Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:06:59.  Memory: start 0001B84C, length 476348.

Command line: +1 Miscel.e Mi_out


C Miscellaneous 1.  N-4 trace of 20 gamma's with paired indices.

	A N,N_
	I i1=N,i2=N,i3=N,i4=N,i5=N,i6=N,i7=N,i8=N,i9=N,iA=N

	Z xx=G(1,"t,"_,i1,i2,i3,i4,i5,i6,i7,i8,i9,iA,i1,i2,i3,i4,i5,i6,i7,i8,i9,iA)

L 1	Id,Gammas
L 9	Id,N=N_+4
	*yep
C To get result as published (Nucl. Phys. B319 (1989) 253):

L 1	Id,Addfa,N_^-1*[N-4]
L 2	Id,N_=N-4
	B [N-4]
	*end
 
xx = 
 + [N-4]
  * ( 1938948096 - 1950961664*N + 845320704*N^2 - 206139904*N^3
  + 31010784*N^4 - 2963856*N^5 + 178416*N^6 - 6456*N^7 + 126*N^8
  - N^9 ) + 0.
 

End run. Time 188 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:10:10.  Memory: start 0001B84C, length 476348.


C Miscellaneous 2.  A test of N-traces.

	I al=N,be=N,mu=N,nu=N,ro=N
	F F
	A N,N_,EP
> P stats
> P list

C The second term is the rotated of the first. The result must be zero.

	Z zero=G(1,2,G6,al,G7,mu,be)*
	       (G(5,5,G6,al,G7,nu,be,ro)-G(5,5,nu,be,ro,G6,al,G7))/4*
	        F(mu,nu,ro)

C The second term is the reversed of the first. The result must be zero.

	Z zerp=G(1,2,G6,al,G7,mu,be)*
	       (G(5,5,G6,al,G7,nu,be,ro)-G(5,5,ro,be,nu,G7,al,G6))/4*
	        F(mu,nu,ro)

L 2	Id,Gammas
L10	Id,N=4-2*EP
	Sum be,mu,nu,ro
	*end


I al=N

A i=i, N, N_, EP

F D, Epf=i, G=i, Gi, G5=i, G6=c, G7, Ug=c, Ubg, DD, DB, DT, DS, DX, 
  DK, DP, DF=u, DC, F

Terms in output 0
Running time 2 sec			Used	Maximum
Generated terms 216 	Input space 	1048 	100000
Equal terms 132     	Output space 	0 	250000
Cancellations 84   	Nr of expr.  	17 	255
Multiplications 2502	String space 	0 	4096
Records written 0 	Merging		0 	0

 
zero = 0.
 
zerp = 0. + 0.
 

End run. Time 2 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:10:13.  Memory: start 0001B84C, length 476348.


C Miscellaneous 3.  Simple freeze example, with B Excl use.

	Common xx
	F F1,F2
	Z xx=F1(a1)*(a1+a2+a3)^2 + F2(a2)*(a1+a2-a3)^2
	B Excl,a1
	*begin
 
xx = 
  + 2*F1(a1)*a2*a3 + F1(a1)*a2^2 + F1(a1)*a3^2 - 2*F2(a2)*a2*a3
  + F2(a2)*a2^2 + F2(a2)*a3^2
 
 + a1
  * ( 2*F1(a1)*a2 + 2*F1(a1)*a3 + 2*F2(a2)*a2 - 2*F2(a2)*a3 )
 
 + a1^2
  * ( F1(a1) + F2(a2) ) + 0.
 

Begin. Time 0 sec.
	Freeze xx
	Z x1=xx
	*begin
 
x1 = + DF(xx,1)
 
 + DF(xx,2)
  * ( a1 )
 
 + DF(xx,3)
  * ( a1^2 ) + 0.
 

Begin. Time 1 sec.
	Z x2=xx
L 2	Id,Expand,xx
	B Excl,a1
	*end
 
x2 = 
  + 2*F1(a1)*a2*a3 + F1(a1)*a2^2 + F1(a1)*a3^2 - 2*F2(a2)*a2*a3
  + F2(a2)*a2^2 + F2(a2)*a3^2
 
 + a1
  * ( 2*F1(a1)*a2 + 2*F1(a1)*a3 + 2*F2(a2)*a2 - 2*F2(a2)*a3 )
 
 + a1^2
  * ( F1(a1) + F2(a2) ) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:10:16.  Memory: start 0001B84C, length 476348.


C Miscellaneous 4.  Example Use statement.

	I al,be=N,ga
	I ia=3,ib=3,ic=3,id=3

	Z xx=F1(al,be,ga,ia,ib,ic,id)*F2(al,be,ga,ia,ib,ic,id)

	Sum al,be,ga,ia,ib,ic,id
	Use mu,nu,3,ic,id,N,na
	*end
 
xx = + F1(mu,na,nu,ic,id,Naa,Nab)*F2(mu,na,nu,ic,id,Naa,Nab) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:10:19.  Memory: start 0001B84C, length 476348.


C Miscellaneous 5.  Example Chain and Use statements.

	I i1,i2,i3,i4,i5,i6
	F Tr

	Z xx =
	 f1(ab1,i2,i3,def)*f2(ab1,i1,i2)*f3(i3,i1,ab3)
	 + f1(ab1,i2,i3,def)*f2(ab1,i2)*f3(i3,ab3)

L 1	Id,Chain,Tr,i1,i2,i3,i4
	*begin
 
xx = + Tr(f1,ab1,def,f3,ab3,f2,ab1)
 
 + f2(ab1)*f1(ab1,def)*f3(ab3) + 0.
 

Begin. Time 1 sec.

C Next, using also the Use statement:

	F X_,Y,Wg,Tr,U
	I mu,nu,ic,id

	Z xx = Wg(mu,ic,id)*U(mu)*X_(nu,ic)*Y(id,nu)

L 1	Id,Chain,Tr,ic,id
L 2	Id,Commu,Tr
	Sum,mu,nu
	Use mu,nu
	*begin
 
xx = + U(mu)*X_(nu)*Wg(mu)*Y(nu) + 0.
 

Begin. Time 1 sec.

C Open ended. Nothing is done:

	F X_,Y,Wg,Tr,U
	I mu,nu,ic,id

	Z xx = Wg(mu,ic,id)*U(mu)*X_(nu,ic)*Y(nu)

L 1	Id,Chain,Tr,ic,id,ie,if
L 2	Id,Commu,Tr
	Sum,mu,nu
	Use mu,nu
	*begin
 
xx = + Wg(mu,ic,id)*U(mu)*X_(nu,ic)*Y(nu) + 0.
 

Begin. Time 1 sec.

C Now specifying the "S option:

	F X_,Y,Wg,Tr,U
	I mu,nu,ic,id

	Z xx = Wg(mu,ic,id)*U(mu)*X_(nu,ic)*Y(nu)

L 1	Id,Chain,"S,Tr,ic,id,ie,if
L 2	Id,Commu,Tr
	Sum,mu,nu
	Use mu,nu
	*end
 
xx = + U(mu)*Y(nu)*X_(nu)*Wg(mu,id) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:10:21.  Memory: start 0001B84C, length 476348.


C Miscellaneous 6.  Example invisible function.

C First a simple expression, no invisible statement.
C Output second differs as F2 is removed before printing:

	F F1,F2
	Z xx=F1(-a,b)*a1*a2*a3^2*F1(a,b,c)
	 - F3(-a,b)*a1*a2^-2*a3^2*F1(a,b,c)
	 + abc*def*a3

L 1	Id,Count,"N,F2,a3,-7 : a1,1,a2,3

	*begin
 
xx = 
 + F2(114,123)*F3(-a,b)*F1(a,b,c)
  * ( - a1*a2^-2*a3^2 )
 
 + F2(114,-124)*F1(-a,b)*F1(a,b,c)
  * ( a1*a2*a3^2 )
 
 + F2(121,-128)
  * ( a3*abc*def ) + 0.
 

Begin. Time 0 sec.


	F F1,F2
	Z xx=F1(-a,b)*a1*a2*a3^2*F1(a,b,c)
	 - F3(-a,b)*a1*a2^-2*a3^2*F1(a,b,c)
	 + abc*def*a3

L 1	Id,Count,"N,F2,a3,-7 : a1,1,a2,3
	Invisible F2
	*begin
 
xx = 
 + F3(-a,b)*F1(a,b,c)
  * ( - a1*a2^-2*a3^2 )
 
 + F1(-a,b)*F1(a,b,c)
  * ( a1*a2*a3^2 )
 
  + a3*abc*def + 0.
 

Begin. Time 0 sec.

C Another example, involving algebraic quantities with negative exponent.

	Z xx=(a+b)^5/a^2
	*begin
 
xx =  + 10*a*b^2 + 5*a^2*b + a^3 + a^-2*b^5 + 5*a^-1*b^4 + 10*b^3 + 0.
 

Begin. Time 0 sec.

	F F1

	Z xx=(a+b)^5/a^2

L 2	Id,Count,"N,F1,a,1
	Invisible F1
	*end
 
xx = 
  + a^-2*b^5
 
  + 5*a^-1*b^4
 
  + 10*b^3
 
  + 10*a*b^2
 
  + 5*a^2*b
 
  + a^3 + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:10:24.  Memory: start 0001B84C, length 476348.


C Miscellaneous 7.  Options in Commu command.

C Without options.

	F f3,f1,f2,f4

	Z xx=f1(a,b,c)*f2(a1,a2)*f3*f4(b1,b2)

L 1	Id,Commu,f1,f3
	*begin
 
xx = + f2(a1,a2)*f4(b1,b2)*f3*f1(a,b,c) + 0.
 

Begin. Time 0 sec.

