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Times-Bold" 8 12 64 "Times-Bold" 17}{SCP_R 1 0 34{COM_R 2 0{TEXT 
6 94 "VERIFICATION OF THE SIMPLEST TOMIMATSU-SATO SOLUTION OF THE
\012                   ERNST EQUATION."}}{COM_R 3 0{TEXT 1 184 "\
015This program was developed in 1986 for the Grad Student Ration
al Calculator program of F. J. Ernst.  Here we rewrite the progra
m for Maple.  Reference: J. Math. Phys. 15, 1409 (1974)."}}{COM_R
 4 0{TEXT 1 57 "\015Employ the FJE ENTERPRISES revision of diffor
ms package:"}}{INP_R 5 0 "> "{TEXT 0 12 "with(share):"}}{INP_R 6 
0 "> "{TEXT 0 46 "readshare(fjeforms,fjeforms);  with(fjeforms):"
}}{COM_R 7 0{TEXT 1 24 "Introduce two constants:"}}{INP_R 8 0 "> \+
"{TEXT 0 25 "defform(p=const,q=const):"}}{COM_R 9 0{TEXT 1 28 "an
d two auxilliary variables"}}{INP_R 10 0 "> "{TEXT 0 11 "v := x^2
-1:"}}{INP_R 11 0 "> "{TEXT 0 11 "w := 1-y^2:"}}{COM_R 12 0{TEXT 
1 267 "Introduce three-dimensional duality operator.  define it b
y giving its value for basic forms (and using linearity).\012This
 choice is equivalent to specifying a conformally flat three-metr
ic (which serves just as well as a flat one for writing out the \
"Ernst Equation\")."}}{INP_R 13 0 "> "{TEXT 0 15 "DIMENSION := 3:
"}}{INP_R 14 0 "> "{TEXT 0 34 "`star`(1) := &^(d(x),d(y),d(phi)):
"}}{INP_R 15 0 "> "{TEXT 0 34 "`star`(&^(d(x),d(y),d(phi))) := 1:
"}}{INP_R 16 0 "> "{TEXT 0 36 "`star`(d(x)) := v * &^(d(y),d(phi)
):"}}{INP_R 17 0 "> "{TEXT 0 34 "`star`(&^(d(y),d(phi))) := d(x)/
v:"}}{INP_R 18 0 "> "{TEXT 0 36 "`star`(d(y)) := w * &^(d(phi),d(
x)):"}}{INP_R 19 0 "> "{TEXT 0 34 "`star`(&^(d(phi),d(x))) := d(y
)/w:"}}{INP_R 20 0 "> "{TEXT 0 38 "`star`(d(phi)) := &^(d(x),d(y)
)/(v*w):"}}{COM_R 21 0{TEXT 1 126 "Numerator and denominator of t
he xi-potential for the\012simplest Tomimatsu-Sato solution.  See
 Phys. Rev. Lett.\01229, 1344 (1972)."}}{INP_R 22 0 "> "{TEXT 0 
53 "num := p^2*(x^4-1)+q^2*(y^4-1)-2*I*p*q*x*y*(x^2-y^2);"}}
{INP_R 23 0 "> "{TEXT 0 37 "den := 2*p*x*(x^2-1)-2*I*q*y*(1-y^2);
"}}{COM_R 24 0{TEXT 1 76 "In the case of the Kerr metric, one wou
ld have\012num := p*x - I*q*y;\012den := 1;"}}{COM_R 25 0{TEXT 1 
90 "Let us now evaluate D *dN - N *dD, where * is the duality\012
operator for differential forms."}}{INP_R 26 0 "> "{TEXT 0 62 "Gr
ad := simpform(expand(den*star(d(num)) - num*star(d(den)))):"}}
{COM_R 27 0{TEXT 1 57 "Left and right sides of \"Ernst Equation\"
 should be equal."}}{INP_R 28 0 "> "{TEXT 0 68 "left := expand((c
c(num)*num - (p^2+q^2)*cc(den)*den)*star(d(Grad)));"}}{INP_R 29 0
 "> "{TEXT 0 75 "right := star(expand(2*(cc(num)*d(num)-(p^2+q^2)
*cc(den)*d(den)) &^ Grad));"}}{INP_R 30 0 "> "{TEXT 0 18 "if left
=right then"}}{INP_R 31 0 "> "{TEXT 0 21 "     Solution := true"}
}{INP_R 32 0 "> "{TEXT 0 4 "else"}}{INP_R 33 0 "> "{TEXT 0 22 "  \+
   Solution := false"}}{INP_R 34 0 "> "{TEXT 0 3 "fi;"}}{INP_R 35
 0 "> "{TEXT 0 0 ""}}}{END}
