Date: Jan 13, 2013 1:27 AM
Author: Tang Laoya
Subject: Ask for help: how to let mathematica output Fortran code with fewest<br> float operations?

Dear all,

I am new to mathematica and I am trying to let mathematicat output some express to Fortran code. However, it seems that it will output some duplicated expressions so that these expressions would be calculated more than once. Is there any good method to define a rule to let mathematica recognize duplicated expressions and assign them to a new variable and then simplify the Fortran code?

Thanks,
Tang Laoya




P.S:

The following is a test code of mathematica and the solution of x, y and z contains many duplicated expression, for example, (-36*a + 20*a**3 - 216*b)**2.

sol = Solve[{x^2 + y^2 + z^2 == 1, x + y + z == a , x*y*z == b}, {x,
y, z}];
xx = x /. sol
yy = y /. sol
zz = z /. sol
Print["Writing Fortran Code . . . : / "];
SetDirectory["F:\\tang\\mathtest"];
strm = OpenWrite["test.f90", FormatType -> FotranForm,
PageWidth -> 70];
(* write subroutine of invisopar*)
WriteString[strm, "subroutine test(x,y,z,a,b)\n"];
WriteString[strm, "implicit none\n"];
WriteString[strm, "real*8::x,y,z,a,b\n"];
nroot = Length[xx];
For[ii = 1, ii <= nroot,
WriteString[strm,
"x = " <> ToString[FortranForm[xx[[ii]]]] <> "\n"]; ii++];
For[ii = 1, ii <= nroot,
WriteString[strm,
"y = " <> ToString[FortranForm[yy[[ii]]]] <> "\n"]; ii++];
For[ii = 1, ii <= nroot,
WriteString[strm,
"z = " <> ToString[FortranForm[zz[[ii]]]] <> "\n"]; ii++];
WriteString[strm, "end subroutine\n"];
Close[strm];
Print["Finished Writing Fortran Code . . . : / "];


When the test.f90 is outputted, the first solution of x is:
x = a/3. + (-6 + 2*a**2)/(3.*2**0.6666666666666666*(-36*a + 20*a**3 + Sqrt(4*(-6 + 2*a**2)**3 + (-36*a + 20*a**3 - 216*b)**2) - 216*b)**0.3333333333333333) - (-36*a + 20*a**3 + Sqrt(4*(-6 + 2*a**2)**3 + (-36*a + 20*a**3 - 216*b)**2) - 216*b)**0.3333333333333333/(6.*2**0.3333333333333333)

I would like that the code is as follows:
tmp0 = 216*b
tmp1 = -36*a + 20*a**3
tmp2 = (tmp1 - tmp0 )**2
tmp3 = -6 + 2*a**2
tmp4 = 4*tmp3**3
tmp5 = Sqrt(tmp4 + tmp2 )
tmp6 = tmp1 + tmp5 - tmp0
tmp7 = tmp6**0.3333333333333333
tmp8 = 2**0.6666666666666666

x = a/3. + tmp3 /(3.*tmp8 *tmp7 ) - tmp7/(6.*tmp8)