031925556411574347221589815561144045720436856225398378692651774154359556\
864675585787709635608831179318485000*cot(1/(1000000+I)^(1/2))^534+202436630474\
497943633303104068979280527241048873621681323108588980677432007488597658726399\
513929987079323061720923063241692838651156655525340084544697406990676806910151\
298796893213148522146957677777542852003253572544885407459313264104560450605896\
18184938420658991410958825095336870344809695377746250*cot(1/(1000000+I)^(1/2))\
^536+1599910509856997109891071524836519798742014406606152614866861921268180021\
402435680948176117626508158558356821379404617483678968988584021746667512131994\
84933606165331069012794486509627880630145943975521249557594940413000*cot(1/(10\
00000+I)^(1/2))^796-6258594206687960273990087772836755712163257836886897068856\
056466886622635727973580845320534263778969705263872619308532905538614572742570\
469475327979856871564254971785300937083099926095232950331307087245117711753705\
07764004253540519664000*cot(1/(1000000+I)^(1/2))^762+5638695247687320145147675\
802252177967678897541389453163326476585625429560799055874113172199211242100218\
470368833599762812439858873827626572961551486716299490859746562223091641940143\
126795429610226444767229154390617796934605150100493879315003361434166957381573\
6929414401149656434270698227842626236250*cot(1/(1000000+I)^(1/2))^528-62579233\
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697673185397211275436379448987143388223229135364308897600914722510637429553684\
9456655541622993337919213102920002255990000*cot(1/(1000000+I)^(1/2))^444+12057\
858574866545789085142219170091663713241509497858415155046448863222025341322318\
065437560194200558514906616755904479833350768785342477822173838106417987259652\
225013812039684237407604101389509006789906486130735330324236827582925425416350\
29852857208559589176460516845623609707970245096325382860625*cot(1/(1000000+I)^\
(1/2))^448-7881716814645664258423153786181464660135914022385293002347840076979\
368818282789125696111998401400392496331592838114412079525174642669597530885828\
281049348341729444162023827429663751696251257850241425893267724445376089104948\
21304964059568956131027259116042753739945755143267068628907638707593860000*cot\
(1/(1000000+I)^(1/2))^446-3918644759606408276181750101944953973453138000808045\
269531535623959215376564139025537372598363359150691500197375164041613366448969\
210354894635583098410315300825502530593273653333377838180698382285932655808380\
131675493860411762357911889124304909029761703333976738149654983912402297702923\
001452627500*cot(1/(1000000+I)^(1/2))^454+702752252206431775486545767885860821\
412012988359918108196723873636369871302768315557283940509725331254054338222506\
993856836980305652461596895059726969147665737611449169441167160632884596008191\
41390810230500*cot(1/(1000000+I)^(1/2))^816+2688574435708286536036279805796057\
874031943539152458019930859363931664930059561644370978807178522430408449917908\
468845081626958686083814863891109072663307041054639444904768698847893463203134\
518400597425435564507935272082360332637387992037132855391981649845448711356350\
976465500211339151010571098750*cot(1/(1000000+I)^(1/2))^452-181510606348072736\
196081374721357174941930701885513122132454228533266355132472846606495370690828\
333990271015951474479552104593072387997293470419064971207308141437443325956916\
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3294566685568520812235287792952172915406324300*cot(1/(1000000+I)^(1/2))^450-79\
316921849018159218314502731581046416656246744555580044768922712093839307061961\
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612256157412632146986502860688318188179330161050933989049862266130558532964864\
58162718322067063531515188620200395709725486785008024370470000*cot(1/(1000000+\
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864361175568835582719308340609111415984993312261518344897787128898028490142315\
3415355113777417250326578359551570505818072989042753925927950054334181500*cot(\
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730609056682221328554262620335425668979477060974140060304262269269980322318237\
78399163125*cot(1/(1000000+I)^(1/2))^456-2316917589576558938650204412548724122\
344964355419197033551109607713887951176415983080477406758178111029206243639616\
416537505776750853400024337581983585358708919350415742663721542137109629107111\
567704534111107189191382412835341215609509848218615309785736259443439979206119\
9746603154143297386000*cot(1/(1000000+I)^(1/2))^410+47548722719494838351305868\
672478156506513745963652774497988927064976094412947128615990876126339644920260\
757667021183291459891365996330583850515739205569414223924802339471161379603859\
103253431858177603917094870391650562344058383875254574879789467218460846592445\
009045775089905877578345128355000*cot(1/(1000000+I)^(1/2))^412-959851150353251\
244340534583027328642030287311052071974513566697666356040003929017357438025070\
644072598140276363498119108861182131559431928478355059669293652891707260195956\
777739092395260468442668886143430817108520226778048321785032773511083541738151\
09613681334582249614268937976403547105090000*cot(1/(1000000+I)^(1/2))^414+1905\
969490573436394070775373074597612224297921117706172283339895893208492086115074\
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29465328577141604877770552253187369871569108549485031875*cot(1/(1000000+I)^(1/\
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068096013743663476851365543542902535500211081670722446385443283195979751123710\
705803511733889964490312408510342138923691012119957425049882750610303871699307\
48090867007744188492371556667561324885355336076755320399332554632500*cot(1/(10\
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124595472949439582756397782101654348412776609179735291350714403392493584549588\
732331544589527040533322470990719945790249999519709396475018059305000910370897\
152823983294206171303014085716166595296312128715459066090673792478765425619892\
500*cot(1/(1000000+I)^(1/2))^422+251437616636813132002594676587932613446565126\
277636772168149132063094627212122951067575267816986569135454913688209337703408\
836793238321925467775162738528246189752001779208618093534691456020552208714085\
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3095265381974375*cot(1/(1000000+I)^(1/2))^424+71535367610313061745698879969400\
770988560787189987961225509988053396207294131280788149527757384226882836069957\
516512007127484126978217209625241758937690749577492954902414093558273901098984\
812263908776203046792422824717114680488135550603325738939190534671373179633699\
1840275407418743443054259250*cot(1/(1000000+I)^(1/2))^420-45996210234803926715\
967609437129677753936685900664622447992815542279447960593825679967372936197708\
753196723233104077684268990193825204209729316284948357114133137731559941394262\
678094344233088589630546869890725642848558232796611421276468955671202009422090\
80809948431420132475293023060767161060000*cot(1/(1000000+I)^(1/2))^426+8277837\
958068397811691642780040504975281404641215826376365062168950291641935274603182\
729373296252273164168982038563635947076655611578998767970181417893011202158761\
510170853189927198333300658420684774303771585855120585097005445013942455072587\
586554369183233910534587050189385786654723962227270000*cot(1/(1000000+I)^(1/2)\
)^428+284743414939392824085455702426737090101906900983980504466027022691061992\
83237072666834490105245313237142106703089000*cot(1/(1000000+I)^(1/2))^924+2552\
991771436277992199862602657482873059023275998231118427290575718080225228343779\
299080430225413840310704100583923294401568768637894251559959118743010386252192\
455982520019373876077877826038127395336209279373778810651898775531010355547187\
1968146606669520438403007227928944637194348184745264142500*cot(1/(1000000+I)^(\
1/2))^432-14656265035835829923956365976443808808947851318245695692726978289831\
369077659044336177793712099721078997644926338046003490793086369648397818638677\
797261734562581869216457541616894357359115274289026375589003334955887919660124\
369311507416578131819914867608144381132555676459346617611929868005492000*cot(1\
/(1000000+I)^(1/2))^430+135957830715437714792922024548031702206362849470010921\
416133918599849170598273022082718717383899576498590977511825323770607870663833\
4815696866772700709347742606303804123006462298452381996277060875*cot(1/(100000\
0+I)^(1/2))^832-43752531259867495293574938025428545043469992878688302650898750\
207717140356964032108318592130600774776508557796195017108257236052854145394386\
723957061916803505501942503084649986325929748573479164570002352873958435342498\
904441864979675934958113331188245969467706382945040411415780286496452362090000\
*cot(1/(1000000+I)^(1/2))^434-701779715927849839410955053399327104097327101709\
437996629783005937825743650376712194999850775339592100351073274313254629984361\
098859044479367285583198705978181995495185447348349021709538568770772945170655\
409677357870735005703288844969117022822704330879355256604217269766110859083816\
5181500*cot(1/(1000000+I)^(1/2))^390+28472289267410678716193316204874660356055\
511323004941665517896256759930567375525765942317683730402724972524770933234882\
255310436739274958539202554428900357270838156823856802097180793180069175201363\
753794842966676284075502421629053055171727354821859064671380352423917181791523\
17309184663750*cot(1/(1000000+I)^(1/2))^388+1352107057697392265642109112832721\
251596633434171971085916837519555429020419890001837772609860338233612418326422\
985384543409691908272896266786510154534848258844279171783901189593946339590275\
624037550422365833103033216077705096107479740086078672651625*cot(1/(1000000+I)\
^(1/2))^736+950220356319270753294980984079236890999858643259206760034793059650\
247281413740131519663097956052254937063084461430635124739824646132076532859598\
092478745940018090438278341618930326740753536223504156355391524356184404498112\
19231102187491268621588692883969052837959995486141968208069973335000*cot(1/(10\
00000+I)^(1/2))^396-4054045444602469280484437321814205997605157487892565294837\
910983566311533664381839246807456626181537715282646577120801522292321172516690\
158194864949009231103227496559351340480404814357490334562925023514451688072289\
8985788044928481041287903984368173201621360076681402214609624600022652890000*c\
ot(1/(1000000+I)^(1/2))^394+17009248047264793102639470535212956436995409795268\
484874471403053124046499600608383352503690467332915950690289855592082212856249\
322455923693835333348719093104730773168383125126453499326457729569291286174042\
