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Re: Deleting Integrate[] transformation rule (some progress)
*To*: mathgroup at smc.vnet.net
*Subject*: [mg87680] Re: Deleting Integrate[] transformation rule (some progress)
*From*: UHAP023 at alpha1.rhbnc.ac.uk
*Date*: Tue, 15 Apr 2008 05:54:51 -0400 (EDT)
*Organization*: Low Temperature Physics, RHUL
*References*: <ftq5ab$it$1@smc.vnet.net> <ftscv1$b81$1@smc.vnet.net> <ftv91s$7ur$1@smc.vnet.net>
Dear All,
Some progress on my original query. I tried the following where
the formulae below are expressions which integrate to elliptic
integrals of the first kind and are from mathematical handbooks.
Unprotect[Integrate];
Integrate[1/Sqrt[1 - m_*Sin[phi_]^2], phi_] :=
HoldForm[Integrate[1/Sqrt[1 - m*Sin[phi]^2], phi]]
Integrate[1/Sqrt[(1 - v_^2)*(1 - k_^2*v_^2)], v_] :=
HoldForm[Integrate[1/Sqrt[(1 - v^2)*(1 - k^2*v^2)], v]]
Protect[Integrate];
Subsequent attempts to integrate (eg. [Integrate[1/Sqrt[1 - a*Sin[b]^2],
b]) do indeed leave the integral undone as required. However more
involved expressions such as;
In[52]:=
Integrate[Sqrt[Rvt^2 + (4*R^4)/Rx^4], R] // InputForm
Out[52]//InputForm=
(R*Sqrt[Rvt^2 + (4*R^4)/Rx^4])/3 -
(I/3*Sqrt[2]*Rvt^2*Sqrt[Rvt^2 + (4*R^4)/Rx^4]*
Sqrt[1 - (2*I*R^2)/(Rvt*Rx^2)]*
Sqrt[1 + (2*I*R^2)/(Rvt*Rx^2)]*Rx^4*
EllipticF[I*ArcSinh[Sqrt[2]*R*Sqrt[I/(Rvt*Rx^2)]],
-1])/(Sqrt[I/(Rvt*Rx^2)]*(4*R^4 + Rvt^2*Rx^4))
still produce the unwanted EllipticF[]. My question is, is this; (a)
because my above HoldForm[] argument expressions are failing to
pattern-match the intermediate expressions produced by Integrate[], which
it then uses to produce results containing calls to EllipticF[], (b)
because Mathematica knows more expressions than I entered above
from my handbook which it can integrate up to EllipticF[], or
(c) something else?
Any ideas?
Thanks
Tom.
Ps. The Email address in the header is just a spam-trap.
--
Tom Crane, Dept. Physics, Royal Holloway, University of London, Egham Hill,
Egham, Surrey, TW20 0EX, England.
Email: T.Crane at rhul dot ac dot uk
Fax: +44 (0) 1784 472794
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