A word to you guys and gals from a Maplesoft's customer. .................................................................. http://www.maplesoft.com/support/ "Maplesoft is committed to providing the lowest level of support for the products it sells." .................................................................. DESCRIPTION: Regression bug. 1 of many 1000s. TEST CASE: int(1/(1+z^2+z^5), z= 0..1); EXPECTED: sum(ln(1-1/z)/(2*z+5*z^4),z= RootOf(1+_Z^2+_Z^5)) .7398318370+0.*I CHECKUP: evalf(Int(1/(1+z^2+z^5), z= 0..1)); .7398318370 --------------- (2005) Maple 10.00 ----------------------------- int(1/(1+z^2+z^5),z = 0 .. 1) --------------- (2004) Maple 9.5.1 ----------------------------- int(1/(1+z^2+z^5),z = 0 .. 1) --------------- (2004) Maple 9.5 ------------------------------- int(1/(1+z^2+z^5),z = 0 .. 1) --------------- (2003) Maple 9 --------------------------------- int(1/(1+z^2+z^5),z = 0 .. 1) --------------- (2002) Maple 8 --------------------------------- sum(_R*ln(-109507419/7363759*_R^2+14455759/7363759-2224698426/736 3759*_R^4+797015325/7363759*_R^3+18837605/7363759*_R),_R = RootOf (3233*_Z^5+27*_Z^3+50*_Z^2-1))-sum(_R*ln(-2224698426/7363759*_R^4 +797015325/7363759*_R^3-109507419/7363759*_R^2+18837605/7363759*_ R+7092000/7363759),_R = RootOf(3233*_Z^5+27*_Z^3+50*_Z^2-1)) ..7398318370+0.*I --------------- (2001) Maple 7 --------------------------------- sum(_R*ln(-109507419/7363759*_R^2+14455759/7363759-2224698426/736 3759*_R^4+797015325/7363759*_R^3+18837605/7363759*_R),_R = RootOf (3233*_Z^5+27*_Z^3+50*_Z^2-1))-sum(_R*ln(-2224698426/7363759*_R^4 +797015325/7363759*_R^3-109507419/7363759*_R^2+18837605/7363759*_ R+7092000/7363759),_R = RootOf(3233*_Z^5+27*_Z^3+50*_Z^2-1)) ..7398318370+0.*I --------------- (2000) Maple 6 --------------------------------- sum(_R*ln(-109507419/7363759*_R^2+14455759/7363759-2224698426/736 3759*_R^4+797015325/7363759*_R^3+18837605/7363759*_R),_R = RootOf (3233*_Z^5+27*_Z^3+50*_Z^2-1))-sum(_R*ln(-2224698426/7363759*_R^4 +797015325/7363759*_R^3-109507419/7363759*_R^2+18837605/7363759*_ R+7092000/7363759),_R = RootOf(3233*_Z^5+27*_Z^3+50*_Z^2-1)) ..7398318370+0.*I --------------- (1997) Maple V Rel 5 --------------------------- sum(_R*ln(14455759/7363759+18837605/7363759*_R-2224698426/7363759 *_R^4+797015325/7363759*_R^3-109507419/7363759*_R^2),_R = RootOf( 3233*_Z^5+27*_Z^3+50*_Z^2-1))-sum(_R*ln(18837605/7363759*_R-22246 98426/7363759*_R^4+797015325/7363759*_R^3-109507419/7363759*_R^2+ 7092000/7363759),_R = RootOf(3233*_Z^5+27*_Z^3+50*_Z^2-1)) ..7398318370 --------------- (1995) Maple V Rel 4 --------------------------- sum(_R*ln(14455759/7363759+18837605/7363759*_R-2224698426/7363759 *_R^4+797015325/7363759*_R^3-109507419/7363759*_R^2),_R = RootOf( 3233*_Z^5+27*_Z^3+50*_Z^2-1))-sum(_R*ln(18837605/7363759*_R-22246 98426/7363759*_R^4+797015325/7363759*_R^3-109507419/7363759*_R^2+ 7092000/7363759),_R = RootOf(3233*_Z^5+27*_Z^3+50*_Z^2-1)) ..7398318370 --------------- (1994) Maple V Rel 3 --------------------------- sum(_R*ln(14455759/7363759+18837605/7363759*_R-2224698426/7363759 *_R^4+797015325/7363759*_R^3-109507419/7363759*_R^2),_R = RootOf( 3233*_Z^5+27*_Z^3+50*_Z^2-1))-sum(_R*ln(-2224698426/7363759*_R^4+ 797015325/7363759*_R^3-109507419/7363759*_R^2+18837605/7363759*_R +7092000/7363759),_R = RootOf(3233*_Z^5+27*_Z^3+50*_Z^2-1)) ..7398318370 ----------------------------------------------------------------- .................................................................. Maple: Unsafe at any evaluation http://maple.bug-list.org/maple-crisis.php Teach, learn, and crash your career using Maple. ..................................................................