104300960083991026979146420584143405736627164672718061739957301099517396592136\
745625*cot(1/(1000000+I)^(1/2))^392+496527238625422886115073562889623132621341\
353659827604662932184012645905732096457382164964136575507417172339042089778751\
904887857092411910579077412408539948204974129778390437393954251676800524680653\
478266662364352619244180931154020701111982328000776980305955525649501369943202\
079996789539150*cot(1/(1000000+I)^(1/2))^400-110700791281731607095294995411056\
037681982904992085731638477082749683588615597490591400905764621553929685573784\
275050237239374632969201896168856727596201819695083002842615800796136002067370\
199234641542964130999459269336831197290824580327568174516122161463232724109149\
2613972449644240432255000*cot(1/(1000000+I)^(1/2))^402-21903070542622067491049\
176244792414626333209889416997613115454466370635473226404110036298383148089558\
316622161048730711495243282787809061566387348610677380372002883099770347816782\
410978274681659867080649460012202994464201766881383105648247488833374057096652\
4513113969570767809608480571170000*cot(1/(1000000+I)^(1/2))^398+24273915124392\
473603089996518511824551442147372186668494537349460809731000970443042327145273\
938335308344180990608123839149374849653467122904736054401524228461085670904374\
921123151444337065796960888901731722816250003629256294634307127315200233220710\
21078012852977870853574330198988352822627500*cot(1/(1000000+I)^(1/2))^404-5235\
064028104396393071686775767599113563470352809606751525168683204005842950883969\
877791313655666524992406168515144971014505448631096826080689350855603309552314\
176619904782903783959855750333222812395750230216565454167126964181243078202588\
521987914769170375952824986694000662745029797956335000*cot(1/(1000000+I)^(1/2)\
)^406+111047443235266945746516662648138618716566936696919202038512819007391809\
156712510919069047062719762495566262803518794556058885450493496664517643344659\
598024963039589111414254203080261328058538991056264383857972217125953722606658\
56243389195127921105374826031979422477736836858930931650116438750*cot(1/(10000\
00+I)^(1/2))^408+1509668091851820420523910759086090932034401719286123900330456\
068487040249052422056097832250309895430688007616028836723924778678164873781225\
900607892771328686837662179046852027100910583734986843308542671633719093108369\
5867853859962735834546027695608370479796593381006303806051588236000*cot(1/(100\
0000+I)^(1/2))^364-49082804956758693475161630590976355425749021415213880503354\
729320268303663773327932244792374607437647984484067932622551248961950188014562\
024354739370890489325756504343395189058453250505669522984415673067894315342439\
60232898299298229384630728216306169712643227404662148035465048392000*cot(1/(10\
00000+I)^(1/2))^362+1356180364116128230620300292142756513337928178348589808384\
694087598021241087555497541111138544154879003708240437114320287140093746333506\
663106673210447856167797158912860392022626982287089073977800125936452168462752\
55058188781620986806301854476449941845725773316595612880560546900153000*cot(1/\
(1000000+I)^(1/2))^368-4563923613857895014842328012310118151144647640922928350\
830586030535040609194634116143951887193310641796981479223040641696692244656530\
618204148660106105463009703258085409549065536146031493463481836874342136340990\
6635686901650272359836021706405757529729036384850683832666031229840744000*cot(\
1/(1000000+I)^(1/2))^366-39612823538167363168939485395458445430825390324470140\
398839004217489935309147325274695289911543295430136000631392199078294087179761\
798270650672850138498605205314919591109752837285543121132790577519067051170670\
5923983850913503260796678083418665292794320227588020741211835234026363479200*c\
ot(1/(1000000+I)^(1/2))^370-16089934453754772718144663086620673516203096732531\
415973786553446415177928216682710759973985094424644715405998683745907795940662\
37522869758792260903680668000*cot(1/(1000000+I)^(1/2))^882+1137391935735268020\
386317847553714037248440528640827068359847853901453255148524083891509617514945\
198975450900660941565136045990690969466474708150764019276750189124365009496402\
981707545185294823794559944089456107849296297434237147174880619919387412511993\
714940041294380299888325848882000*cot(1/(1000000+I)^(1/2))^372-321038335685062\
719269426223553325561247005024154132201064572731258921469179124492248702714623\
600207715859016243960449973268429922519657955595749603759927697127975837958365\
661891919281560107345154944549429318489485675841846364555435042001818596371378\
9570022078041174391832108698319396000*cot(1/(1000000+I)^(1/2))^374-24301418214\
664797616065884920314638623020621607732563585380295575337016295543248771968456\
078013181669902134766740051234763562545451564119640854315676042243033868707149\
279074599394569241107334893022717625750727321546892547251915493475625783703266\
534886566154459931250518536738678047720000*cot(1/(1000000+I)^(1/2))^378+890824\
459835324744072078084859848410197806494328398749407901284433000176002357855264\
574021960876462899502412095386709588945200050963235284587496684191997953910074\
798590145852590166091563063821218950744427098290860075695903476115701845271003\
7292929221058660553429854473789450554733785000*cot(1/(1000000+I)^(1/2))^376-17\
186395340327287861368731059412452356943592632844004685961070834846898769429708\
556930346315133403381816955064429915255006588685875595967628926748612551808317\
400341350893179651399554125040097839467050849492267957944543221150005304598860\
4109384222380169637853590998893821617010995175880000*cot(1/(1000000+I)^(1/2))^\
382+65176464396839703213281772261426002942682900593292566835274015619503031442\
501918880419940158349726275376603105614120747411770559166866129570307385652405\
422016026902936361851915784926428333574437222197997206828472957546237235240816\
142772993089787101085646548771017668988967072318150732000*cot(1/(1000000+I)^(1\
/2))^380-113588988507349391663488785012544688652057520237873490781373849714652\
776548156910981684423115829724895743537934976986598188234132849673222269197218\
858127169906105347121887921731227295161470715165336700873539130570646620750769\
7533912501757760118876851102017574750802564508687438182160497500*cot(1/(100000\
0+I)^(1/2))^386+44558282077069984941165316071994156320827441881930048213018603\
648227613564622528088343686303567351432679883783436094336281156885447127910361\
697283007354763804630756086431644093753796679194813062825169245107829675070727\
24572878537502293480)
EXPECTED: cos(1/((1+1/1000000*I))^(1/2))/sin(1/((1+1/1000000*I))^(1/2))
COMMENT: Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2 calculate this
limit in 2-3 seconds and show the very short answers from 60
to 750 symbols long.
|
BUG # 50 limit: SIMPLE LIMIT RETURNS UNEVALUATED
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
These trivial limits are calculated correctly.
limit(1/(z-1),z = 1);
limit(1/(z-1)^(1/2),z = 1);
undefined
undefined
However, the following limits of the same nature are returned unevaluated.
limit(1/(z-1)^(1/3),z = 1);
ACTUAL: limit(1/(z-1)^(1/3),z = 1)
EXPECTED: undefined
COMMENT: seq(limit(1/(z-1)^(1/k),z = 1), k=1..10);
undefined,
undefined,
limit(1/(z-1)^(1/3),z = 1),
limit(1/(z-1)^(1/4),z = 1),
limit(1/(z-1)^(1/5),z = 1)
limit(1/(z-1)^(1/6),z = 1)
limit(1/(z-1)^(1/7),z = 1)
limit(1/(z-1)^(1/8),z = 1)
limit(1/(z-1)^(1/9),z = 1)
limit(1/(z-1)^(1/10),z = 1)
COMMENT: MuPAD 2.5.2 returns unevaluated for all these limits.
::::::::::::::::::::::::::::::::::::::::::::::::: 50%
|
BUG # 51 limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(StruveL(2,z),z = infinity);
ACTUAL: -infinity
EXPECTED: infinity
CHECKUP: evalf(Limit(StruveL(2,z),z = 10^6),20);
.12100755984539526566e434292
COMMENT: seq(limit(StruveL(k,z),z = infinity), k=2..11);
-infinity, -infinity, -infinity, -infinity, -infinity,\
-infinity, -infinity, -infinity, -infinity, -infinity
|
BUG # 52 asympt: INVALID FUNCTION IS RETURNED
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: convert(asympt(BesselI(1/3,-z),z, 1), polynom);
ACTUAL: 1/2*I*2^(1/2)/Pi^(1/2)*exp(-z)*(1/z)^(1/2)
EXPECTED: (1+sqrt(3)*I)*exp(z)/(2*sqrt(2*Pi*z))
CHECKUP: evalf(subs(z=10^9, (1+sqrt(3)*I)*exp(z)/(2*sqrt(2*Pi*z))));
evalf(subs(z=10^9, BesselI(1/3,-z)));
.5048145892e434294477+.8743645172e434294477*I
.5048145896e434294477+.8743645174e434294477*I
HINT: func := BesselI(1/3,-z):
bb := convert(asympt(func,z, 6), polynom);
plot(abs(bb), z=10..20);
plot(abs(func), z=10..20);
EXAMPLE 2: convert(series(BesselI(1/3,-z), z= infinity, 1), polynom);
ACTUAL: 1/2*I*2^(1/2)/Pi^(1/2)*exp(-z)*(1/z)^(1/2)
EXPECTED: 1/4*exp(z)*(1+I*3^(1/2))*2^(1/2)/z^(1/2)/Pi^(1/2)
CHECKUP: evalf(subs(z=10^9, (1+sqrt(3)*I)*exp(z)/(2*sqrt(2*Pi*z))));
evalf(subs(z=10^9, BesselI(1/3,-z)));
.5048145892e434294477+.8743645172e434294477*I
.5048145896e434294477+.8743645174e434294477*I
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BUG # 53 limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(BesselI(1/3,-z),z = infinity);
ACTUAL: 0
EXPECTED: infinity+infinity*I*3^(1/2)
CHECKUP: evalf(Limit(BesselI(1/3,-z),z = 100),20);
evalf(Limit(BesselI(1/3,-z),z = 1000),20);
.53657616541791312670e42+.92937718063430792012e42*I
.12427739685615449007e433+.21525476558726023661e433*I
divAngle := evalf(Limit(BesselI(1/3,-z),z = 1000),20):
evalf(Im(divAngle)/Re(divAngle));
evalf(sqrt(3));
1.732050807
1.732050808
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BUG # 54 product: SPURIOUS DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
evalf(Product(1+1/n, n=1..infinity));
ACTUAL: 2.000000000
EXPECTED: infinity
CHECKUP: seq(evalf(Product(1+1/n, n=1..10^k)), k=1..5);
11.00000000, 101.0000000, 1001.000000, 10001.00000, 100001.0000
WORKAROUND: evalf(product(1+1/n, n=1..infinity));
Float(infinity)
The same problem with
evalf(Product(1+1/(n-1), n=2..infinity));
evalf(Product(1+1/(n+2), n=1..infinity));
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BUG # 55 int: Error, (in X) too many levels of recursion
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
restart;
int(sqrt(z)*(1-z^2)^(1/3), z= -1..0);
ACTUAL: Error, (in type/algext) too many levels of recursion
EXPECTED: 16/13*I*3^(1/2)/GAMMA(2/3)*GAMMA(3/4)*sin(1/12*Pi)*GAMMA(11/12)
.5270334611*I
CHECKUP: evalf(Int(sqrt(z)*(1-z^2)^(1/3), z= -1..0));
0.+.5270334606*I
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BUG # 56 int: MEANINGLESS OUTPUT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
The answer to a definite integral depends on the integration variable.