C With the "B option:

	F f3,f1,f2,f4

	Z xx=f1(a,b,c)*f2(a1,a2)*f3*f4(b1,b2)

L 1	Id,Commu,"B,f1,f3
	*begin
 
xx = + f3*f1(a,b,c)*f2(a1,a2)*f4(b1,b2) + 0.
 

Begin. Time 0 sec.

C With the "N option:
 
	F f3,f1,f2,f4

	Z xx=f1(a,b,c)*f2(a1,a2)*f3*f4(b1,b2)
L 1	Id,Commu,"N,f1,f3
	*begin
 
xx = + f2(a1,a2)*f4(b1,b2)*f1(a,b,c)*f3 + 0.
 

Begin. Time 0 sec.

C With both "B and "N option:
 
	F f3,f1,f2,f4

	Z xx=f1(a,b,c)*f2(a1,a2)*f3*f4(b1,b2)
L 1	Id,Commu,"N,"B,f1,f3
	*end
 
xx = + f1(a,b,c)*f3*f2(a1,a2)*f4(b1,b2) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:10:26.  Memory: start 0001B84C, length 476348.


C Miscellaneous 8.  Example symmetrization X-expressions and substitions.

	F F1
	X BAC(b1,b2,a1,a2,c1,c2): F1(a1,a2,b1,b2,c1,c2)
	X BAC~AB(b1,b2,a1,a2,c1,c2): F1(a1,a2,b1,b2,c1,c2)
	X K~BAC~AB(b1,b2,a1,a2,c1,c2): F1(a1,a2,b1,b2,c1,c2)
	X L~BAC~AB(x1,x2;b1,b2,a1,a2,c1,c2;z1,z2): F1(x1,x2,a1,a2,b1,b2,c1,c2,z1,z2)
> P lists

	Z xx = t1*ABC(1,2,3,4,5,6)
	     + t2*ABCAB(1,2,3,4,5,6)
	     + t3*KABCAB(1,2,3,4,5,6)
	     + t4*LABCAB(xx1,xx2,1,2,3,4,5,6,yy1,yy2)
	     + labck(p1,p2,y1,y2,y3,q1,q2)

L 2	Id,l~bac~k(x1~,x2~;xb~,xa~,xc~;z1~,z2~): hello*F1(x1,x2,xa,xb,xc,z1,z2)
	*end


A i=i, t1, t2, t3, t4, xx1, xx2, yy1, yy2, p1, p2, y1, y2, y3, q1, 
  q2, hello

F D, Epf=i, G=i, Gi, G5=i, G6=c, G7, Ug=c, Ubg, DD, DB, DT, DS, DX, 
  DK, DP, DF=u, DC, F1, labck

E ABC=X1, ABCAB=X1, KABCAB=X1, LABCAB=X1
 
xx = 
 + F1(xx1,xx2,1,2,3,4,5,6,yy1,yy2)
  * ( t4 )
 
 + F1(p1,p2,y1,y2,y3,q1,q2)
  * ( hello )
 
 + F1(1,2,3,4,5,6)
  * ( t1 + t2 + t3 ) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:10:29.  Memory: start 0001B84C, length 476348.


C Miscellaneous 9.  Switches Sw0 etc. Run with S=62. The Synonym statement.

C If on the command line S=# is specified (# byte size, range -128,127)
  then Sw0=#. Default setting is zero.

	Synonym Xxx = _Sw0

	Set _Sw9 = 3
	Set _Sw1 = 2-3*(22/2-4)
	Set _Sw2 = 2-(22&2-4)*_Sw9
	Set _Sw3 = 6
	Set _Sw4 = 1 | 0x20

	Z xx = (a + b) ^ 3 + a0^_Sw0 + a1^_Sw1 + a2^_Sw2 + a3^_Sw3 + a4*_Sw4

	Gotoif 20, _Sw3 > 5


L 2	Id,b = a + c

	*end
 
xx = 
  + a0^62 + a1^-19 + a2^8 + a3^6 + 33*a4 + 6*a*c^2 + 12*a^2*c
  + 8*a^3 + c^3 + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:10:31.  Memory: start 0001B84C, length 476348.


C Miscellaneous 10. Trace of 12 gamma's. Writes xg12.

	V p1,p2,p3,p4,p5,p6,p7,p8,p9,pA,pB,pC,pD,pE,pF
	Common xx
	*fix

Begin. Time 0 sec.
	Z xx = G(1,1,p1,p2,p3,p4,p5,p6,p7,p8,p9,pA,pB,pC)
> P stats
	Show
L 1	Id,Gammas
	B p1,p2
> P noutput
	*begin

Terms in output 4383
Running time 10 sec			Used	Maximum
Generated terms 5139 	Input space 	758 	100000
Equal terms 714     	Output space 	128716 	250000
Cancellations 42   	Nr of expr.  	18 	255
Multiplications 31546	String space 	0 	4096
Records written 0 	Merging		0 	0


Begin. Time 12 sec.
	Write xg12
	*end

Terms in output 0
Running time 14 sec			Used	Maximum
Generated terms 0 	Input space 	86 	100000
Equal terms 0     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	7 	255
Multiplications 0	String space 	0 	4096
Records written 27 	Merging		0 	0

At end: 0 bytes.

End run. Time 14 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:10:48.  Memory: start 0001B84C, length 476348.


C Miscellaneous 11. Numerical evaluation of previous. Needs xg12.

	V p1,p2,p3,p4,p5,p6,p7,p8,p9,pA,pB,pC,pD,pE,pF
	Enter xg12
	*fix

Begin. Time 2 sec.

	Z xxx=xx

	*yep

C If there is no numerical factor in the above trace then this
 must be the outcome, using the numbers below.

 Terms out 4383, in 4383.

 Terms in output 1
 Running time 33 sec			Used	Maximum
 Generated terms 4383 	Input space 	2726 	100000
 Equal terms 4382     	Output space 	32 	250000
 Cancellations 0   	Nr of expr.  	6 	255
 Multiplications 8766	String space 	0 	4096
 Records written 20 	Merging		0 	0

 
 xx =  + .3025863551D+48 + 0.

> P Stats
> P ninput

Terms out 4383, in 4383.

Terms in output 1
Running time 33 sec			Used	Maximum
Generated terms 4383 	Input space 	2726 	100000
Equal terms 4382     	Output space 	32 	250000
Cancellations 0   	Nr of expr.  	7 	255
Multiplications 8766	String space 	0 	4096
Records written 20 	Merging		0 	0

 
xxx =  + .3025863551D+48 + 0.
 

End run. Time 33 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:11:24.  Memory: start 0001B84C, length 476348.


C Miscellaneous 12. Trace of 14 or 16 gamma's.
C By default the 14 gamma case is done. If on the command line
  a non-zero Sw0 is specified (with the S=.. option) then the 16 gamma
  case is executed.

	Large 5
> P stats
	V p1,p2,p3,p4,p5,p6,p7,p8,p9,pA,pB,pC,pE,pF,pG,pH
	B p1Dp2,p1Dp3,p1Dp4,p1Dp5,p1Dp6,p1Dp7,p1Dp8,p1Dp9,p1DpA,p1DpB,p1DpC,
	  p1DpE,p1DpF,p1DpG,p1DpH

	Gotoifn 16,_Sw0=0

	Z xx=
	  G(1,p1)*G(1,p2)*G(1,p3)*G(1,p4)
	 *G(1,p5)*G(1,p6)*G(1,p7)*G(1,p8)
	 *G(1,p9)*G(1,pA)*G(1,pB)*G(1,pC)
	 *G(1,pE)*G(1,pF)
	Goto 20



L 1	Id,Trick,Trace,1
	Outlimit,6500000
> P noutput
	Showl
	*yep

Terms in output 7038
Running time 17 sec			Used	Maximum
Generated terms 8192 	Input space 	882 	100000
Equal terms 1096     	Output space 	215968 	250000
Cancellations 58   	Nr of expr.  	20 	255
Multiplications 55468	String space 	0 	4096
Records written 0 	Merging		0 	0

At 22 sec: 68484 bytes. Subfile TAPB000L, 140778 bytes.

Terms in output 14141
Running time 36 sec			Used	Maximum
Generated terms 16384 	Input space 	882 	100000
Equal terms 2125     	Output space 	196816 	250000
Cancellations 118   	Nr of expr.  	20 	255
Multiplications 106125	String space 	0 	4096
Records written 15 	Merging		0 	0

At 44 sec: 139808 bytes. Subfile TAPC000L, 140770 bytes.

Terms in output 21505
Running time 56 sec			Used	Maximum
Generated terms 24576 	Input space 	882 	100000
Equal terms 2833     	Output space 	185136 	250000
Cancellations 238   	Nr of expr.  	20 	255
Multiplications 151655	String space 	0 	4096
Records written 30 	Merging		0 	0

At 64 sec: 194086 bytes. Subfile TAPD000L, 133954 bytes.
At 75 sec: 226744 bytes. Subfile TAPE000L, 72640 bytes.

Terms in output 27006
Running time 78 sec			Used	Maximum
Generated terms 31599 	Input space 	882 	100000
Equal terms 4001     	Output space 	250048 	250076
Cancellations 592   	Nr of expr.  	20 	255
Multiplications 194076	String space 	0 	4096
Records written 52 	Merging		0 	2


Terms in output 26931
Running time 94 sec			Used	Maximum
Generated terms 31599 	Input space 	882 	100000
Equal terms 4076     	Output space 	111888 	250076
Cancellations 592   	Nr of expr.  	20 	255
Multiplications 194076	String space 	0 	4096
Records written 91 	Merging		0 	5

At 96 sec: 205180 bytes. Subfile TAP4002L, 432030 bytes.

