Bug in Mathematica 7.0.1 multiple integration?
- To: mathgroup at smc.vnet.net
- Subject: [mg116268] Bug in Mathematica 7.0.1 multiple integration?
- From: Scott Hemphill <hemphill at hemphills.net>
- Date: Wed, 9 Feb 2011 02:10:03 -0500 (EST)
- Reply-to: hemphill at alumni.caltech.edu
I just observed this in a naive method for calculating the volume of a
hypersphere. It works for n = 1..4, but fails for n greater than 4:
Mathematica 7.0 for Linux x86 (64-bit)
Copyright 1988-2009 Wolfram Research, Inc.
In[1]:= n=5
Out[1]= 5
In[2]:= vars = Table[Symbol["x"<>ToString[k]],{k,n}]
Out[2]= {x1, x2, x3, x4, x5}
In[3]:= lims = Sqrt[Table[1-Take[vars,k-1].Take[vars,k-1],{k,n}]]
2 2 2 2 2 2
Out[3]= {1, Sqrt[1 - x1 ], Sqrt[1 - x1 - x2 ], Sqrt[1 - x1 - x2 - x3 ],
2 2 2 2
> Sqrt[1 - x1 - x2 - x3 - x4 ]}
In[4]:= args = Table[{vars[[k]],-lims[[k]],lims[[k]]},{k,n}]
2 2
Out[4]= {{x1, -1, 1}, {x2, -Sqrt[1 - x1 ], Sqrt[1 - x1 ]},
2 2 2 2
> {x3, -Sqrt[1 - x1 - x2 ], Sqrt[1 - x1 - x2 ]},
2 2 2 2 2 2
> {x4, -Sqrt[1 - x1 - x2 - x3 ], Sqrt[1 - x1 - x2 - x3 ]},
2 2 2 2 2 2 2 2
> {x5, -Sqrt[1 - x1 - x2 - x3 - x4 ], Sqrt[1 - x1 - x2 - x3 - x4 ]}}
In[5]:= Integrate @@ Prepend[args,1]
Out[5]= 0
Scott
--
Scott Hemphill hemphill at alumni.caltech.edu
"This isn't flying. This is falling, with style." -- Buzz Lightyear