EXAMPLE 1: int(sqrt(z)*(1-z^2)^(1/3), z=-1..1);
ACTUAL: 16/13*3^(1/2)*sin(1/12*Pi)*(z^(1/2)+(-z)^(1/2))/z^(1/2)/GAMMA(2/3)*GAMMA(3/4)*\
GAMMA(11/12)
.5270334609*(z^(1/2)+(-1.*z)^(1/2))/z^(1/2)
EXPECTED: (16/13+16/13*I)*3^(1/2)*sin(1/12*Pi)/GAMMA(2/3)*GAMMA(3/4)*GAMMA(11/12)
.5270334609+.5270334609*I
CHECKUP: evalf(Int(sqrt(z)*(1-z^2)^(1/3), z=-1..1));
.5270334606+.5270334606*I
EXAMPLE 2: int(sqrt(z)*(1+I*z)^(1/3), z= -1..1);
ACTUAL: 2/3*(hypergeom([-1/3, 3/2],[5/2],-I)*z^(1/2)+(-z)^(1/2)*hypergeom([-1/3, 3/2],\
[5/2],I))/z^(1/2)
.6666666667*((1.039515376+.1842244656*I)*z^(1/2)+(1.039515376-.1842244656*I)*(\
-1.*z)^(1/2))/z^(1/2)
EXPECTED: 2/3*hypergeom([-1/3, 3/2],[5/2],-I)+2/3*I*hypergeom([-1/3, 3/2],[5/2],I)
.8158265611+.8158265611*I
CHECKUP: evalf(Int(sqrt(z)*(1+I*z)^(1/3), z= -1..1));
.8158265611+.8158265611*I
The same problem with
int(sqrt(z)*(z^2-1)^(1/3), z= -1..1);
int(sqrt(z)*(1-z^2)^(1/4), z=-1..1);
int(sqrt(z)*(1-z^4)^(1/4), z=-1..1);
int(sqrt(z)*(1-z^6)^(1/4), z=-1..1);
int(sqrt(z)*(1-z^4)^(1/3), z=-1..1);
int(sqrt(z)*(1-z^6)^(1/3), z=-1..1);
int(sqrt(z)*(1-I*z)^(1/3), z= -1..1);
int(sqrt(-z)*(1+I*z)^(1/3), z= -1..1);
int(sqrt(-z)*(1-I*z)^(1/3), z= -1..1);
int(sqrt(z)*(1+I*z^2)^(1/3), z= -1..1);
int(sqrt(z)*(1-I*z^2)^(1/3), z= -1..1);
int(sqrt(z)*(I*z^2-1)^(1/3), z= -1..1);
int(sqrt(z)*(I*z^2+1)^(1/3), z= -1..1);
int(sqrt(z)*(1+sqrt(I)*z)^(1/3), z= -1..1);
int(sqrt(z)*(1-sqrt(I)*z)^(1/3), z= -1..1);
int(sqrt(z)/(1+sqrt(I)*z)^(1/3), z= -1..1);
int(sqrt(z)/(1-sqrt(I)*z)^(1/3), z= -1..1);
int((1+sqrt(I)*z)^(1/3)/sqrt(z), z= -1..1);
int((1-sqrt(I)*z)^(1/3)/sqrt(z), z= -1..1);
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BUG # 57 int: INVALID MAGNITUDE OF THE REAL-VALUED INTEGRAL
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
int(sin(z)/sqrt(sin(z)+cos(z)), z = 0..1);
ACTUAL: 1-2^(3/4)*EllipticK(1/2*2^(1/2))+1/2*2^(3/4)*EllipticF(2^(1/2)*(2^(1/2)/(2+2^(\
1/2)))^(1/2), 1/2*2^(1/2)) + 2^(3/4)*EllipticPi(1/2, 1/2*2^(1/2))-1/2*2^(3/4)*\
EllipticPi(2^(1/2)*(2^(1/2)/(2+2^(1/2)))^(1/2),1/2,1/2*2^(1/2))-2*2^(1/4)+1/2*\
2^(3/4)*EllipticF(2^(1/2)*(2^(1/2)*(cos(1)+sin(1))/(cos(1)*2^(1/2)+sin(1)*2^(1\
/2)+2))^(1/2),1/2*2^(1/2))-1/2*2^(3/4)*EllipticPi(2^(1/2)*(2^(1/2)*(cos(1)+sin\
(1))/(cos(1)*2^(1/2)+sin(1)*2^(1/2)+2))^(1/2),1/2,1/2*2^(1/2))+(cos(1)+sin(1))\
^(1/2)
.3667522890181217179596219379180129921565149408568
EXPECTED: 1+2^(1/4)*EllipticE(1/2*(2^(1/2)-1)^(1/2)*2^(1/4), 2^(1/2))-((cos(1)-sin(1))*(\
cos(1)+sin(1))^(1/2)+2^(1/4)*EllipticE(1/2*(2^(1/2)-cos(1)-sin(1))^(1/2)*2^(1/\
4),2^(1/2))*(1-sin(2))^(1/2))/(cos(1)-sin(1))
.394189453481633709060360647714985535816755861009144
CHECKUP: evalf(Int(sin(z)/sqrt(sin(z)+cos(z)), z = 0..1), 51);
.394189453481633709060360647714985535816755861009144
The same problem with
int(sin(z)*sqrt(sin(z)+cos(z)), z = 0..1);
int(cos(z)/sqrt(sin(z)+cos(z)), z = 0..1);
int(cos(z)*(sin(z)+cos(z))^(1/2), z = 0..1);
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BUG # 58 int: MEANINGLESS OUTPUT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
The output contains a substring trunc(`limit/mrv/Re`(1)) .
int(sqrt(tan(z)), z= 0..Pi);
ACTUAL: 1/2*I*2^(1/2)*Pi-1/2*I*exp(1/2*I*trunc(`limit/mrv/Re`(1))*Pi)*2^(1/2)*Pi
EXPECTED: sqrt(2)*Pi*(1+I)/2
2.221441469+2.221441469*I
CHECKUP: evalf(Int(sqrt(tan(z)), z= 0..Pi/2))+
evalf(Int(sqrt(tan(z)), z= Pi/2+1/10^8..Pi-1/10^8, method = _Sinc));
2.221441469+2.221241468*I
The same problem with
int(sqrt(tan(z)), z= 0..Pi, 'CauchyPrincipalValue');
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BUG # 59 int: MEANINGLESS OUTPUT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
The output contains a substring trunc(`limit/mrv/Re`(1)) .
int(sqrt(sinh(z)), z = -1..1);
ACTUAL: -(-2*(-I*(exp(1)^2-1+2*I*exp(1))/exp(1))^(1/2)*(-I*(-exp(1)^2+1+2*I*exp(1))/ex\
p(1))^(1/2)*(I*(exp(1)^2-1)/exp(1))^(1/2)*exp(1)*2^(1/2)*sinh(1)^(1/2)*Ellipti\
cE(1/2*2^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2),1/2*2^(1/2))*exp(-2)-2*(-I*(exp(1)\
^2-1+2*I*exp(1))/exp(1))^(1/2)*(-I*(-exp(1)^2+1+2*I*exp(1))/exp(1))^(1/2)*(I*(\
exp(1)^2-1)/exp(1))^(1/2)*exp(1)*2^(1/2)*sinh(1)^(1/2)*EllipticE(1/2*2^(1/2)*(\
I*exp(-1)-I*exp(1)+2)^(1/2),1/2*2^(1/2))+(-I*(exp(1)^2-1+2*I*exp(1))/exp(1))^(\
1/2)*(-I*(-exp(1)^2+1+2*I*exp(1))/exp(1))^(1/2)*(I*(exp(1)^2-1)/exp(1))^(1/2)*\
exp(1)*2^(1/2)*sinh(1)^(1/2)*EllipticF(1/2*2^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2\
),1/2*2^(1/2))*exp(-2)+(-I*(exp(1)^2-1+2*I*exp(1))/exp(1))^(1/2)*(-I*(-exp(1)^\
2+1+2*I*exp(1))/exp(1))^(1/2)*(I*(exp(1)^2-1)/exp(1))^(1/2)*exp(1)*2^(1/2)*sin\
h(1)^(1/2)*EllipticF(1/2*2^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2),1/2*2^(1/2))+2*(\
-I*exp(-1)+I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1))\
^(1/2)*exp(-1)*exp(-1/2*I*trunc(`limit/mrv/Re`(1))*Pi)*((exp(1)^2-1)/exp(1))^(\
1/2)*EllipticE(1/2*2^(1/2)*(-I*exp(-1)+I*exp(1)+2)^(1/2),1/2*2^(1/2))*exp(1)^2\
+2*(-I*exp(-1)+I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp\
(1))^(1/2)*exp(-1)*exp(-1/2*I*trunc(`limit/mrv/Re`(1))*Pi)*((exp(1)^2-1)/exp(1\
))^(1/2)*EllipticE(1/2*2^(1/2)*(-I*exp(-1)+I*exp(1)+2)^(1/2),1/2*2^(1/2))-(-I*\
exp(-1)+I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1))^(1\
/2)*exp(-1)*exp(-1/2*I*trunc(`limit/mrv/Re`(1))*Pi)*((exp(1)^2-1)/exp(1))^(1/2\
)*EllipticF(1/2*2^(1/2)*(-I*exp(-1)+I*exp(1)+2)^(1/2),1/2*2^(1/2))*exp(1)^2-(-\
I*exp(-1)+I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1)+2)^(1/2)*(I*exp(-1)-I*exp(1))^\
(1/2)*exp(-1)*exp(-1/2*I*trunc(`limit/mrv/Re`(1))*Pi)*((exp(1)^2-1)/exp(1))^(1\
/2)*EllipticF(1/2*2^(1/2)*(-I*exp(-1)+I*exp(1)+2)^(1/2),1/2*2^(1/2))+4*((exp(1\
)^2-1)/exp(1))^(1/2)*sinh(1)^(1/2)*EllipticE(1/2*2^(1/2))*exp(1)^2*exp(-2)+4*(\
(exp(1)^2-1)/exp(1))^(1/2)*sinh(1)^(1/2)*EllipticE(1/2*2^(1/2))*exp(1)^2+4*((e\
xp(1)^2-1)/exp(1))^(1/2)*sinh(1)^(1/2)*EllipticE(1/2*2^(1/2))*exp(-2)+4*((exp(\
1)^2-1)/exp(1))^(1/2)*sinh(1)^(1/2)*EllipticE(1/2*2^(1/2))-2*((exp(1)^2-1)/exp\
(1))^(1/2)*sinh(1)^(1/2)*EllipticK(1/2*2^(1/2))*exp(1)^2*exp(-2)-2*((exp(1)^2-\
1)/exp(1))^(1/2)*sinh(1)^(1/2)*EllipticK(1/2*2^(1/2))*exp(1)^2-2*((exp(1)^2-1)\
/exp(1))^(1/2)*sinh(1)^(1/2)*EllipticK(1/2*2^(1/2))*exp(-2)-2*((exp(1)^2-1)/ex\
p(1))^(1/2)*sinh(1)^(1/2)*EllipticK(1/2*2^(1/2))+4*I*((exp(1)^2-1)/exp(1))^(1/\
2)*sinh(1)^(1/2)*EllipticE(1/2*2^(1/2))-2*I*((exp(1)^2-1)/exp(1))^(1/2)*sinh(1\