C The set of numbers below is for randomly chosen four-vectors.

C Result should be:
  14 G:
 xx =  + .9427566923E+56 + 0.
 
 Running time 225 (91 first part) sec with *yep.
 Running time 180 sec (no *yep).
 Generated terms 31599


  16 G:
 xx =  + .7804709442D+64 + 0.

 Running time 1820 (1027 first part) sec with *yep
 Running time 1185 sec (no *yep).
 Generated terms 197541


> P ninput
> P output

Terms in output 1
Running time 136 sec			Used	Maximum
Generated terms 8192 	Input space 	2720 	100000
Equal terms 8191     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 16384	String space 	0 	4096
Records written 97 	Merging		0 	0


Terms in output 1
Running time 176 sec			Used	Maximum
Generated terms 16384 	Input space 	2720 	100000
Equal terms 16383     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 32768	String space 	0 	4096
Records written 97 	Merging		0 	0


Terms in output 1
Running time 215 sec			Used	Maximum
Generated terms 24576 	Input space 	2720 	100000
Equal terms 24575     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 49152	String space 	0 	4096
Records written 97 	Merging		0 	0


Terms out 26931, in 26931.

Terms in output 1
Running time 227 sec			Used	Maximum
Generated terms 26931 	Input space 	2720 	100000
Equal terms 26930     	Output space 	32 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 53862	String space 	0 	4096
Records written 97 	Merging		0 	0

 
xx =  + .9427566923D+56 + 0.
 
At end: 0 bytes.

End run. Time 227 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 22:15:13.  Memory: start 0001B84C, length 476348.


C Miscellaneous 12. Trace of 14 or 16 gamma's.
C By default the 14 gamma case is done. If on the command line
  a non-zero Sw0 is specified (with the S=.. option) then the 16 gamma
  case is executed.

	Large 5
> P stats
	V p1,p2,p3,p4,p5,p6,p7,p8,p9,pA,pB,pC,pE,pF,pG,pH
	B p1Dp2,p1Dp3,p1Dp4,p1Dp5,p1Dp6,p1Dp7,p1Dp8,p1Dp9,p1DpA,p1DpB,p1DpC,
	  p1DpE,p1DpF,p1DpG,p1DpH

	Gotoifn 16,_Sw0=0


	Z xx=
	  G(1,p1)*G(1,p2)*G(1,p3)*G(1,p4)
	 *G(1,p5)*G(1,p6)*G(1,p7)*G(1,p8)
	 *G(1,p9)*G(1,pA)*G(1,pB)*G(1,pC)
	 *G(1,pE)*G(1,pF)
	 *G(1,pG)*G(1,pH)


L 1	Id,Trick,Trace,1
	Outlimit,6500000
> P noutput
	Showl
	*yep

Terms in output 7036
Running time 19 sec			Used	Maximum
Generated terms 8192 	Input space 	940 	100000
Equal terms 1050     	Output space 	233126 	250000
Cancellations 106   	Nr of expr.  	22 	255
Multiplications 59236	String space 	0 	4096
Records written 0 	Merging		0 	0

At 23 sec: 79326 bytes. Subfile TAPB000L, 147210 bytes.

Terms in output 14158
Running time 40 sec			Used	Maximum
Generated terms 16384 	Input space 	940 	100000
Equal terms 2038     	Output space 	223452 	250000
Cancellations 188   	Nr of expr.  	22 	255
Multiplications 112503	String space 	0 	4096
Records written 15 	Merging		0 	0

At 45 sec: 161436 bytes. Subfile TAPC000L, 146700 bytes.

Terms in output 21360
Running time 60 sec			Used	Maximum
Generated terms 24576 	Input space 	940 	100000
Equal terms 2938     	Output space 	225034 	250000
Cancellations 278   	Nr of expr.  	22 	255
Multiplications 159185	String space 	0 	4096
Records written 30 	Merging		0 	0

At 66 sec: 231982 bytes. Subfile TAPD000L, 145170 bytes.

Terms in output 28540
Running time 81 sec			Used	Maximum
Generated terms 32768 	Input space 	940 	100000
Equal terms 3902     	Output space 	224030 	250000
Cancellations 326   	Nr of expr.  	22 	255
Multiplications 212836	String space 	0 	4096
Records written 45 	Merging		0 	0

At 87 sec: 307816 bytes. Subfile TAPE000L, 147210 bytes.

Terms in output 35498
Running time 102 sec			Used	Maximum
Generated terms 40960 	Input space 	940 	100000
Equal terms 5077     	Output space 	211536 	250000
Cancellations 385   	Nr of expr.  	22 	255
Multiplications 267861	String space 	0 	4096
Records written 60 	Merging		0 	0

At 110 sec: 388308 bytes. Subfile TAPF000L, 147200 bytes.

Terms in output 42454
Running time 123 sec			Used	Maximum
Generated terms 49152 	Input space 	940 	100000
Equal terms 6250     	Output space 	196490 	250000
Cancellations 448   	Nr of expr.  	22 	255
Multiplications 321386	String space 	0 	4096
Records written 75 	Merging		0 	0

At 135 sec: 468400 bytes. Subfile TAP8001L, 292260 bytes.

Terms in output 49925
Running time 148 sec			Used	Maximum
Generated terms 57344 	Input space 	940 	100000
Equal terms 6809     	Output space 	198430 	250000
Cancellations 610   	Nr of expr.  	22 	255
Multiplications 367786	String space 	0 	4096
Records written 105 	Merging		1 	0

At 160 sec: 533130 bytes. Subfile TAP7001L, 287910 bytes.

Terms in output 56755
Running time 175 sec			Used	Maximum
Generated terms 65536 	Input space 	940 	100000
Equal terms 7940     	Output space 	193514 	250000
Cancellations 841   	Nr of expr.  	22 	255
Multiplications 423773	String space 	0 	4096
Records written 134 	Merging		2 	0

At 187 sec: 602044 bytes. Subfile TAPA001L, 294280 bytes.

Terms in output 63772
Running time 200 sec			Used	Maximum
Generated terms 73728 	Input space 	940 	100000
Equal terms 9073     	Output space 	179966 	250000
Cancellations 883   	Nr of expr.  	22 	255
Multiplications 478673	String space 	0 	4096
Records written 164 	Merging		3 	0

At 214 sec: 662064 bytes. Subfile TAP6001L, 294300 bytes.

Terms in output 70776
Running time 226 sec			Used	Maximum
Generated terms 81920 	Input space 	940 	100000
Equal terms 10182     	Output space 	164666 	250000
Cancellations 962   	Nr of expr.  	22 	255
Multiplications 530539	String space 	0 	4096
Records written 194 	Merging		4 	0

At 239 sec: 738080 bytes. Subfile TAP9001L, 294090 bytes.

Terms in output 78339
Running time 251 sec			Used	Maximum
Generated terms 90112 	Input space 	940 	100000
Equal terms 10656     	Output space 	179390 	250000
Cancellations 1117   	Nr of expr.  	22 	255
Multiplications 577370	String space 	0 	4096
Records written 224 	Merging		5 	0

At 268 sec: 800136 bytes. Subfile TAPC002L, 431770 bytes.

Terms in output 85369
Running time 280 sec			Used	Maximum
Generated terms 98304 	Input space 	940 	100000
Equal terms 11718     	Output space 	172910 	250000
Cancellations 1217   	Nr of expr.  	22 	255
Multiplications 627074	String space 	0 	4096
Records written 268 	Merging		6 	0

At 297 sec: 872596 bytes. Subfile TAPD002L, 438170 bytes.

Terms in output 92984
Running time 308 sec			Used	Maximum
Generated terms 106496 	Input space 	940 	100000
Equal terms 12151     	Output space 	189318 	250000
Cancellations 1361   	Nr of expr.  	22 	255
Multiplications 674084	String space 	0 	4096
Records written 312 	Merging		7 	0

At 325 sec: 937298 bytes. Subfile TAPE002L, 438270 bytes.

Terms in output 100557
Running time 338 sec			Used	Maximum
Generated terms 114688 	Input space 	940 	100000
Equal terms 12681     	Output space 	199160 	250000
Cancellations 1450   	Nr of expr.  	22 	255
Multiplications 722936	String space 	0 	4096
Records written 356 	Merging		8 	0

At 354 sec: 1001692 bytes. Subfile TAPF002L, 439830 bytes.

Terms in output 108749
Running time 367 sec			Used	Maximum
Generated terms 122880 	Input space 	940 	100000
Equal terms 12681     	Output space 	229966 	250000
Cancellations 1450   	Nr of expr.  	22 	255
Multiplications 769277	String space 	0 	4096
Records written 400 	Merging		9 	0

At 380 sec: 1061372 bytes. Subfile TAPB002L, 441410 bytes.

Terms in output 116412
Running time 396 sec			Used	Maximum
Generated terms 131072 	Input space 	1066 	100000
Equal terms 13210     	Output space 	234588 	250000
Cancellations 1450   	Nr of expr.  	22 	255
Multiplications 819923	String space 	0 	4096
Records written 444 	Merging		10 	0

At 412 sec: 1116502 bytes. Subfile TAP7002L, 578850 bytes.
At 444 sec: 1173138 bytes. Subfile TAP8002L, 579090 bytes.

Terms in output 124249
Running time 445 sec			Used	Maximum
Generated terms 139264 	Input space 	1066 	100000
Equal terms 13565     	Output space 	14798 	250000
Cancellations 1450   	Nr of expr.  	22 	255
Multiplications 870416	String space 	0 	4096
Records written 560 	Merging		12 	0

At 475 sec: 1231368 bytes. Subfile TAP9002L, 583140 bytes.