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5/3/2006 6:17:43 PM

In article <1146680263.908226.205180@i40g2000cwc.googlegroups.com>, Vladimir Bondarenko <vb@cybertester.com> wrote: >TEST CASE: int(1/(1+z^2+z^5), z= 0..1); > >EXPECTED: sum(ln(1-1/z)/(2*z+5*z^4),z= RootOf(1+_Z^2+_Z^5)) > > .7398318370+0.*I > >CHECKUP: evalf(Int(1/(1+z^2+z^5), z= 0..1)); > > .7398318370 > > >--------------- (2005) Maple 10.00 ----------------------------- >int(1/(1+z^2+z^5),z = 0 .. 1) Evidently Maple is unsure about whether the denominator has roots in the interval [0,1]. This works: int(1/(1+z^2+z^5),z = 0 .. 1, continuous); Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada

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5/3/2006 7:16:19 PM

Robert Israel writes http://groups.google.com/group/sci.math.symbolic/msg/58d77d3e5ff5635b RI> Evidently Maple is unsure about whether RI> the denominator has roots in the interval [0,1] My _second_ customer's remark about this Maple regression bug. Maple is _sure_ that the denominator has no roots in the [0,1]. readlib(iscont): # for compatibility with Maple V Rel 5/4/3 iscont(1/(1+z^2+z^5), z= 0..1); --------------- (2005) Maple 10.00 --------------------------- true --------------- (2004) Maple 9.5.1 --------------------------- true --------------- (2004) Maple 9.5 ----------------------------- true --------------- (2003) Maple 9 ------------------------------- true --------------- (2002) Maple 8 ------------------------------- true --------------- (2001) Maple 7 ------------------------------- true --------------- (2000) Maple 6 ------------------------------- true --------------- (1997) Maple V Rel 5 ------------------------- true --------------- (1995) Maple V Rel 4 ------------------------- true --------------- (1994) Maple V Rel 3 ------------------------- true --------------------------------------------------------------- readlib(discont): # for compatibility with Maple V Rel 5/4/3 s := discont(1/(1+z^2+z^5), z); evalf(s); --------------- (2005) Maple 10.00 --------------------------- s := {RootOf(1+_Z^2+_Z^5,-1.193859111)} {-1.193859111} --------------- (2004) Maple 9.5.1 --------------------------- s := {RootOf(1+_Z^2+_Z^5,-1.193859111)} {-1.193859111} --------------- (2004) Maple 9.5 ----------------------------- s := {RootOf(1+_Z^2+_Z^5,-1.193859111)} {-1.193859111} --------------- (2003) Maple 9 ------------------------------- s := {RootOf(1+_Z^2+_Z^5,-1.193859111)} {-1.193859111} --------------- (2002) Maple 8 ------------------------------- s := {RootOf(1+_Z^2+_Z^5,-1.193859111)} {-1.193859111} --------------- (2001) Maple 7 ------------------------------- s := {RootOf(1+_Z^2+_Z^5,-1.193859111)} {-1.193859111} --------------- (2000) Maple 6 ------------------------------- s := {RootOf(1+_Z^2+_Z^5,-1.193859111)} {-1.193859111} --------------- (1997) Maple V Rel 5 ------------------------- s := {RootOf(1+_Z^2+_Z^5,-1.193859111)} {-1.193859111} --------------- (1995) Maple V Rel 4 ------------------------- s := {RootOf(1+_Z^2+_Z^5,-1.193859111)} {-1.193859111} --------------- (1994) Maple V Rel 3 ------------------------- s := {RootOf(1+_Z^2+_Z^5,-1.193859111)} {-1.193859111} --------------------------------------------------------------- Vladimir Bondarenko VM and GEMM architect Co-founder, CEO, Mathematical Director http://www.cybertester.com/ Cyber Tester, LLC http://maple.bug-list.org/ Maple Bugs Encyclopaedia http://www.CAS-testing.org/ CAS Testing

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5/4/2006 1:01:35 AM

In article <1146704495.900898.208170@e56g2000cwe.googlegroups.com>, Vladimir Bondarenko <vb@cybertester.com> wrote: >Robert Israel writes > >http://groups.google.com/group/sci.math.symbolic/msg/58d77d3e5ff5635b > >RI> Evidently Maple is unsure about whether >RI> the denominator has roots in the interval [0,1] > >My _second_ customer's remark about this Maple regression bug. > >Maple is _sure_ that the denominator has no roots in the [0,1]. >readlib(iscont): # for compatibility with Maple V Rel 5/4/3 >iscont(1/(1+z^2+z^5), z= 0..1); My statement was not intended to be taken quite literally. Maple is a computer program, so it can't be "sure" about anything. More to the point, if one Maple command "knows" something, there's no guarantee that a different command also "knows" it. Apparently int does not use iscont to check for singularities. Actually it would have been more accurate to say that Maple isn't sure that the antiderivative doesn't have discontinuities on the interval. The antiderivative is a linear combination of logarithms, and logarithms have branch cuts. If the path of integration crossed a branch cut, int(f(x),x=a..b) = F(b) - F(a) would probably be wrong, even though f itself has no singularities on that path. So you really should do > iscont(int(1/(1+x^2+x^5),x), x=0..1); This also returns true (correctly). But, as I said, int does not seem to use iscont. What it does use is discont: the idea is, rather than just checking whether F is continuous on the interval, you want to know where any possible discontinuities are, and then you can get a correct answer by taking into account the one-sided limits of F at those points. Unfortunately, discont does not seem to work properly for a sum over RootOf's. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada

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5/4/2006 3:59:12 AM

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