)^(1/2)*EllipticK(1/2*2^(1/2))*exp(1)^2+4*I*((exp(1)^2-1)/exp(1))^(1/2)*sinh(1\
)^(1/2)*EllipticE(1/2*2^(1/2))*exp(1)^2*exp(-2)-2*I*((exp(1)^2-1)/exp(1))^(1/2\
)*sinh(1)^(1/2)*EllipticK(1/2*2^(1/2))-2*I*((exp(1)^2-1)/exp(1))^(1/2)*sinh(1)\
^(1/2)*EllipticK(1/2*2^(1/2))*exp(-2)+4*I*((exp(1)^2-1)/exp(1))^(1/2)*sinh(1)^\
(1/2)*EllipticE(1/2*2^(1/2))*exp(1)^2+4*I*((exp(1)^2-1)/exp(1))^(1/2)*sinh(1)^\
(1/2)*EllipticE(1/2*2^(1/2))*exp(-2)-2*I*((exp(1)^2-1)/exp(1))^(1/2)*sinh(1)^(\
1/2)*EllipticK(1/2*2^(1/2))*exp(1)^2*exp(-2))/(exp(1)^2+1)/((exp(1)^2-1)/exp(1\
))^(1/2)/sinh(1)^(1/2)/(exp(-2)+1)
-.1566053511-.8472130901*I+(-1.537820820+.8472130832*I)*exp(-1.570796327*I*tru\
nc(`limit/mrv/Re`(1)))
EXPECTED: -(1+I)*(-2*(-I*(exp(2)-1+2*I*exp(1)))^(1/2)*(-I*(-exp(2)+1+2*I*exp(1)))^(1/2)*\
EllipticE(1/2*2^(1/2)*exp(-1/2)*(I-I*exp(2)+2*exp(1))^(1/2),1/2*2^(1/2))-2*I*(\
-I*(exp(2)-1+2*I*exp(1)))^(1/2)*(-I*(-exp(2)+1+2*I*exp(1)))^(1/2)*EllipticE(1/\
2*2^(1/2)*exp(-1/2)*(I-I*exp(2)+2*exp(1))^(1/2),1/2*2^(1/2))+(-I*(exp(2)-1+2*I\
*exp(1)))^(1/2)*(-I*(-exp(2)+1+2*I*exp(1)))^(1/2)*EllipticF(1/2*2^(1/2)*exp(-1\
/2)*(I-I*exp(2)+2*exp(1))^(1/2),1/2*2^(1/2))+I*(-I*(exp(2)-1+2*I*exp(1)))^(1/2\
)*(-I*(-exp(2)+1+2*I*exp(1)))^(1/2)*EllipticF(1/2*2^(1/2)*exp(-1/2)*(I-I*exp(2\
)+2*exp(1))^(1/2),1/2*2^(1/2))+2*exp(2)*EllipticE(1/2*2^(1/2))+2*EllipticE(1/2\
*2^(1/2))-exp(2)*EllipticK(1/2*2^(1/2))-EllipticK(1/2*2^(1/2))+2*I*exp(2)*Elli\
pticE(1/2*2^(1/2))+2*I*EllipticE(1/2*2^(1/2))-I*exp(2)*EllipticK(1/2*2^(1/2))-\
I*EllipticK(1/2*2^(1/2)))/(exp(2)+1)
.6906077365+.6906077335*I
CHECKUP: evalf(Int(sqrt(sinh(z)), z = -1..1));
.6906077360+.6906077360*I
The same problem with
int(sinh(z)^(1/2),z = -1..1);
int(tan(z)^(1/2),z = 0..Pi);
int((-sinh(z-1))^(1/2),z = 0..Pi);
int(tan(z)^(1/2),z = 1..2)
int((-sinh(z-1))^(1/2),z = 1..2)
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BUG # 60 int: Error, (in X) must be 3 or 1 real roots for a real cubic
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
int(sqrt(1+I*z^3), z= -1..1);
ACTUAL: Error, (in int/ellalg/trxstandard) must be 3 or 1 real roots for a real cubic
EXPECTED: 2/5*(1-I)^(1/2)+2/5*(1+I)^(1/2)+3/5*hypergeom([1/3, 1/2],[4/3],-I)+3/5*\
hypergeom([1/3, 1/2],[4/3],I)
2.031186687
CHECKUP: fnormal(evalf(Int(sqrt(1+I*z^3), z= -1..1)));
2.031186688+0.*I
The same problem with
int(sqrt(1+I*z^3), z= 0..1);
int(sqrt(1+I*z^3)/(z-1), z= 0..1);
int(sqrt(1-I*z^3)/(z-1), z= 0..1);
int(1/((z-1)*sqrt(1+I*z^3)), z= 0..1);
int(1/((z-1)*sqrt(1-I*z^3)), z= 0..1);
int(sqrt(1+I*z^3)/(z^2-1), z= 0..1);
int(sqrt(1-I*z^3)/(z^2-1), z= 0..1);
int(1/((z^2-1)*sqrt(1+I*z^3)), z= 0..1);
int(1/((z^2-1)*sqrt(1-I*z^3)), z= 0..1);
int(sqrt(1+I*z^3)/(z^2-z), z= 0..1);
int(sqrt(1-I*z^3)/(z^2-z), z= 0..1);
int(1/((z^2-z)*sqrt(1+I*z^3)), z= 0..1);
int(1/((z^2-z)*sqrt(1-I*z^3)), z= 0..1);
int(1/sqrt(1+I*z^3), z= -1..1);
int(1/sqrt(1+I*z^3), z= -infinity..infinity);
int(1/sqrt(1+I*z^3), z= 0..1);
int(1/sqrt(1+I*z^3), z= 0..Pi);
int(1/sqrt(1+I*z^3), z= 0..infinity);
int(1/sqrt(1+I*z^3), z= 1..2);
int(1/sqrt(1-I*z^3), z= -1..1);
int(1/sqrt(1-I*z^3), z= -infinity..infinity);
int(1/sqrt(1-I*z^3), z= 0..1);
int(1/sqrt(1-I*z^3), z= 0..Pi);
int(1/sqrt(1-I*z^3), z= 0..infinity);
int(1/sqrt(1-I*z^3), z= 1..2);
int(sqrt(1+I*z^3), z= -1..1);
int(sqrt(1+I*z^3), z= 0..1);
int(sqrt(1+I*z^3), z= 0..Pi);
int(sqrt(1+I*z^3), z= 1..2);
int(sqrt(1-I*z^3), z= -1..1);
int(sqrt(1-I*z^3), z= 0..1);
int(sqrt(1-I*z^3), z= 0..Pi);
int(sqrt(1-I*z^3), z= 1..2);
int(sqrt(z^2+z+1)*sqrt(1+I*z), z= 0..1);
int(sqrt(z^2+z+1)*sqrt(1-I*z), z= 0..1);
int(sqrt(z^2+z+1)/sqrt(1+I*z), z= 0..1);
int(sqrt(z^2+z+1)/sqrt(1-I*z), z= 0..1);
int(sqrt(z^2-z+1)*sqrt(1+I*z), z= 0..1);
int(sqrt(z^2-z+1)*sqrt(1-I*z), z= 0..1);
int(sqrt(z^2-z+1)/sqrt(1+I*z), z= 0..1);
int(sqrt(z^2-z+1)/sqrt(1-I*z), z= 0..1);
int(z/(z-1)*sqrt(1+I*z^3), z= 0..1);
int(z/(z-1)*sqrt(1-I*z^3), z= 0..1);
int(z/(z-1)/sqrt(1+I*z^3), z= 0..1);
int(z/(z-1)/sqrt(1-I*z^3), z= 0..1);
::::::::::::::::::::::::::::::::::::::::::::::::: 60%
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BUG # 61 int: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
int(sin(z)*ln(1-z), z= 0..1);
ACTUAL: undefined
EXPECTED: gamma*cos(1)-cos(1)*Ci(1)-sin(1)*Si(1);
-.6665306159
CHECKUP: evalf(Int(sin(z)*ln(1-z), z= 0..1));
-.6665306158
HINT: plot(sin(z)*ln(1-z), z= 0..1);
The same problem with
int(cos(z)*ln(1-z), z=0..1);
int(sin(2*z)*ln(1-z), z= 0..1);
int(cos(2*z)*ln(1-z), z= 0..1);
int(sin(3*z)*ln(1-z), z= 0..1);
int(cos(3*z)*ln(1-z), z= 0..1);
int(sin(z)^2*ln(1-z), z= 0..1);
int(cos(z)*ln(1-z), z= 0..1);
int(cos(z)^2*ln(1-z), z= 0..1);
int(sin(5*z)^3*ln(1-z), z= 0..1);
int(cos(7*z)^4*ln(1-z), z= 0..1);
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BUG # 62 int: INVALID MAGNITUDE OF THE REAL AND IMAGINARY PARTS
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
int(sqrt(z)*(I*z)^(1/3), z=0..1);
ACTUAL: 6/11*I
.5454545455*I
EXPECTED: 3*sqrt(3)/11+3*I/11
.4723774930+.2727272727*I
CHECKUP: evalf(Int(sqrt(z)*(I*z)^(1/3), z=0..1));
.4723774930+.2727272727*I
The same problem with
int(sqrt(z)*(I*z)^(1/4), z=0..1);
int(z^(1/3)*(I*z)^(1/4), z=0..1);
int(z^(1/3)*(I*z)^(3/4), z=0..1);
int(sqrt(z)*(I*z)^(1/5), z=0..1);
int(sqrt(z)*(I*z)^(2/5), z=0..1);
int(sqrt(z)*(I*z)^(3/5), z=0..1);
int(sqrt(z)*(I*z)^(4/5), z=0..1);
int(sqrt(z)*(I*z)^(1/6), z=0..1);
int(sqrt(z)*(I*z)^(1/7), z=0..1);
int(sqrt(z)*(I*z)^(2/7), z=0..1);
int(sqrt(z)*(I*z)^(3/7), z=0..1);
int(sqrt(z)*(I*z)^(4/7), z=0..1);
int(sqrt(z)*(I*z)^(5/7), z=0..1);
|
BUG # 63 int: INVALID INDEFINITE INTEGRATION
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: restart;
func := sqrt(1+sqrt(1-z)):
zero:= simplify(func - diff(int(func, z),z)):
[coulditbe(zero = 0),is(zero=0)];
ACTUAL: [true, false]
EXPECTED: [true, true]
IMPLICATIONS: Maple calculates incorrectly definite integrals involving sqrt(sqrt(z)-1)
EXAMPLE 2: int(sqrt(1+sqrt(1-z)), z= 0..1);
ACTUAL: 8/15*2^(1/2)
.7542472330
EXPECTED: 8*sqrt(2)/15 + 8/15
1.287580566
CHECKUP: evalf(Int(sqrt(1+sqrt(1-z)), z= 0..1));
1.287580567
The same problem with
int(1/sqrt(1+sqrt(1-z)), z= 0..1);
|
BUG # 64 plot: INVALID GRAPH
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
plot(abs(z)-sqrt(I*z)*sqrt(-I*z),z = -1..1);
ACTUAL: Numerous spurious vertical lines.