Terms in output 132329
Running time 477 sec			Used	Maximum
Generated terms 147456 	Input space 	1066 	100000
Equal terms 13677     	Output space 	45654 	250000
Cancellations 1450   	Nr of expr.  	22 	255
Multiplications 917036	String space 	0 	4096
Records written 619 	Merging		13 	0

At 507 sec: 1290092 bytes. Subfile TAPA002L, 585720 bytes.

Terms in output 140119
Running time 510 sec			Used	Maximum
Generated terms 155648 	Input space 	1066 	100000
Equal terms 14079     	Output space 	55990 	250000
Cancellations 1450   	Nr of expr.  	22 	255
Multiplications 966565	String space 	0 	4096
Records written 678 	Merging		14 	0

At 538 sec: 1343066 bytes. Subfile TAP6002L, 581790 bytes.

Terms in output 147484
Running time 543 sec			Used	Maximum
Generated terms 163840 	Input space 	1066 	100000
Equal terms 14864     	Output space 	67224 	250000
Cancellations 1492   	Nr of expr.  	22 	255
Multiplications 1020026	String space 	0 	4096
Records written 736 	Merging		15 	0

At 575 sec: 1399908 bytes. Subfile TAPC003L, 725940 bytes.

Terms in output 154782
Running time 580 sec			Used	Maximum
Generated terms 172032 	Input space 	1066 	100000
Equal terms 15689     	Output space 	66426 	250000
Cancellations 1561   	Nr of expr.  	22 	255
Multiplications 1071422	String space 	0 	4096
Records written 809 	Merging		16 	0

At 612 sec: 1455336 bytes. Subfile TAPD003L, 726160 bytes.

Terms in output 161966
Running time 617 sec			Used	Maximum
Generated terms 180224 	Input space 	1066 	100000
Equal terms 16667     	Output space 	61904 	250000
Cancellations 1591   	Nr of expr.  	22 	255
Multiplications 1122800	String space 	0 	4096
Records written 882 	Merging		17 	0

At 651 sec: 1512074 bytes. Subfile TAPB003L, 725980 bytes.

Terms in output 168706
Running time 654 sec			Used	Maximum
Generated terms 188416 	Input space 	1132 	100000
Equal terms 17543     	Output space 	47218 	250000
Cancellations 2167   	Nr of expr.  	22 	255
Multiplications 1183520	String space 	0 	4096
Records written 955 	Merging		18 	0

At 690 sec: 1570656 bytes. Subfile TAPE003L, 730200 bytes.

Terms in output 175817
Running time 693 sec			Used	Maximum
Generated terms 196608 	Input space 	1132 	100000
Equal terms 18192     	Output space 	41624 	250000
Cancellations 2599   	Nr of expr.  	22 	255
Multiplications 1246988	String space 	0 	4096
Records written 1028 	Merging		19 	0

At 712 sec: 1585470 bytes. Subfile TAPF002L, 626720 bytes.

Terms in output 176007
Running time 715 sec			Used	Maximum
Generated terms 197541 	Input space 	1132 	100000
Equal terms 18756     	Output space 	239886 	239908
Cancellations 2778   	Nr of expr.  	22 	255
Multiplications 1253864	String space 	0 	4096
Records written 1091 	Merging		20 	2


Terms in output 166533
Running time 847 sec			Used	Maximum
Generated terms 197541 	Input space 	1132 	100000
Equal terms 27078     	Output space 	145128 	239908
Cancellations 3930   	Nr of expr.  	22 	255
Multiplications 1253864	String space 	0 	4096
Records written 1390 	Merging		20 	25

At 849 sec: 1291124 bytes. Subfile TAP400EL, 3004516 bytes.

C The set of numbers below is for randomly chosen four-vectors.

C Result should be:
  14 G:
 xx =  + .9427566923E+56 + 0.
 
 Running time 225 (91 first part) sec with *yep.
 Running time 180 sec (no *yep).
 Generated terms 31599


  16 G:
 xx =  + .7804709442D+64 + 0.

 Running time 1820 (1027 first part) sec with *yep
 Running time 1185 sec (no *yep).
 Generated terms 197541


> P ninput
> P output

Terms in output 1
Running time 891 sec			Used	Maximum
Generated terms 8192 	Input space 	2720 	100000
Equal terms 8191     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 16384	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 933 sec			Used	Maximum
Generated terms 16384 	Input space 	2720 	100000
Equal terms 16383     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 32768	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 975 sec			Used	Maximum
Generated terms 24576 	Input space 	2720 	100000
Equal terms 24575     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 49152	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1017 sec			Used	Maximum
Generated terms 32768 	Input space 	2720 	100000
Equal terms 32767     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 65536	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1059 sec			Used	Maximum
Generated terms 40960 	Input space 	2720 	100000
Equal terms 40959     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 81920	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1101 sec			Used	Maximum
Generated terms 49152 	Input space 	2720 	100000
Equal terms 49151     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 98304	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1143 sec			Used	Maximum
Generated terms 57344 	Input space 	2720 	100000
Equal terms 57343     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 114688	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1185 sec			Used	Maximum
Generated terms 65536 	Input space 	2720 	100000
Equal terms 65535     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 131072	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1227 sec			Used	Maximum
Generated terms 73728 	Input space 	2720 	100000
Equal terms 73727     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 147456	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1270 sec			Used	Maximum
Generated terms 81920 	Input space 	2720 	100000
Equal terms 81919     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 163840	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1312 sec			Used	Maximum
Generated terms 90112 	Input space 	2720 	100000
Equal terms 90111     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 180224	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1354 sec			Used	Maximum
Generated terms 98304 	Input space 	2720 	100000
Equal terms 98303     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 196608	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1396 sec			Used	Maximum
Generated terms 106496 	Input space 	2720 	100000
Equal terms 106495     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 212992	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1438 sec			Used	Maximum
Generated terms 114688 	Input space 	2720 	100000
Equal terms 114687     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 229376	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1480 sec			Used	Maximum
Generated terms 122880 	Input space 	2720 	100000
Equal terms 122879     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 245760	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1522 sec			Used	Maximum
Generated terms 131072 	Input space 	2720 	100000
Equal terms 131071     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 262144	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1565 sec			Used	Maximum
Generated terms 139264 	Input space 	2720 	100000
Equal terms 139263     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 278528	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1607 sec			Used	Maximum
Generated terms 147456 	Input space 	2720 	100000
Equal terms 147455     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 294912	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1649 sec			Used	Maximum
Generated terms 155648 	Input space 	2720 	100000
Equal terms 155647     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 311296	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms in output 1
Running time 1691 sec			Used	Maximum
Generated terms 163840 	Input space 	2720 	100000
Equal terms 163839     	Output space 	0 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 327680	String space 	0 	4096
Records written 1398 	Merging		0 	0


Terms out 166533, in 166533.

Terms in output 1
Running time 1705 sec			Used	Maximum
Generated terms 166533 	Input space 	2720 	100000
Equal terms 166532     	Output space 	32 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 333066	String space 	0 	4096
Records written 1398 	Merging		0 	0

 
xx =  + .7804709442D+64 + 0.
 
At end: 0 bytes.

End run. Time 1705 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Fri Sep  6 1991 20:21:17.  Memory: start 0001B890, length 476348.


C Miscellaneous 13. Indexed file manipulations.

> P ni
> P no

Begin. Time 0 sec.
> P no
> P no
J1=1 in process ...
J1=2 in process ...
J1=3 in process ...
J1=4 in process ...
J1=5 in process ...
J1=6 in process ...
J1=7 in process ...
J1=8 in process ...
J1=9 in process ...
J1=10 in process ...
> P ou
 
