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*From*: Steven M. Christensen <stevec at yoda.physics.unc.edu>
*Date*: Wed, 7 Apr 93 10:24:50 +0200
*Apparently-to*: mathgroup-send at yoda.physics.unc.edu
Hi mathgroup, dear Wolfram Researcher
A trivial Integral like Int(z^-(3/2) dz) takes almost a minute if the
function is within a product of some constant parameters, which could
be pulled out very easily automatically (for some reasons I want such
trivial integrals to be integrated automatically). Look at the
example below where I ask Mma to perform just the above Integral, which takes
51 Seconds, then I introduce a function FastInt that pulls out the
constants first and then starts integrating - this takes only 0.07 Seconds!!
Crazy - isn't it?
I think Mma should do such simple transformation on its own, or at least
supply a function like FastInt (perhaps a bit smarter than this) performing
these transformations.
I also found that the same behaviour slows down Solve substantially, when
there are too many Symbols (constants) involved.
Mathematica 2.1 for SPARC
Copyright 1988-92 Wolfram Research, Inc.
-- OPEN LOOK graphics initialized --
-- Laserprinter -Psp(arc) installed. Use PSPrint[ -Graphics- ] --
In[1]:= ff:=(-(1.2154068053283*10^-14)*2^(7/8)*c^(7/4)*cm^(3/4)*Mdot^(7/4)*qm^(7/8)* q0^(7/8)*Second*xi^(7/4)*Csc[phi]^(3/2))/ (D^2*g^(3/4)*Lambda*nu^(1/2)*(1 + xi)^(7/8)*z^(1/2)*Csc[alpha]^(3/2))
In[2]:= Timing[Integrate[ff,z]]
-14 7/8 7/4 3/4 7/4 7/8 7/8
Out[2]= {51.7167 Second, (-2.43081 10 2 c cm Mdot qm q0
7/4 3/2
> Second xi Sqrt[z] Csc[phi] ) /
2 3/4 7/8 3/2
> (D g Lambda Sqrt[nu] (1 + xi) Csc[alpha] )}
In[3]:= FastInt[f_,z_Symbol]:=((Int[f,z] //. Int[$a_ $f_,$z_]:>$a Int[$f,$z] /; D[$a,$z]==0) /. Int->Integrate)
In[4]:= Timing[FastInt[ff,z]]
-14 7/8 7/4 3/4 7/4 7/8
Out[4]= {0.0666667 Second, (-2.43081 10 2 c cm Mdot qm
7/8 7/4 3/2
> q0 Second xi Sqrt[z] Csc[phi] ) /
2 3/4 7/8 3/2
> (D g Lambda Sqrt[nu] (1 + xi) Csc[alpha] )}
Heino
```
(o o)
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