EXPECTED: The straight line y = 0 .
COMMENT: Derive 5.06 and MuPAD 2.5.2 shows the straight line y = 0.
|
BUG # 65 evalf: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
evalf(Sum(1/n,n = 1..infinity));
infinity
However, for the following simple sum Maple yields a senseless answer,
actually this sum cannot be negative.
evalf(Sum(exp(n), n= 0..infinity));
ACTUAL: -.5819767069
EXPECTED: infinity
CHECKUP: seq(evalf(Sum(exp(n), n= 0..k)), k=1000..1002);
evalf(sum(exp(n), n= 0..infinity));
.3116606613e435, .8471815123e435, .2302878110e436
Float(infinity)
COMMENT: Derive 5.06 and Mathematica 4.2.1 calculate it correctly.
APPROX(SUM(EXP(n), n, 0, inf))
inf
NSum[Exp[n], {n, 0, Infinity}]
ComplexInfinity
|
BUG # 66 plot: DISAPPEARED GRAPH
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
One can see only the axes without any vestige of the graph.
plot(exp(z), z= 0..100);
COMMENT: Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2 draw it
correctly.
|
BUG # 67 sum: SPURIOUS DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
sum(1/(n*(n^4+1)), n= 1..infinity);
ACTUAL: -infinity*signum(-1+1/4*Sum(1, _alpha = RootOf(_Z^4+1)))+gamma-Sum(-1/4*Psi(1-\
_alpha),_alpha = RootOf(_Z^4+1))
Float(undefined)-0.*I
EXPECTED: gamma-Sum(-1/4*Psi(1-_alpha),_alpha = RootOf(_Z^4+1))
.5350348873
CHECKUP: evalf(Sum(1/(n*(n^4+1)), n= 1..infinity));
.5350348873
The same problem with
sum(1/(n*(1+n^5)), n=1..infinity);
sum(1/(n*(1+n^8)), n=1..infinity);
sum(1/(n*(1+n^10)), n=1..infinity);
sum(1/(n*(1+n^11)), n=1..infinity);
COMMENT: Maple also yields invalid outputs for
evalf(sum(1/(n*(1+n^6)), n=1..infinity));
evalf(sum(1/(n*(1+n^7)), n=1..infinity));
evalf(sum(1/(n*(1+n^9)), n=1..infinity));
evalf(sum(1/(n*(1+n^12)), n=1..infinity));
Float(-infinity)+0.*I
Float(-infinity)-0.*I
Float(infinity)+0.*I
Float(infinity)-0.*I
COMMENT: Mathematica 4.2.1 calculates these sums correctly.
|
BUG # 68 sum: SPURIOUS DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
sum(1/(n*(n^3-2)), n=2..infinity);
ACTUAL: signum(1/6*Sum(1,_alpha = RootOf(_Z^3-2))-1/2)*infinity-Sum(1/6*Psi(2-_alpha),\
_alpha = RootOf(_Z^3-2))+1/2-1/2*gamma
Float(infinity)-0.*I
EXPECTED: 1/2-1/2*gamma-Sum(1/6*Psi(2-_alpha),_alpha = RootOf(_Z^3-2));
.1043077220
CHECKUP: evalf(Sum(1/(n*(n^3-2)), n=2..infinity));
.1043077220
The same problem with
> evalf(sum(1/(n*(n^3-2)), n=2..infinity));
evalf(sum(1/(n*(n^4-2)), n=2..infinity));
evalf(sum(1/(n*(n^5-2)), n=2..infinity));
evalf(sum(1/(n*(n^3-3)), n=2..infinity));
evalf(sum(1/(n*(n^4-3)), n=2..infinity));
evalf(sum(1/(n*(n^5-3)), n=2..infinity));
Float(infinity)-0.*I
Float(undefined)-0.*I
Float(undefined)-0.*I
Float(undefined)-0.*I
Float(undefined)-0.*I
Float(infinity)-0.*I
COMMENT: Mathematica 4.2.1 calculates these sums correctly.
|
BUG # 69 evalf: ADDITIVITY PROPERTY FAILS
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
These two approximations are valid.
evalf(Sum(1/(2^n),n = 0 .. infinity));
2.000000000
evalf(Sum((-1)^n/(2^(n+1)),n = 0 .. infinity));
.3333333333
However, an attempt to approximate the sum of the summands does
not return a number despite the fact that the summand has none
singularity over the summation region.
evalf(Sum(1/(2^n)+(-1)^n/(2^(n+1)),n = 0 .. infinity));
ACTUAL: Sum(1/(2^n)+(-1)^n/(2^(n+1)),n = 0 .. infinity)
EXPECTED: 2.333333333 # 2.000000000 + .3333333333
CHECKUP: evalf(sum(1/(2^n)+(-1)^n/(2^(n+1)),n = 0 .. infinity));
2.333333333
|
BUG # 70 sum: Error, (in sum/polynom) wrong number (or type) ...
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
These sums are okay.
sum(harmonic(n), n=2..infinity);
sum(Heaviside(n), n=2..infinity);
infinity
infinity
However, the sum of their summands invokes an error message.
sum(harmonic(n)*Heaviside(n), n=2..infinity);
ACTUAL: Error, (in sum/polynom) wrong number (or type) of parameters
in function series
EXPECTED: infinity
CHECKUP: evalf(Sum(harmonic(n)*Heaviside(n), n=2..1000));
6491.956331
::::::::::::::::::::::::::::::::::::::::::::::::: 70%
|
BUG # 71 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(exp((1-z)^(2/3)),z = infinity);
ACTUAL: exp(-infinity+infinity*I*3^(1/2))
evalf(%);
undefined+undefined*I
EXPECTED: 0
CHECKUP: limit(exp((1-z)^(2/3)),z = 1000000.);
-.1464858820e-2171+.3047113864e-2171*I
COMMENT: Derive 5.06, Mathematica 4.2.1 and MuPAD 2.5.2 calculate
this limit correctly.
LIM(EXP((1 - z)^(2/3)), z, inf)
0
Limit[Exp[(1 - z)^(2/3)], z -> Infinity]
0
limit(exp((1-z)^(2/3)),z = infinity);
0
|
BUG # 72 limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(StruveL(0,z),z = infinity);
ACTUAL: 0
EXPECTED: infinity
CHECKUP: evalf(limit(StruveL(0,z),z = 10^6), 20);
.12100780186087797958e434292
EXAMPLE 2: limit(StruveL(1,z),z = infinity);
ACTUAL: -2/Pi
EXPECTED: infinity
CHECKUP: evalf(limit(StruveL(1,z),z = 10^6), 20);
.12100774135696192315e434292
EXAMPLE 3: limit(StruveH(1,I*z),z = infinity);
ACTUAL: 2/Pi
EXPECTED: -infinity
CHECKUP: evalf(limit(StruveH(1,I*z),z = 10^10));
Float(-infinity)
WORKAROUND: limit(convert(series(StruveL(0,z),z = infinity,1), polynom),\
z=infinity);
infinity
limit(convert(asympt(StruveL(0,z),z), polynom), z=infinity);
infinity
The same problem with
limit(StruveL(1,z),z = -infinity);
limit(StruveH(0,I*z),z = infinity);
limit(StruveL(1,z)/arcsec(z),z = -infinity);
limit(StruveL(1,z)*arcsec(z),z = -infinity);
|
BUG # 73 plot: GRAPH IS TOTALLY ABSENT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
plot(Im(StruveH(0,I*z)),z = 0..100);
ACTUAL: Only the axes are shown; none vestige of the graph can be seen.
EXPECTED: Both the axes and graph are shown.
The same problem with
plot(Im(StruveH(2,I*z)),z = 0..100);
plot(Im(StruveH(4,I*z)),z = 0..100);
plot(Im(StruveH(6,I*z)),z = 0..100);
COMMENT: Mathematica 4.2.1 draws both the axes and graphs correctly.
Plot[Im[StruveH[0, I*z]], {z, -100, 0}]
Plot[Im[StruveH[2, I*z]], {z, -100, 0}]
Plot[Im[StruveH[4, I*z]], {z, -100, 0}]
Plot[Im[StruveH[6, I*z]], {z, -100, 0}]
|
BUG # 74 plot: GRAPH IS TOTALLY ABSENT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
plot(BesselI(0,z), z = -100..0);
ACTUAL: Only the axes are shown; none vestige of the graph can be seen.
EXPECTED: Both the axes and graph are shown.
The same problem with
plot(BesselI(1,z), z = -100..0);
plot(BesselI(2,z), z = -100..0);
plot(BesselI(3,z), z = -100..0);
plot(BesselI(4,z), z = -100..0);
plot(BesselI(5,z),z = -100..0);
COMMENT: Mathematica 4.2.1 and MuPAD draw both the axes and graphs correctly.