RES = 
  + .35541E+4*aa*del^2*x*y^2 + .16569E+4*aa*del^2*x*y^3 + .24728E+4
  *aa*del^2*x*y^4 - .38162E+3*aa*del^2*x*y^5 - .25775E+4*aa*del^2*x
  *y^6 - .31556E+4*aa*del^2*x*y^8 - .39727E+4*aa*del^2*x*y^9
  - .3985E+3*aa*del^2*x*y^10 + .97005E+3*aa*del^2*x*y^11 - .13703E+4
  *aa*del^2*x*y^13 + .13617E+4*aa*del^2*x*y^14 - .13703E+4*aa*del^2
  *x*y^15 + .50306E+3*aa*del^2*x*y^16 - .13703E+4*aa*del^2*x*y^18
  + .25674E+4*aa*del^2*x*y^19 - .13703E+4*aa*del^2*x*y^21
  - .10314E+4*aa*del^2*x^4*y^2 - .64721E+3*aa*del^2*x^4*y^3
  - .93765E+3*aa*del^2*x^4*y^4 - .58098E+3*aa*del^2*x^4*y^5
  + .90183E+3*aa*del^2*x^4*y^6 + .13588E+4*aa*del^2*x^4*y^8
  + .15225E+4*aa*del^2*x^4*y^9 - .3274E+3*aa*del^2*x^4*y^10
  - .3855E+3*aa*del^2*x^4*y^11 + .55424E+3*aa*del^2*x^4*y^13
  + .187E+3*aa*del^2*x^4*y^14 + .55424E+3*aa*del^2*x^4*y^15
  - .14186E+3*aa*del^2*x^4*y^16 + .55424E+3*aa*del^2*x^4*y^18
  - .87003E+3*aa*del^2*x^4*y^19 + .55424E+3*aa*del^2*x^4*y^21
  + .45882E+5*aa*del^2*x^6*y^2 + .21084E+5*aa*del^2*x^6*y^3
  + .31573E+5*aa*del^2*x^6*y^4 - .62806E+4*aa*del^2*x^6*y^5
  - .33013E+5*aa*del^2*x^6*y^6 - .39906E+5*aa*del^2*x^6*y^8
  - .50622E+5*aa*del^2*x^6*y^9 - .59759E+4*aa*del^2*x^6*y^10
  + .12324E+5*aa*del^2*x^6*y^11 - .17388E+5*aa*del^2*x^6*y^13
  + .18765E+5*aa*del^2*x^6*y^14 - .17388E+5*aa*del^2*x^6*y^15
  + .6507E+4*aa*del^2*x^6*y^16 - .17388E+5*aa*del^2*x^6*y^18
  + .32933E+5*aa*del^2*x^6*y^19 - .17388E+5*aa*del^2*x^6*y^21
  - 3267621/4096*aa*del^2*x^24*y^7*g^-2 - .57556E+5*aa*x*y^2
  - .27699E+5*aa*x*y^3 - .41425E+5*aa*x*y^4 + .26853E+4*aa*x*y^5
  + .42633E+5*aa*x*y^6 + .53477E+5*aa*x*y^8 + .66391E+5*aa*x*y^9
  + .4079E+4*aa*x*y^10 - .16258E+5*aa*x*y^11 + .23011E+5*aa*x*y^13
   - .19333E+5*aa*x*y^14 + .23011E+5*aa*x*y^15 - .8137E+4*aa*x*y^16
   + .23011E+5*aa*x*y^18 - .42306E+5*aa*x*y^19 + .23011E+5*aa*x*y^21
   + .15156E+5*aa*x^4*y^2 + .94213E+4*aa*x^4*y^3 + .13867E+5*aa*x^4
  *y^4 + .83805E+4*aa*x^4*y^5 - .13252E+5*aa*x^4*y^6 - .19966E+5*aa
  *x^4*y^8 - .22372E+5*aa*x^4*y^9 + .48109E+4*aa*x^4*y^10
  + .56647E+4*aa*x^4*y^11 - .81443E+4*aa*x^4*y^13 - .23898E+4*aa*x^4
  *y^14 - .81443E+4*aa*x^4*y^15 + .20846E+4*aa*x^4*y^16 - .81443E+4
  *aa*x^4*y^18 + .12785E+5*aa*x^4*y^19 - .81443E+4*aa*x^4*y^21
  - .74604E+6*aa*x^6*y^2 - .35534E+6*aa*x^6*y^3 - .53217E+6*aa*x^6
  *y^4 + .52279E+5*aa*x^6*y^5 + .54923E+6*aa*x^6*y^6 + .68217E+6*aa
  *x^6*y^8 + .85186E+6*aa*x^6*y^9 + .63869E+5*aa*x^6*y^10
  - .2081E+6*aa*x^6*y^11 + .29426E+6*aa*x^6*y^13 - .2652E+6*aa*x^6
  *y^14 + .29426E+6*aa*x^6*y^15 - .10565E+6*aa*x^6*y^16 + .29426E+6
  *aa*x^6*y^18 - .54565E+6*aa*x^6*y^19 + .29426E+6*aa*x^6*y^21
  + 363069/1024*aa*x^24*y^7*g^-2 - .20852E+4*aa^2*del^2*x*y^2
  - .85027E+3*aa^2*del^2*x*y^3 - .12517E+4*aa^2*del^2*x*y^4
  + .47597E+3*aa^2*del^2*x*y^5 + .18673E+4*aa^2*del^2*x*y^6
  + .10539E+4*aa^2*del^2*x*y^8 + .22387E+4*aa^2*del^2*x*y^9
  + .10313E+4*aa^2*del^2*x*y^10 - .60672E+3*aa^2*del^2*x*y^11
  + .60576E+3*aa^2*del^2*x*y^13 - .12411E+4*aa^2*del^2*x*y^14
  + .60576E+3*aa^2*del^2*x*y^15 - .5722E+3*aa^2*del^2*x*y^16
  + .60576E+3*aa^2*del^2*x*y^18 - .2032E+4*aa^2*del^2*x*y^19
  + .60576E+3*aa^2*del^2*x*y^21 + .33746E+4*aa^2*del^2*x^4*y^2
  + .15521E+4*aa^2*del^2*x^4*y^3 + .23093E+4*aa^2*del^2*x^4*y^4
  - .53788E+3*aa^2*del^2*x^4*y^5 - .24209E+4*aa^2*del^2*x^4*y^6
  - .28847E+4*aa^2*del^2*x^4*y^8 - .36929E+4*aa^2*del^2*x^4*y^9
  - .48981E+3*aa^2*del^2*x^4*y^10 + .89091E+3*aa^2*del^2*x^4*y^11
  - .1252E+4*aa^2*del^2*x^4*y^13 + .14341E+4*aa^2*del^2*x^4*y^14
  - .1252E+4*aa^2*del^2*x^4*y^15 + .47973E+3*aa^2*del^2*x^4*y^16
  - .1252E+4*aa^2*del^2*x^4*y^18 + .24156E+4*aa^2*del^2*x^4*y^19
  - .1252E+4*aa^2*del^2*x^4*y^21 - .2168E+5*aa^2*del^2*x^6*y^2
  - .8468E+4*aa^2*del^2*x^6*y^3 - .12462E+5*aa^2*del^2*x^6*y^4
  + .53793E+4*aa^2*del^2*x^6*y^5 + .20544E+5*aa^2*del^2*x^6*y^6
  + .87286E+4*aa^2*del^2*x^6*y^8 + .23133E+5*aa^2*del^2*x^6*y^9
  + .12952E+5*aa^2*del^2*x^6*y^10 - .64923E+4*aa^2*del^2*x^6*y^11
  + .58052E+4*aa^2*del^2*x^6*y^13 - .14013E+5*aa^2*del^2*x^6*y^14
  + .58052E+4*aa^2*del^2*x^6*y^15 - .67972E+4*aa^2*del^2*x^6*y^16
  + .58052E+4*aa^2*del^2*x^6*y^18 - .22777E+5*aa^2*del^2*x^6*y^19
  + .58052E+4*aa^2*del^2*x^6*y^21 + 1089207/4096*aa^2*del^2*x^24*y^7
  *g^-2 + .48987E+5*aa^2*x*y^2 + .20908E+5*aa^2*x*y^3 + .30936E+5*aa^2
  *x*y^4 - .95254E+4*aa^2*x*y^5 - .406E+5*aa^2*x*y^6 - .31394E+5*aa^2
  *x*y^8 - .53072E+5*aa^2*x*y^9 - .17593E+5*aa^2*x*y^10 + .13835E+5
  *aa^2*x*y^11 - .15843E+5*aa^2*x*y^13 + .25702E+5*aa^2*x*y^14
  - .15843E+5*aa^2*x*y^15 + .11006E+5*aa^2*x*y^16 - .15843E+5*aa^2
  *x*y^18 + .42994E+5*aa^2*x*y^19 - .15843E+5*aa^2*x*y^21
  - .5516E+5*aa^2*x^4*y^2 - .26318E+5*aa^2*x^4*y^3 - .38986E+5*aa^2
  *x^4*y^4 + .47398E+4*aa^2*x^4*y^5 + .40446E+5*aa^2*x^4*y^6
  + .49731E+5*aa^2*x^4*y^8 + .6249E+5*aa^2*x^4*y^9 + .54287E+4*aa^2
  *x^4*y^10 - .15174E+5*aa^2*x^4*y^11 + .21391E+5*aa^2*x^4*y^13
  - .20005E+5*aa^2*x^4*y^14 + .21391E+5*aa^2*x^4*y^15 - .78159E+4*aa^2
  *x^4*y^16 + .21391E+5*aa^2*x^4*y^18 - .40197E+5*aa^2*x^4*y^19
  + .21391E+5*aa^2*x^4*y^21 + .55493E+6*aa^2*x^6*y^2 + .23103E+6*aa^2
  *x^6*y^3 + .34274E+6*aa^2*x^6*y^4 - .11941E+6*aa^2*x^6*y^5
  - .46993E+6*aa^2*x^6*y^6 - .32848E+6*aa^2*x^6*y^8 - .59607E+6*aa^2
  *x^6*y^9 - .22645E+6*aa^2*x^6*y^10 + .15765E+6*aa^2*x^6*y^11
  - .17302E+6*aa^2*x^6*y^13 + .30899E+6*aa^2*x^6*y^14 - .17302E+6*aa^2
  *x^6*y^15 + .13342E+6*aa^2*x^6*y^16 - .17302E+6*aa^2*x^6*y^18
  + .50271E+6*aa^2*x^6*y^19 - .17302E+6*aa^2*x^6*y^21 - 121023/4096
  *aa^2*x^24*y^7*g^-2 + .20158E+3*aa^3*del^2*x*y^2 - .2828E+2*aa^3
  *del^2*x*y^3 - .26651E+2*aa^3*del^2*x*y^4 - .98891E+1*aa^3*del^2
  *x*y^5 - .38789E+3*aa^3*del^2*x*y^6 + .14614E+3*aa^3*del^2*x*y^8
   - .30426E+3*aa^3*del^2*x*y^9 - .34772E+3*aa^3*del^2*x*y^10
  + .32197E+3*aa^3*del^2*x*y^11 + .72688E+2*aa^3*del^2*x*y^13
  + .2178E+3*aa^3*del^2*x*y^14 + .72688E+2*aa^3*del^2*x*y^15
  + .24209E+3*aa^3*del^2*x*y^16 + .72688E+2*aa^3*del^2*x*y^18
  + .51076E+3*aa^3*del^2*x*y^19 + .72688E+2*aa^3*del^2*x*y^21
  - .13244E+4*aa^3*del^2*x^4*y^2 - .49977E+3*aa^3*del^2*x^4*y^3
  - .73425E+3*aa^3*del^2*x^4*y^4 + .34252E+3*aa^3*del^2*x^4*y^5
  + .13348E+4*aa^3*del^2*x^4*y^6 + .40021E+3*aa^3*del^2*x^4*y^8
  + .14168E+4*aa^3*del^2*x^4*y^9 + .92421E+3*aa^3*del^2*x^4*y^10
  - .41305E+3*aa^3*del^2*x^4*y^11 + .33248E+3*aa^3*del^2*x^4*y^13
  - .92102E+3*aa^3*del^2*x^4*y^14 + .33248E+3*aa^3*del^2*x^4*y^15
  - .4714E+3*aa^3*del^2*x^4*y^16 + .33248E+3*aa^3*del^2*x^4*y^18
  - .15046E+4*aa^3*del^2*x^4*y^19 + .33248E+3*aa^3*del^2*x^4*y^21
  + .2132E+3*aa^3*del^2*x^6*y^2 - .13327E+4*aa^3*del^2*x^6*y^3
  - .17577E+4*aa^3*del^2*x^6*y^4 + .50334E+3*aa^3*del^2*x^6*y^5
  - .26877E+4*aa^3*del^2*x^6*y^6 + .27275E+4*aa^3*del^2*x^6*y^8
  - .14046E+4*aa^3*del^2*x^6*y^9 - .29407E+4*aa^3*del^2*x^6*y^10
  + .35497E+4*aa^3*del^2*x^6*y^11 + .16228E+4*aa^3*del^2*x^6*y^13
  + .11876E+4*aa^3*del^2*x^6*y^14 + .16228E+4*aa^3*del^2*x^6*y^15
  + .23639E+4*aa^3*del^2*x^6*y^16 + .16228E+4*aa^3*del^2*x^6*y^18
  + .40198E+4*aa^3*del^2*x^6*y^19 + .16228E+4*aa^3*del^2*x^6*y^21
  - .11143E+5*aa^3*x*y^2 - .27399E+4*aa^3*x*y^3 - .42244E+4*aa^3*x
  *y^4 + .23856E+4*aa^3*x*y^5 + .13551E+5*aa^3*x*y^6 + .80727E+3*aa^3
  *x*y^8 + .13118E+5*aa^3*x*y^9 + .10336E+5*aa^3*x*y^10 - .7167E+4
  *aa^3*x*y^11 + .10152E+4*aa^3*x*y^13 - .87238E+4*aa^3*x*y^14
  + .10152E+4*aa^3*x*y^15 - .62122E+4*aa^3*x*y^16 + .10152E+4*aa^3
  *x*y^18 - .16255E+5*aa^3*x*y^19 + .10152E+4*aa^3*x*y^21
  + .36798E+5*aa^3*x^4*y^2 + .15167E+5*aa^3*x^4*y^3 + .22452E+5*aa^3
  *x^4*y^4 - .84435E+4*aa^3*x^4*y^5 - .3191E+5*aa^3*x^4*y^6
  - .20287E+5*aa^3*x^4*y^8 - .39449E+5*aa^3*x^4*y^9 - .16511E+5*aa^3
  *x^4*y^10 + .10548E+5*aa^3*x^4*y^11 - .11169E+5*aa^3*x^4*y^13
  + .21444E+5*aa^3*x^4*y^14 - .11169E+5*aa^3*x^4*y^15 + .93958E+4*aa^3
  *x^4*y^16 - .11169E+5*aa^3*x^4*y^18 + .34405E+5*aa^3*x^4*y^19
  - .11169E+5*aa^3*x^4*y^21 - .8044E+5*aa^3*x^6*y^2 - .78659E+4*aa^3
  *x^6*y^3 - .14091E+5*aa^3*x^6*y^4 + .16215E+5*aa^3*x^6*y^5
  + .12183E+6*aa^3*x^6*y^6 - .2756E+5*aa^3*x^6*y^8 + .10168E+6*aa^3
  *x^6*y^9 + .108E+6*aa^3*x^6*y^10 - .76539E+5*aa^3*x^6*y^11
  - .75765E+4*aa^3*x^6*y^13 - .76872E+5*aa^3*x^6*y^14 - .75765E+4*aa^3
  *x^6*y^15 - .65812E+5*aa^3*x^6*y^16 - .75765E+4*aa^3*x^6*y^18
  - .15354E+6*aa^3*x^6*y^19 - .75765E+4*aa^3*x^6*y^21 - 1573299/65536
  *aa^3*x^24*y^7*g^-2 + .85081E+2*aa^4*del^2*x*y^2 + .6109E+2*aa^4
  *del^2*x*y^3 + .78139E+2*aa^4*del^2*x*y^4 - .32304E+2*aa^4*del^2
  *x*y^5 - .23034E+2*aa^4*del^2*x*y^6 - .49416E+2*aa^4*del^2*x*y^8
   - .24881E+2*aa^4*del^2*x*y^9 - .35665E+2*aa^4*del^2*x*y^10
  - .11046E+3*aa^4*del^2*x*y^11 - .46039E+2*aa^4*del^2*x*y^13
  + .40027E+2*aa^4*del^2*x*y^14 - .46039E+2*aa^4*del^2*x*y^15
  - .239E+2*aa^4*del^2*x*y^16 - .46039E+2*aa^4*del^2*x*y^18
  + .91274E+1*aa^4*del^2*x*y^19 - .46039E+2*aa^4*del^2*x*y^21
  - .44942E+2*aa^4*del^2*x^4*y^2 - .12015E+3*aa^4*del^2*x^4*y^3
  - .1607E+3*aa^4*del^2*x^4*y^4 + .59189E+2*aa^4*del^2*x^4*y^5
  - .11961E+3*aa^4*del^2*x^4*y^6 + .18713E+3*aa^4*del^2*x^4*y^8
  - .40313E+2*aa^4*del^2*x^4*y^9 - .14219E+3*aa^4*del^2*x^4*y^10
  + .24678E+3*aa^4*del^2*x^4*y^11 + .13234E+3*aa^4*del^2*x^4*y^13
  + .29932E+2*aa^4*del^2*x^4*y^14 + .13234E+3*aa^4*del^2*x^4*y^15
  + .14198E+3*aa^4*del^2*x^4*y^16 + .13234E+3*aa^4*del^2*x^4*y^18
  + .2038E+3*aa^4*del^2*x^4*y^19 + .13234E+3*aa^4*del^2*x^4*y^21
  + .11232E+4*aa^4*del^2*x^6*y^2 + .62043E+3*aa^4*del^2*x^6*y^3
  + .78625E+3*aa^4*del^2*x^6*y^4 - .3333E+3*aa^4*del^2*x^6*y^5
  - .5759E+3*aa^4*del^2*x^6*y^6 - .36885E+3*aa^4*del^2*x^6*y^8
  - .47674E+3*aa^4*del^2*x^6*y^9 - .75435E+3*aa^4*del^2*x^6*y^10
  - .10016E+4*aa^4*del^2*x^6*y^11 - .38932E+3*aa^4*del^2*x^6*y^13
  + .62239E+3*aa^4*del^2*x^6*y^14 - .38932E+3*aa^4*del^2*x^6*y^15
  - .45913E+2*aa^4*del^2*x^6*y^16 - .38932E+3*aa^4*del^2*x^6*y^18
  + .54767E+3*aa^4*del^2*x^6*y^19 - .38932E+3*aa^4*del^2*x^6*y^21
  - .19712E+4*aa^4*x*y^2 - .17886E+4*aa^4*x*y^3 - .23787E+4*aa^4*x
  *y^4 + .83443E+3*aa^4*x*y^5 - .13629E+3*aa^4*x*y^6 + .24306E+4*aa^4
  *x*y^8 + .66506E+3*aa^4*x*y^9 - .45934E+3*aa^4*x*y^10 + .2836E+4
  *aa^4*x*y^11 + .15951E+4*aa^4*x*y^13 - .48874E+3*aa^4*x*y^14
  + .15951E+4*aa^4*x*y^15 + .11625E+4*aa^4*x*y^16 + .15951E+4*aa^4
  *x*y^18 + .86152E+3*aa^4*x*y^19 + .15951E+4*aa^4*x*y^21
  - .35659E+4*aa^4*x^4*y^2 + .41264E+3*aa^4*x^4*y^3 + .39902E+3*aa^4
  *x^4*y^4 + .51389E+3*aa^4*x^4*y^5 + .68676E+4*aa^4*x^4*y^6
  - .30917E+4*aa^4*x^4*y^8 + .50412E+4*aa^4*x^4*y^9 + .66575E+4*aa^4
  *x^4*y^10 - .50845E+4*aa^4*x^4*y^11 - .12352E+4*aa^4*x^4*y^13