Table[Plot[BesselI[k, z], {z, -100, 0}], {k, 0, 5}]
plotfunc2d(besselI(0,z),besselI(1,z),besselI(2,z),besselI(3,z),besselI(4,z),\
besselI(5,z),z = -100..0);
|
BUG # 75 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(tanh(arcsec(z)),z = 1/2);
ACTUAL: undefined
EXPECTED: tanh(arcsec(1/2))
3.854535294*I
HINT: plot(Re(tanh(arcsec(z))),z = 1/2..1);
plot(Im(tanh(arcsec(z))),z = 1/2..1);
WORKAROUND: limit(simplify(convert(series(tanh(arcsec(z)),z = 1/2,1), polynom)), z=1/2);
(exp(Pi)*(2*I+I*3^(1/2))^(2*I)-1)/(exp(Pi)*(2*I+I*3^(1/2))^(2*I)+1)
.2614497841e-8+3.854535294*I
|
BUG # 76 limit: Error, (in X) too many levels of recursion
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(BesselY(2,sqrt(z))-sqrt(sec(z-1)), z=-infinity);
ACTUAL: Error, (in type/radalgnum) too many levels of recursion
EXPECTED: undefinite
|
BUG # 77 evalf: Error, (in X) invalid assignment to Digits
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
evalf(limit(BesselY(0, sqrt(z)),z = -10^20));
ACTUAL: Error, (in evalf/Bessel/asymptJY) invalid assignment to Digits
EXPECTED: undefined
CHECKUP: seq(evalf(limit(BesselY(0,sqrt(z)),z = -10^k)), k=17..19);
0.+.1410271793e137335970*I,
0.+.1009629179e434294478*I,
.1003286720e1373359701+.6836559561e1373359733*I
HINT: plot(Im(BesselY(0,sqrt(z))), z=-1000..-800);
plot(Re(BesselY(0,sqrt(z))), z=-1000..-800);
|
BUG # 78 limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(BesselY(0, sqrt(z)),z = -infinity);
ACTUAL: 0
EXPECTED: I*infinity
CHECKUP: evalf(limit(BesselY(0,sqrt(z)),z = -10000), 30);
0.+.107375170713107382351972085760e43*I
HINT: plot(Im(BesselY(0,sqrt(z))), z=-1000..-800);
plot(Re(BesselY(0,sqrt(z))), z=-1000..-800);
EXAMPLE 2: limit(BesselY(1, sqrt(z)),z = -infinity);
ACTUAL: 0
EXPECTED: -infinity
CHECKUP: evalf(limit(BesselY(1,sqrt(z)),z = -10000), 30);
-.106836939033816248120614576322e43+0.*I
The same problem with
limit(BesselY(2, sqrt(z)),z = -infinity);
limit(BesselY(3, sqrt(z)),z = -infinity);
limit(BesselY(4, sqrt(z)),z = -infinity);
limit(BesselY(5, sqrt(z)),z = -infinity);
limit(BesselY(6, sqrt(z)),z = -infinity);
limit(BesselY(1/3,z^(1/2))*Shi(1/z),z = -infinity);
|
BUG # 79 limit: INVALID MAGNITUDE OF THE IMAGINARY PART
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(tan(-1+sqrt(1-BesselI(1/3,z))), z=-infinity);
ACTUAL: 0
EXPECTED: -I
CHECKUP: evalf(limit(tan(-1+sqrt(1-BesselI(1/3,z))), z=-1000));
0.-1.000000000*I
COMMENT: Mathematica 4.2.1 calculates it correctly.
The same problem with
limit(tan(-1+sqrt(1-BesselI(2/3,z))), z=-infinity);
limit(tan(-1+sqrt(1-BesselI(1/4,z))), z=-infinity);
limit(tan(-1+sqrt(1-BesselI(1/5,z))), z=-infinity);
limit(tan(-1+sqrt(1-BesselI(2/5,z))), z=-infinity);
limit(tan(-1+sqrt(1-BesselI(3/5,z))), z=-infinity);
|
BUG # 80 limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(sqrt(sin(BesselK(0,z))+cos(BesselK(0,z))),z = -infinity);
ACTUAL: 1
EXPECTED: undefined
CHECKUP: seq(evalf(limit(sqrt(sin(BesselK(0,z))+cos(BesselK(0,z))),\
z = -k)), k=10..15);
.5482176791e1921-.2270734880e1921*I,
.1027104357e4973-.4254367986e4972*I,
.4199489742e12927-.1739480193e12927*I,
.2170490296e33731-.8990455280e33730*I,
.5054780882e88288-.2093757979e88288*I,
.4754790048e231705-.1969498250e231705*I
The same problem with
limit(sqrt(sin(BesselK(1,z))+cos(BesselK(0,z))),z = -infinity);
limit(sqrt(sin(BesselK(1,z))+cos(BesselK(1,z))),z = -infinity);
limit(sqrt(sin(BesselK(1/3,z))+cos(BesselK(1/3,z))),z = -infinity);
limit(sqrt(sin(BesselK(2/3,z))+cos(BesselK(1/4,z))),z = -infinity);
limit(1/sqrt(2*sin(BesselK(1/4,z))+cos(2*BesselK(1/4,z))),z = -infinity);
::::::::::::::::::::::::::::::::::::::::::::::::: 80%
|
BUG # 81 limit: INVALID MAGNITUDE OF THE REAL-VALUED LIMIT
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(StruveL(0, z)/(1-StruveL(0, z)),z = infinity);
ACTUAL: 0
EXPECTED: -1
CHECKUP: evalf(Limit(StruveL(0, z)/(1-StruveL(0, z)),z = infinity));
-1.000000000
EXAMPLE 2: limit(StruveL(1, z)/(1-StruveL(1, z)),z = infinity);
ACTUAL: -2/(Pi+2)
-0.3889845296
EXPECTED: -1
CHECKUP: evalf(Limit(StruveL(1, z)/(1-StruveL(1, z)),z = infinity));
-1.000000000
|
BUG # 82 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(tan(-1+sqrt(1-BesselI(1/2,z))), z=-infinity);
ACTUAL: undefined
EXPECTED: -I
CHECKUP: evalf(limit(tan(-1+sqrt(1-BesselI(1/2,z))), z=-100));
0.-1.000000000*I
HINT: plot(Im(tan(-1+sqrt(1-BesselI(1/2,z)))), z=-900..-1000);
plot(Re(tan(-1+sqrt(1-BesselI(1/2,z)))), z=-900..-1000);
|
BUG # 83 limit: TRIVIAL LIMIT CANNOT BE DONE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(sec(z)*cos(z),z = infinity);
ACTUAL: limit(sec(z)*cos(z),z = infinity);
EXPECTED: 1
WORKAROUND: limit(simplify(sec(z)*cos(z)),z = infinity);
1
HINT: plot(sec(z)*cos(z),z = 0..10^10);
plot(sec(z)*cos(z),z = -infinity..infinity);
EXAMPLE 2: limit(csc(z)*sin(z),z = infinity);
ACTUAL: limit(csc(z)*sin(z),z = infinity)
EXPECTED: 1
WORKAROUND: limit(simplify(csc(z)*sin(z)),z = infinity);
1
HINT: plot(csc(z)*sin(z), z= 0..10^10);
plot(csc(z)*sin(z), z= -infinity..infinity);
COMMENT: Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2 calculate the limits correctly.
|
BUG # 84 limit: TRIVIAL LIMIT CANNOT BE DONE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
The argument of the limits shown below is a smooth function at the limit point so it is enough
just so substitute the proper value of the variable into the function to get the valid answer.
Maple calculates this trivial limit correctly.
limit(arccsc(1/z)^2,z = 1);
1/4*Pi^2 ## = arccsc(1/z)^2
However, this trivial limit is returned unevaluated.
limit(arccsc(1/z)^2,z = 2);
ACTUAL: limit(arccsc(1/z)^2,z = 2)
EXPECTED: arccsc(1/2)^2 or -ln(-2*I+I*3^(1/2))^2
.7330229932-4.137345261*I
CHECKUP: evalf(Limit(arccsc(1/z)^2,z = 2));
.7330229980-4.137345254*I
WORKAROUND: subs(z=2, arccsc(1/z)^2);
COMMENT: Derive 5.06 and Mathematica 4.2.1 6 calculate it correctly.
LIM(ACSC(1/z)^2, z, 2)
- LN(2 - SQRT(3))^2 + pi^2/4 + pi*#I*LN(2 - SQRT(3))
0.7330229980 - 4.137345254*#I
Limit[ArcCsc[1/z]^2, z -> 2]
ArcSin[2]^2
0.733023 - 4.13735 I
|
BUG # 85 limit: TRIVIAL LIMIT CANNOT BE DONE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
Many integrals in Maple are computed via StruveL/StruveH functions.
The argument of the limits shown below is a smooth function at the limit
point so it is enough just so substitute z = 1 into the function.
limit(StruveL(2,z), z = 1);
ACTUAL: limit(StruveL(2,z), z = 1);
EXPECTED: StruveL(2,1)
COMMENT: If n is add all is right.
seq(limit(StruveL(2*k+1,z), z = 1), k=0..5);
StruveL(1,1), StruveL(3,1), StruveL(5,1), StruveL(7,1),
StruveL(9,1), StruveL(11,1)
However, at the even n Maple cannot calculate the limit.
seq(limit(StruveL(2*k,z), z = 1), k=0..5);
limit(StruveL(0,z),z = 1), limit(StruveL(2,z),z = 1),
limit(StruveL(4,z),z = 1), limit(StruveL(6,z),z = 1),
limit(StruveL(8,z),z = 1), limit(StruveL(10,z),z = 1)
COMMENT: The same holds for StruveH.
|
BUG # 86 limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(sqrt(-signum(sqrt(z^2+I*z+1)-1)),z = infinity);
ACTUAL: I
EXPECTED: -I
CHECKUP: fnormal(evalf(limit(sqrt(-signum(sqrt(z^2+I*z+1)-1)),z = 10^10)));
fnormal(evalf(Limit(sqrt(-signum(sqrt(z^2+I*z+1)-1)),z = infinity)));
0.-1.000000000*I
0.-1.000000000*I
|
BUG # 87 limit: Error, (in X) too many levels of recursion
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(EllipticPi(2,z)+exp(z), z=-infinity);
ACTUAL: Error, (in depends/internal) too many levels of recursion
EXPECTED: 0
CHECKUP: evalf(limit(EllipticPi(2,z)+exp(z), z=-10000));
.1570796346e-3-.9343828485e-3*I
|
BUG # 88 evalf: SPURIOUS DIVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(EllipticPi(2,z), z=-infinity);
ACTUAL: infinity
EXPECTED: 0.