  - .4171E+4*aa^4*x^4*y^14 - .12352E+4*aa^4*x^4*y^15 - .42168E+4*aa^4
  *x^4*y^16 - .12352E+4*aa^4*x^4*y^18 - .90267E+4*aa^4*x^4*y^19
  - .12352E+4*aa^4*x^4*y^21 - .34173E+5*aa^4*x^6*y^2 - .23668E+5*aa^4
  *x^6*y^3 - .31867E+5*aa^4*x^6*y^4 + .12287E+5*aa^4*x^6*y^5
  + .11775E+5*aa^4*x^6*y^6 + .27733E+5*aa^4*x^6*y^8 + .19497E+5*aa^4
  *x^6*y^9 + .64399E+4*aa^4*x^6*y^10 + .28261E+5*aa^4*x^6*y^11
  + .19528E+5*aa^4*x^6*y^13 - .14894E+5*aa^4*x^6*y^14 + .19528E+5*aa^4
  *x^6*y^15 + .7546E+4*aa^4*x^6*y^16 + .19528E+5*aa^4*x^6*y^18
  - .6102E+4*aa^4*x^6*y^19 + .19528E+5*aa^4*x^6*y^21 - 121023/65536
  *aa^4*x^24*y^7*g^-2 - .13597E+2*aa^5*del^2*x*y^2 - .40164E-1*aa^5
  *del^2*x*y^3 + .15167*aa^5*del^2*x*y^4 - .37238*aa^5*del^2*x*y^5
   + .8688E+1*aa^5*del^2*x*y^6 - .18595E+1*aa^5*del^2*x*y^8
  + .33814E+1*aa^5*del^2*x*y^9 + .15456E+2*aa^5*del^2*x*y^10
  + .64262E+1*aa^5*del^2*x*y^11 - .2311E+1*aa^5*del^2*x*y^13
  - .83391E+1*aa^5*del^2*x*y^14 - .2311E+1*aa^5*del^2*x*y^15
  - .52149E+1*aa^5*del^2*x*y^16 - .2311E+1*aa^5*del^2*x*y^18
  - .12768E+2*aa^5*del^2*x*y^19 - .2311E+1*aa^5*del^2*x*y^21
  + .63286E+2*aa^5*del^2*x^4*y^2 + .28653E+2*aa^5*del^2*x^4*y^3
  + .3472E+2*aa^5*del^2*x^4*y^4 - .14374E+2*aa^5*del^2*x^4*y^5
  - .34192E+2*aa^5*del^2*x^4*y^6 - .10259E+2*aa^5*del^2*x^4*y^8
  - .21276E+2*aa^5*del^2*x^4*y^9 - .53028E+2*aa^5*del^2*x^4*y^10
  - .56917E+2*aa^5*del^2*x^4*y^11 - .13107E+2*aa^5*del^2*x^4*y^13
  + .35961E+2*aa^5*del^2*x^4*y^14 - .13107E+2*aa^5*del^2*x^4*y^15
  + .20649E+1*aa^5*del^2*x^4*y^16 - .13107E+2*aa^5*del^2*x^4*y^18
  + .36883E+2*aa^5*del^2*x^4*y^19 - .13107E+2*aa^5*del^2*x^4*y^21
  - .78419E+2*aa^5*del^2*x^6*y^2 + .47056E+2*aa^5*del^2*x^6*y^3
  + .59128E+2*aa^5*del^2*x^6*y^4 - .27374E+2*aa^5*del^2*x^6*y^5
  + .7152E+2*aa^5*del^2*x^6*y^6 - .46646E+2*aa^5*del^2*x^6*y^8
  + .21398E+2*aa^5*del^2*x^6*y^9 + .12507E+3*aa^5*del^2*x^6*y^10
  - .24153E+2*aa^5*del^2*x^6*y^11 - .52818E+2*aa^5*del^2*x^6*y^13
  - .56567E+2*aa^5*del^2*x^6*y^14 - .52818E+2*aa^5*del^2*x^6*y^15
  - .7361E+2*aa^5*del^2*x^6*y^16 - .52818E+2*aa^5*del^2*x^6*y^18
  - .12424E+3*aa^5*del^2*x^6*y^19 - .52818E+2*aa^5*del^2*x^6*y^21
  + .83445E+3*aa^5*x*y^2 + .3061E+3*aa^5*x*y^3 + .3968E+3*aa^5*x*y^4
   - .17765E+3*aa^5*x*y^5 - .58883E+3*aa^5*x*y^6 - .1128E+3*aa^5*x
  *y^8 - .44823E+3*aa^5*x*y^9 - .72165E+3*aa^5*x*y^10 - .41174E+3*aa^5
  *x*y^11 - .15168E+3*aa^5*x*y^13 + .52786E+3*aa^5*x*y^14
  - .15168E+3*aa^5*x*y^15 + .15765E+3*aa^5*x*y^16 - .15168E+3*aa^5
  *x*y^18 + .6803E+3*aa^5*x*y^19 - .15168E+3*aa^5*x*y^21 - .23224E+4
  *aa^5*x^4*y^2 - .1504E+4*aa^5*x^4*y^3 - .20158E+4*aa^5*x^4*y^4
  + .82833E+3*aa^5*x^4*y^5 + .10148E+4*aa^5*x^4*y^6 + .15092E+4*aa^5
  *x^4*y^8 + .13247E+4*aa^5*x^4*y^9 + .81326E+3*aa^5*x^4*y^10
  + .18111E+4*aa^5*x^4*y^11 + .11962E+4*aa^5*x^4*y^13 - .11662E+4*aa^5
  *x^4*y^14 + .11962E+4*aa^5*x^4*y^15 + .32755E+3*aa^5*x^4*y^16
  + .11962E+4*aa^5*x^4*y^18 - .74692E+3*aa^5*x^4*y^19 + .11962E+4*aa^5
  *x^4*y^21 + .74058E+4*aa^5*x^6*y^2 + .15038E+4*aa^5*x^6*y^3
  + .18533E+4*aa^5*x^6*y^4 - .9616E+3*aa^5*x^6*y^5 - .64954E+4*aa^5
  *x^6*y^6 + .10602E+4*aa^5*x^6*y^8 - .41094E+4*aa^5*x^6*y^9
  - .8466E+4*aa^5*x^6*y^10 - .19754E+4*aa^5*x^6*y^11 + .8145E+2*aa^5
  *x^6*y^13 + .52247E+4*aa^5*x^6*y^14 + .8145E+2*aa^5*x^6*y^15
  + .28856E+4*aa^5*x^6*y^16 + .8145E+2*aa^5*x^6*y^18 + .8274E+4*aa^5
  *x^6*y^19 + .8145E+2*aa^5*x^6*y^21 - .56793*aa^6*del^2*x*y^2
  - .80209*aa^6*del^2*x*y^3 - .89216*aa^6*del^2*x*y^4 + .36005*aa^6
  *del^2*x*y^5 + .15571*aa^6*del^2*x*y^6 + .2028*aa^6*del^2*x*y^8
  + 5220352557/68719476736*aa^6*del^2*x*y^9 + .36513*aa^6*del^2*x*y^10
   + .13207E+1*aa^6*del^2*x*y^11 + .33163*aa^6*del^2*x*y^13
  - .37375*aa^6*del^2*x*y^14 + .33163*aa^6*del^2*x*y^15 + .48033*aa^6
  *del^2*x*y^16 + .33163*aa^6*del^2*x*y^18 + .91979E-1*aa^6*del^2*x
  *y^19 + .33163*aa^6*del^2*x*y^21 - .22123E+1*aa^6*del^2*x^4*y^2
  + .33085E+1*aa^6*del^2*x^4*y^3 + .39029E+1*aa^6*del^2*x^4*y^4
  - .17751E+1*aa^6*del^2*x^4*y^5 + .20567E+1*aa^6*del^2*x^4*y^6
  - .17733E+1*aa^6*del^2*x^4*y^8 + .33631*aa^6*del^2*x^4*y^9
  + .39857E+1*aa^6*del^2*x^4*y^10 - .26782E+1*aa^6*del^2*x^4*y^11
  - .25496E+1*aa^6*del^2*x^4*y^13 - .16388E+1*aa^6*del^2*x^4*y^14
  - .25496E+1*aa^6*del^2*x^4*y^15 - .35192E+1*aa^6*del^2*x^4*y^16
  - .25496E+1*aa^6*del^2*x^4*y^18 - .45527E+1*aa^6*del^2*x^4*y^19
  - .25496E+1*aa^6*del^2*x^4*y^21 - .14091E+2*aa^6*del^2*x^6*y^2
  - .75077E+1*aa^6*del^2*x^6*y^3 - .83845E+1*aa^6*del^2*x^6*y^4
  + .31381E+1*aa^6*del^2*x^6*y^5 + .62217E+1*aa^6*del^2*x^6*y^6
  + .14951E+1*aa^6*del^2*x^6*y^8 + .23942E+1*aa^6*del^2*x^6*y^9
  + .12596E+2*aa^6*del^2*x^6*y^10 + .17251E+2*aa^6*del^2*x^6*y^11
  + .21031E+1*aa^6*del^2*x^6*y^13 - .89854E+1*aa^6*del^2*x^6*y^14
  + .21031E+1*aa^6*del^2*x^6*y^15 + .14678E+1*aa^6*del^2*x^6*y^16
  + .21031E+1*aa^6*del^2*x^6*y^18 - .64874E+1*aa^6*del^2*x^6*y^19
  + .21031E+1*aa^6*del^2*x^6*y^21 + .87415E+1*aa^6*x*y^2 + .64599E+2
  *aa^6*x*y^3 + .81758E+2*aa^6*x*y^4 - .35344E+2*aa^6*x*y^5
  + .24656E+2*aa^6*x*y^6 - .55922E+2*aa^6*x*y^8 - .44457E+1*aa^6*x
  *y^9 + .4718E+2*aa^6*x*y^10 - .80574E+2*aa^6*x*y^11 - .57323E+2*aa^6
  *x*y^13 - .48168E+1*aa^6*x*y^14 - .57323E+2*aa^6*x*y^15
  - .55979E+2*aa^6*x*y^16 - .57323E+2*aa^6*x*y^18 - .6241E+2*aa^6*x