CHECKUP: evalf(Limit(EllipticPi(2,z), z=-10^13));
.1570796327e-12-.3007345009e-11*I
The same problem with
evalf(Limit(EllipticPi(2,z)*exp(z), z=-infinity));
evalf(Limit(EllipticPi(2,z)+exp(z), z=-infinity));
|
BUG # 89 limit: Error, (in X) invalid terms in sum
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(Pi-arccot(sin(z)), z=infinity);
ACTUAL: Error, (in limit/range) invalid terms in sum
EXPECTED: 1/4*Pi .. 3/4*Pi
.7853981635 .. 2.356194490
HINT: plot(Pi-arccot(sin(z)), z=0..100);
WORKAROUND: limit(arctan(sin(z))+Pi/2, z=infinity);
1/4*Pi .. 3/4*Pi
The same problem with
limit(Pi-arccot(cos(z)), z=infinity);
limit(Pi-arccot(sin(z)), z=-infinity);
limit(Pi-arccot(cos(z)), z=-infinity);
limit(Pi-arccot(cos((z))), z=infinity);
limit(Pi-arccot(cos(sqrt(z))), z=infinity);
limit(Pi-arccot(cos(sqrt(-z))), z=-infinity);
limit(Pi-arccot(cos(sqrt(1-z))), z=-infinity);
limit(Pi-arccot(cos(1+sqrt(1-z))), z=-infinity);
limit(Pi-arccot(cos(-1+sqrt(1-z))), z=-infinity);
limit(Pi-arccot(cos(-1+sqrt(1-z))-1), z=-infinity);
limit(Pi-arccot(cos(-1+(1-z)^(1/2))-1), z=-infinity);
|
BUG # 90 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit((exp(sqrt(-z))),z = infinity);
ACTUAL: undefined+undefined*I
EXPECTED: -1-I .. 1+I
CHECKUP: seq(evalf(limit(expand((exp(I*sqrt(z)))),z = 10^k)), k=5..10);
-.4774096142+.8786808654*I, .5623790763+.8268795405*I,\
-.2615753829+.9651830649*I, -.9521553683-.3056143889*I,\
.8799440665-.4750776122*I, -.9993608074+.3574879797e-1*I
WORKAROUND: limit(expand((exp(I*sqrt(z)))),z = infinity);
-1-I .. 1+I
COMMENT: Mathematica 4.2.1 calculates it correctly.
Limit[Exp[Sqrt[-z]], z -> Infinity]
(1 + I) Interval[{-1, 1}]
::::::::::::::::::::::::::::::::::::::::::::::::: 90%
|
BUG # 91 limit: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(tan(sqrt(z)),z = -infinity);
ACTUAL: undefined
EXPECTED: I
CHECKUP: seq(evalf(limit(tan(sqrt(z)),z = -10^k)), k=7..10);
1.000000000*I, 1.*I, 1.000000000*I, 1.*I
|
BUG # 92 limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(AiryAi(sqrt(z)),z = -infinity);
ACTUAL: 0
EXPECTED: undefined
CHECKUP: seq(evalf(limit(AiryAi(sqrt(z)),z = -10^k)), k=10..13);
.8684731304e6474078+.8806659285e6474078*I,
.3812263500e36406425-.3489738753e36406425*I,
-.5767685690e204728379+.1184876142e204728381*I,
.1522631815e1151272295-.1019600743e1151272295*I
EXAMPLE 2: limit(AiryBi(sqrt(z)),z = -infinity);
ACTUAL: 0
EXPECTED: undefined
CHECKUP: seq(evalf(limit(AiryBi(sqrt(z)),z = -10^k)), k=10..13);
-.8806659285e6474078+.8684731304e6474078*I,
.3489738753e36406425+.3812263500e36406425*I,
-.1184876142e204728381-.5767685658e204728379*I,
.1019600742e1151272295+.1522631815e1151272295*I
|
BUG # 93 limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(FresnelS((-z)^(1/3)),z = infinity);
ACTUAL: 1/2
EXPECTED: undefined
CHECKUP: evalf(Limit(FresnelS((-z)^(1/3)),z = 1000));
.9550051175e57-.1660299772e58*I
The same problem with
limit(FresnelC((-z)^(1/3)),z = infinity);
limit(FresnelS((-z)^(2/3)),z = infinity);
limit(FresnelC((-z)^(2/3)),z = infinity);
limit(FresnelS((-z)^(1/4)),z = infinity);
limit(FresnelC((-z)^(1/4)),z = infinity);
limit(FresnelS((-z)^(3/4)),z = infinity);
limit(FresnelC((-z)^(3/4)),z = infinity);
|
BUG # 94 int: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
int(exp(-2*z + abs(1-z^2)), z= 0..infinity);
ACTUAL: undefined
EXPECTED: infinity
CHECKUP: evalf(Int(exp(-2*z + abs(1-z^2)), z= 0..infinity));
Float(infinity)
|
BUG # 95 limit: SPURIOUS CONVERGENCE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(cos(sqrt(1-z))/(1-z), z = infinity);
ACTUAL: 0
EXPECTED: -infinity
CHECKUP: evalf(Limit(cos(sqrt(1-z))/(1-z),z = 10000));
-.1337488633e40
The same problem with
limit(cos(-1+sqrt(1-z))/(1-z),z = infinity);
limit(cos(1+sqrt(1-z))/(1-z),z = infinity);
limit(cos(-1+sqrt(1-z))/(1-z),z = infinity);
limit(cos(-1+sqrt(1-z))/(1-z^(1/3)),z = infinity);
limit(cos(-1+sqrt(1-z))*ln(z)/(1-z^(1/3)),z = infinity);
|
BUG # 96 limit: INVALID OUTPUT SIGN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: limit(FresnelS(z),z = -infinity);
ACTUAL: 1/2
EXPECTED: -1/2
CHECKUP: seq(evalf(limit(FresnelS(z),z = -10^k)), k=100..103);
-.5000000000, -.5000000000, -.5000000000, -.5000000000
EXAMPLE 2: limit(FresnelC(z),z = -infinity);
ACTUAL: 1/2
EXPECTED: -1/2
CHECKUP: seq(evalf(limit(FresnelC(z),z = -10^k)), k=100..103);
-.5000000000, -.5000000000, -.5000000000, -.5000000000
The same problem with
limit(FresnelS(z)*Si(z),z = -infinity);
limit(FresnelS(z)*Ci(z),z = -infinity);
limit(FresnelC(z)*Si(z),z = -infinity);
limit(FresnelC(z)*Ci(z),z = -infinity);
limit(FresnelS(z)*arctan(z),z = -infinity);
limit(FresnelC(z)*arctan(z),z = -infinity);
limit(FresnelS(z+arctan(z)),z = -infinity);
limit(FresnelC(z+arctan(z)),z = -infinity);
limit(BesselJ(1,FresnelC(z)),z = -infinity);
limit(BesselJ(1,FresnelS(z)),z = -infinity);
A similar problem with
limit(FresnelS(sqrt(-z)),z = infinity);
limit(FresnelC(sqrt(-z)),z = infinity);
|
BUG # 97 limit: INVALID DIVERGENCE TYPE
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
limit(1/KelvinKer(0,z),z = infinity);
ACTUAL: -infinity
EXPECTED: -infinity..infinity or undefined
CHECKUP: seq(evalf(limit(1/KelvinKer(0,z),z = 10^k)), k=4..9);
-.6967140106e3073-0.*I,
.4587483394e30712-0.*I,
-.3724641372e307096-0.*I,
-.1408425312e3070930-0.*I,
.1635087033e30709262-0.*I,
-.3393380936e307092578-0.*I
|
BUG # 98 int: INVALID MAGNITUDE OF THE REAL-VALUED INTEGRAL
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
EXAMPLE 1: int(sin(z)*arctanh(z), z= 0..1);
ACTUAL: 1/2*Pi^(3/2)*(4/Pi^(3/2) - 4/Pi^(3/2)*Sum((-1)^(2*_k2)*(-Pi*tan(Pi*_k2)-Psi(1+\
_k2)-Psi(5/2+_k2)-2*ln(2))*2^(-2*_k2)*cos(Pi*_k2)*2^(2*_k2)*(1+_k2)/GAMMA(4+2*\
_k2),_k2 = 0 .. infinity))
2.411313648
EXPECTED: -1/2*cos(1)*(gamma-Ci(2)+ln(2))+1/2*sin(1)*Si(2)
.4465329907
CHECKUP: evalf(Int(sin(z)*arctanh(z), z= 0..1));
.4465329905
EXAMPLE 2: int(cos(z)*arctanh(z), z= 0..1);
ACTUAL: 1/2*Pi^(3/2)*(2/Pi^(1/2)*cos(1)-2/Pi^(1/2)*sin(1))
-.9461493090
EXPECTED: 1/2*(gamma-2*Ci(1)+Ci(2)+ln(2))*sin(1)+1/2*cos(1)*(2*Si(1)-Si(2))
.5060008712
CHECKUP: evalf(Int(cos(z)*arctanh(z), z= 0..1));
.5060008712
COMMENT: Mathematica 4.2.1 calculates these integrals correctly.
|
BUG # 99 int: SPURIOUS undefined
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
int(sin(z)/2^z, z=0..infinity);
ACTUAL: undefined
EXPECTED: 1/(1+ln(2)^2))
.6754689210
The same problem with
int(cos(z)/2^z, z=0..infinity);
|
BUG # 100 simplify: IDENTITY IS BROKEN
`Maple 8.01, IBM INTEL NT, May 1 2002 Build ID 119670`
This bug was introduced in `Maple 7.00, IBM INTEL NT, May 28 2001 Build ID 96223` .
The following 4 expressions are simplified correctly into 0.
expr := sqrt((99+I)^(3/2)): evalf(expr - simplify(expr));
expr := sqrt((99-I)^(3/2)): evalf(expr - simplify(expr));
expr := sqrt((99*I)^(3/2)): evalf(expr - simplify(expr));
expr := sqrt((99/I)^(3/2)): evalf(expr - simplify(expr));
0.-.1e-9*I
0.+.1e-9*I
0.-.1e-7*I
0.+.1e-7*I
However, their counterparts show TERRIBLE bug manifestations!
expr := sqrt((100+I)^(3/2)): evalf(expr - simplify(expr));
expr := sqrt((100-I)^(3/2)): evalf(expr - simplify(expr));
expr := sqrt((100*I)^(3/2)): evalf(expr - simplify(expr));
expr := sqrt((100/I)^(3/2)): evalf(expr - simplify(expr));
ACTUAL: -28.46076575-.2134526304*I # <---------------------------------
-28.46076575+.2134526304*I # <-- All these 4 numbers must be
-10.89136142-26.29407246*I # <-- equal to zero identically
-10.89136142+26.29407246*I # <---------------------------------
EXPECTED: 0.
0.
0.
0.
COMMENT: Derive 5.06, Mathematica 4.2.1, and MuPAD 2.5.2 calculate it
correctly.
The same problem with
expr := 1/10709*sqrt(10709)*sqrt(32230+10*I-1103027/(103-10*I)^(3/2)+107090*I/\
(103-10*I)^(3/2)):
evalf(expr);
evalf(simplify(expr));
ACTUAL: .9088156160e-1-2.611004196*I
1.706291978-.1119792733e-2*I
EXPECTED: 1.706291978-.1119792733e-2*I
1.706291978-.1119792733e-2*I
IMPLICATION: evalf(limit((1/(z^2-I*z+3)-1/(z^2-I*z+3)^(1/2)+3)^(1/2),z = 10));
ACTUAL: .9088156160e-1-2.611004196*I
EXPECTED: 1.706291978-.1119792733e-2*I
COMMENT: seq(evalf(limit((1/(z^2-I*z+3)-1/(z^2-I*z+3)^(1/2)+3)^(1/2),
z = k)), k =1..10);
1.657258306-.4070486549e-3*I,
1.662844802-.4110381255e-2*I,
1.672198935-.4524844638e-2*I,
1.680681699-.3835496552e-2*I,
1.687556357-.3070973420e-2*I,
1.693021914-.2446838594e-2*I,
1.697394301-.1969780540e-2*I,
1.700939497-.1608623980e-2*I,
1.703856885-.1333012836e-2*I,
.9088156160e-1-2.611004196*I
expr :=1/1709*sqrt(10709)*sqrt(32230+10*I-1103027/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
.5694854553-16.36117258*I
10.69203089-.7016887291e-2*I
expr := 1/1709*sqrt(10709)*sqrt(3223+10*I-1103027/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
.4818240181-19.33786916*I
2.821844747-.2658713805e-1*I
expr := 1/1709*sqrt(10709)*sqrt(3223+10*I-110327/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
2.543303771+6.170050035*I
3.374313545+.5188398623e-1*I
expr := 1/1709*sqrt(1709)*sqrt(3223+10*I-110327/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
1.016002572+2.464820277*I
1.347975527+.2072668789e-1*I
expr := 1/1709*sqrt(189)*sqrt(3223+10*I-110327/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
.3378739259+.8196814914*I
.4482722740+.6892706377e-2*I
expr := 1/1709*sqrt(189)*sqrt(3223+10*I-11327/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
.5864760130+.5472823080*I
.4549530485+.7759039308e-2*I
expr := 1/179*sqrt(189)*sqrt(3223+10*I-11327/(103-10*I)^(3/2)+107090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
5.599371544+5.225170193*I
4.343657877+.7407931944e-1*I
expr := 1/179*sqrt(189)*sqrt(3223+10*I-11327/(103-10*I)^(3/2)+17090*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
3.577207487+1.204307534*I
4.351448828+.1661035412e-1*I
expr := 1/179*sqrt(189)*sqrt(3223+10*I-11327/(103-10*I)^(3/2)+197*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
3.567417936-.1051135961*I
4.352994237+.5846248394e-2*I
expr := 1/179*sqrt(189)*sqrt(3223+10*I-1327/(103-10*I)^(3/2)+197*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
4.273152266+.7095780736e-2*I
4.359359359+.6767448511e-2*I
expr := 1/179*sqrt(189)*sqrt(323+10*I-1327/(103-10*I)^(3/2)+197*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
1.074415515+.2822125249e-1*I
1.377758712+.2141284980e-1*I
expr := 1/179*sqrt(89)*sqrt(323+10*I-1327/(103-10*I)^(3/2)+197*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
.7372866537+.1936602042e-1*I
.9454471721+.1469395048e-1*I
expr := 1/179*sqrt(89)*sqrt(323+10*I-1327/(13-10*I)^(3/2)+197*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
.9269541531+.1780782420e-1*I
.9308404777-.9617677861e-2*I
expr := 1/179*sqrt(89)*sqrt(33+10*I-1327/(13-10*I)^(3/2)+197*I/(103-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
.2410132201+.6849017073e-1*I
.2492610255-.3591625958e-1*I
expr := sqrt(89)*sqrt(33+10*I-1327/(13-10*I)^(3/2)+197*I/(101-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
43.16247440+12.80979177*I
44.61565061-6.423929822*I
expr := sqrt(89)*sqrt(33+10*I-137/(13-10*I)^(3/2)+197*I/(101-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
55.36458611+21.97402995*I
53.68513721+7.023786746*I
expr := sqrt(89)*sqrt(33+10*I-137/(13-10*I)^(3/2)+97*I/(101-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
54.05776912+14.54242933*I
53.68663849+6.943411760*I
expr := sqrt(89)*sqrt(33+10*I-17/(13-10*I)^(3/2)+97*I/(101-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
55.12969449+15.47364059*I
54.66113471+8.044001111*I
expr := sqrt(89)*sqrt(13+10*I-17/(13-10*I)^(3/2)+97*I/(101-10*I)^(3/2)):
evalf(expr); evalf(simplify(expr));
38.77848308+21.99820650*I
35.95400873+12.22935200*I
expr := sqrt(89)*sqrt(13+10*I-17/(13-10*I)^(3/2)+97*I/(101-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
39.94907946+21.54482542*I
35.96860209+12.22651401*I
expr := sqrt(89)*sqrt(13+I-17/(13-10*I)^(3/2)+97*I/(101-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
35.98964102+12.78690005*I
33.84669659+1.160249635*I
expr := sqrt(29)*sqrt(13+I-17/(13-10*I)^(3/2)+97*I/(101-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
20.54383462+7.299099203*I
19.32058553+.6623010384*I
expr := sqrt(29)*sqrt(2+I-17/(13-10*I)^(3/2)+97*I/(101-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
13.29995017+11.27459013*I
7.532100287+1.698867956*I
expr := sqrt(29)*sqrt(2+I-17/(3-10*I)^(3/2)+97*I/(101-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
13.36197413+10.93942120*I
8.013219032+1.125243166*I
expr := sqrt(29)*sqrt(2+I-17/(3-10*I)^(3/2)+97*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
13.43587731+11.03426592*I
8.013513923+1.127800842*I
expr := sqrt(29)*sqrt(2+I-17/(3-10*I)^(3/2)+87*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
12.90718557+10.36304628*I
8.011301768+1.110016225*I
expr := sqrt(29)*sqrt(2+I-17/(3-7*I)^(3/2)+87*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
12.70932168+10.15657639*I
7.899496715+.5339720053*I
expr := sqrt(8)*sqrt(2+I-17/(3-7*I)^(3/2)+87*I/(100-I)^(3/2)):
evalf(expr);evalf(simplify(expr));
6.675262776+5.334495264*I
4.149018940+.2804558370*I
expr := sqrt(3)*sqrt(2+I-17/(3-7*I)^(3/2)+87*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
4.087746927+3.266697859*I
2.540744835+.1717434241*I
expr := sqrt(2+I-17/(3-7*I)^(3/2)+87*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
2.360061788+1.886028888*I
1.466899714+.9915611210e-1*I
expr := sqrt(2+I-7/(3-7*I)^(3/2)+87*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
2.397443833+1.954283845*I
1.457902582+.2603693280*I
expr := sqrt(2+I-7/(3-7*I)^(3/2)+17*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
1.605887074+.7384964577*I
1.454264995+.2369579674*I
expr := sqrt(2+I-7/(3-I)^(3/2)+17*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
1.258172283+.8432721708*I
.9736619297+.2255807954*I
expr := sqrt(2-7/(3-I)^(3/2)+17*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
1.070701246+.5239385632*I
.9887056974-.2835632162*I
expr := sqrt(2-1/(3-I)^(3/2)+17*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
1.457634607+.5547172622*I
1.357501883-.2413783869e-1*I
expr := sqrt(2-1/(1-I)^(3/2)+17*I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
1.385395901+.4151662476*I
1.345850725-.1977727670*I
expr := sqrt(2-1/(1-I)^(3/2)+I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
1.341273943-.1675126870*I
1.346804173-.2035716309*I
expr := sqrt(1-1/(1-I)^(3/2)+I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
.9119512444-.2463732612*I
.9272868784-.2956702271*I
expr := sqrt(1-1/(1+I)^(3/2)+I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
.9431118647+.3442451174*I
.9275992701+.2966485030*I
expr := sqrt(1+1/(1+I)^(3/2)+I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
1.125132094-.1996924656*I
1.134011954-.2417709275*I
expr := sqrt(1+I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
1.000498272+.4996572969e-1*I
.9999926267+.4999099490e-3*I
expr := sqrt(1+I/(100-I)^(3/2)):
evalf(expr,30); evalf(simplify(expr),30);
1.00049827229562744544995570763+.499657296914860586609692818080e-1*I
.999992626021405252853971985591+.499909948628481845881797005918e-3*I
expr := sqrt(1/(1+I)^(3/2)+I/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
.6037622114-.3721339260*I
.6407823963-.4278693105*I
expr := sqrt(1/(1+I)^(3/2)+1/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
.6949131925-.3941803677*I
.6416844166-.4280352181*I
expr := sqrt(1/(1+I)^(3/2)+1/(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
.6949131925-.3941803677*I
.6416844166-.4280352181*I
expr := sqrt(1/(1+I)^(3/2)+(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
3.199861153-.1092770355*I
31.62673671-.2458268876*I
expr := sqrt((1+I)^(3/2)+(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
3.269450548+.2146803153*I
31.63307235-.2125352919*I
expr := sqrt(I^(3/2)+(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
3.049731243+.9133692640e-1*I
31.61180952-.2260698760*I
expr := sqrt(I^(1/2)+(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
3.273220722+.8510060939e-1*I
31.63416891-.2259100874*I
expr := sqrt(1+(100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
3.316645348-.2261330490e-1*I
31.63887947-.2370511022*I
expr := sqrt((100-I)^(3/2)):
evalf(expr); evalf(simplify(expr));
3.162307306-.2371695893e-1*I
31.62307306-.2371695893*I
expr := sqrt((10^(10^2)+I)^(3/2)): evalf(expr - simplify(expr));
-.1000000000e76-.7500000000e-25*I
expr := sqrt((100+I)^(5/2)): evalf(expr - simplify(expr));
-313.0605968-3.913330834*I
expr := sqrt((1+100*I)^(5/2)): evalf(expr - simplify(expr));
-116.1876574+290.7278447*I
expr := ((1+100*I)^(3/2))^(1/3): evalf(expr - simplify(expr));
-5.575459692-5.519983861*I
expr := ((100+I)^(3/2))^(1/3): evalf(expr-simplify(expr));
-7.845663381-.3922733623e-1*I
expr := ((100+I)^(5/2))^(1/4): evalf(expr-simplify(expr));
-16.00470224-.1000273572*I
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