  *y^19 - .57323E+2*aa^6*x*y^21 + .33542E+3*aa^6*x^4*y^2 + .18969E+1
  *aa^6*x^4*y^3 - .92615E+1*aa^6*x^4*y^4 - .19643*aa^6*x^4*y^5
  - .31878E+3*aa^6*x^4*y^6 + .13307E+3*aa^6*x^4*y^8 - .15488E+3*aa^6
  *x^4*y^9 - .46849E+3*aa^6*x^4*y^10 - .53939E+2*aa^6*x^4*y^11
  + .81537E+2*aa^6*x^4*y^13 + .24435E+3*aa^6*x^4*y^14 + .81537E+2*aa^6
  *x^4*y^15 + .18612E+3*aa^6*x^4*y^16 + .81537E+2*aa^6*x^4*y^18
  + .44308E+3*aa^6*x^4*y^19 + .81537E+2*aa^6*x^4*y^21 + .75838E+3*aa^6
  *x^6*y^2 + .90312E+3*aa^6*x^6*y^3 + .11252E+4*aa^6*x^6*y^4
  - .48333E+3*aa^6*x^6*y^5 - .20493E+3*aa^6*x^6*y^6 - .59417E+3*aa^6
  *x^6*y^8 - .3334E+3*aa^6*x^6*y^9 - .16421E+3*aa^6*x^6*y^10
  - .12535E+4*aa^6*x^6*y^11 - .65421E+3*aa^6*x^6*y^13 + .36668E+3*aa^6
  *x^6*y^14 - .65421E+3*aa^6*x^6*y^15 - .45912E+3*aa^6*x^6*y^16
  - .65421E+3*aa^6*x^6*y^18 - .10051E+3*aa^6*x^6*y^19 - .65421E+3*aa^6
  *x^6*y^21 + .63274E-1*aa^7*del^2*x*y^2 - .14271E-1*aa^7*del^2*x*y^3
   - .15233E-1*aa^7*del^2*x*y^4 + .95265E-2*aa^7*del^2*x*y^5
  - .26517E-1*aa^7*del^2*x*y^6 + .28871E-2*aa^7*del^2*x*y^8
  - .24143E-2*aa^7*del^2*x*y^9 - .66162E-1*aa^7*del^2*x*y^10
  - .32312E-1*aa^7*del^2*x*y^11 + .91306E-2*aa^7*del^2*x*y^13
  + .50986E-1*aa^7*del^2*x*y^14 + .91306E-2*aa^7*del^2*x*y^15
  + .31903E-1*aa^7*del^2*x*y^16 + .91306E-2*aa^7*del^2*x*y^18
  + .57351E-1*aa^7*del^2*x*y^19 + .91306E-2*aa^7*del^2*x*y^21
  - .51514*aa^7*del^2*x^4*y^2 - .15111*aa^7*del^2*x^4*y^3
  - .16094*aa^7*del^2*x^4*y^4 + .45511E-1*aa^7*del^2*x^4*y^5
  + .22114*aa^7*del^2*x^4*y^6 + .88882E-2*aa^7*del^2*x^4*y^8
  + .48261E-1*aa^7*del^2*x^4*y^9 + .50625*aa^7*del^2*x^4*y^10
  + .536*aa^7*del^2*x^4*y^11 - .15643E-2*aa^7*del^2*x^4*y^13
  - .36828*aa^7*del^2*x^4*y^14 - .15643E-2*aa^7*del^2*x^4*y^15
  - .32047E-1*aa^7*del^2*x^4*y^16 - .15643E-2*aa^7*del^2*x^4*y^18
  - .30702*aa^7*del^2*x^4*y^19 - .15643E-2*aa^7*del^2*x^4*y^21
  + .47053*aa^7*del^2*x^6*y^2 - .48735*aa^7*del^2*x^6*y^3
  - .53361*aa^7*del^2*x^6*y^4 + .2477*aa^7*del^2*x^6*y^5 - .25702*aa^7
  *del^2*x^6*y^6 + .12136*aa^7*del^2*x^6*y^8 - 1587633147/68719476736
  *aa^7*del^2*x^6*y^9 - .59189*aa^7*del^2*x^6*y^10 + .21921*aa^7*del^2
  *x^6*y^11 + .24114*aa^7*del^2*x^6*y^13 + .3652*aa^7*del^2*x^6*y^14
   + .24114*aa^7*del^2*x^6*y^15 + .56012*aa^7*del^2*x^6*y^16
  + .24114*aa^7*del^2*x^6*y^18 + .68601*aa^7*del^2*x^6*y^19
  + .24114*aa^7*del^2*x^6*y^21 - .15801E+2*aa^7*x*y^2 - .41587E+1*aa^7
  *x*y^3 - .44647E+1*aa^7*x*y^4 + .1482E+1*aa^7*x*y^5 + .87726E+1*aa^7
  *x*y^6 - .56087*aa^7*x*y^8 + .33812E+1*aa^7*x*y^9 + .16362E+2*aa^7
  *x*y^10 + .13189E+2*aa^7*x*y^11 - .34854*aa^7*x*y^13 - .10007E+2
  *aa^7*x*y^14 - .34854*aa^7*x*y^15 - .24005E+1*aa^7*x*y^16
  - .34854*aa^7*x*y^18 - .11429E+2*aa^7*x*y^19 - .34854*aa^7*x*y^21
   + .50553E+2*aa^7*x^4*y^2 + .44968E+2*aa^7*x^4*y^3 + .5359E+2*aa^7
  *x^4*y^4 - .22737E+2*aa^7*x^4*y^5 - .21818E+2*aa^7*x^4*y^6
  - .18617E+2*aa^7*x^4*y^8 - .17361E+2*aa^7*x^4*y^9 - .31936E+2*aa^7
  *x^4*y^10 - .71753E+2*aa^7*x^4*y^11 - .25129E+2*aa^7*x^4*y^13
  + .27773E+2*aa^7*x^4*y^14 - .25129E+2*aa^7*x^4*y^15 - .1675E+2*aa^7
  *x^4*y^16 - .25129E+2*aa^7*x^4*y^18 + .11931E+2*aa^7*x^4*y^19
  - .25129E+2*aa^7*x^4*y^21 - .15112E+3*aa^7*x^6*y^2 + .74458E+1*aa^7
  *x^6*y^3 + .13868E+2*aa^7*x^6*y^4 - .10447E+2*aa^7*x^6*y^5
  + .99474E+2*aa^7*x^6*y^6 - .34197E+2*aa^7*x^6*y^8 + .31849E+2*aa^7
  *x^6*y^9 + .18532E+3*aa^7*x^6*y^10 + .69017E+2*aa^7*x^6*y^11
  - .3803E+2*aa^7*x^6*y^13 - .10302E+3*aa^7*x^6*y^14 - .3803E+2*aa^7
  *x^6*y^15 - .64198E+2*aa^7*x^6*y^16 - .3803E+2*aa^7*x^6*y^18
  - .15298E+3*aa^7*x^6*y^19 - .3803E+2*aa^7*x^6*y^21 + 92945475/137438953472
  *aa^8*del^2*x*y^2 + .67903E-3*aa^8*del^2*x*y^3 + .67903E-3*aa^8*del^2
  *x*y^4 - .22715E-3*aa^8*del^2*x*y^5 - .24032E-3*aa^8*del^2*x*y^6
   - 92945475/137438953472*aa^8*del^2*x*y^10 - 728619003/549755813888
  *aa^8*del^2*x*y^11 + 92945475/137438953472*aa^8*del^2*x*y^14
  - .43871E-3*aa^8*del^2*x*y^16 + 259884261/2199023255552*aa^8*del^2
  *x*y^19 + .49631E-2*aa^8*del^2*x^4*y^2 - .12023E-1*aa^8*del^2*x^4
  *y^3 - .12535E-1*aa^8*del^2*x^4*y^4 + .53931E-2*aa^8*del^2*x^4*y^5
   - .25032E-2*aa^8*del^2*x^4*y^6 + .1179E-2*aa^8*del^2*x^4*y^8
  - 7735203/274877906944*aa^8*del^2*x^4*y^9 - .61422E-2*aa^8*del^2
  *x^4*y^10 + .98361E-2*aa^8*del^2*x^4*y^11 + .28151E-2*aa^8*del^2
  *x^4*y^13 + .41686E-2*aa^8*del^2*x^4*y^14 + .28151E-2*aa^8*del^2
  *x^4*y^15 + .12454E-1*aa^8*del^2*x^4*y^16 + .28151E-2*aa^8*del^2
  *x^4*y^18 + .11334E-1*aa^8*del^2*x^4*y^19 + .28151E-2*aa^8*del^2
  *x^4*y^21 + .34861E-1*aa^8*del^2*x^6*y^2 + .80517E-2*aa^8*del^2*x^6
  *y^3 + .82298E-2*aa^8*del^2*x^6*y^4 - .14909E-2*aa^8*del^2*x^6*y^5
   - .13504E-1*aa^8*del^2*x^6*y^6 - 9945261/137438953472*aa^8*del^2
  *x^6*y^8 - .1171E-2*aa^8*del^2*x^6*y^9 - .34789E-1*aa^8*del^2*x^6
  *y^10 - .36409E-1*aa^8*del^2*x^6*y^11 + .94584E-3*aa^8*del^2*x^6
  *y^13 + 2043628785/68719476736*aa^8*del^2*x^6*y^14 + .94584E-3*aa^8
  *del^2*x^6*y^15 + .36733E-2*aa^8*del^2*x^6*y^16 + .94584E-3*aa^8
  *del^2*x^6*y^18 + .22191E-1*aa^8*del^2*x^6*y^19 + .94584E-3*aa^8
  *del^2*x^6*y^21 - .16108*aa^8*x*y^2 - .78334*aa^8*x*y^3
  - .86672*aa^8*x*y^4 + .36735*aa^8*x*y^5 - .45644E-2*aa^8*x*y^6
  + .19164*aa^8*x*y^8 + .52899E-1*aa^8*x*y^9 - .30562E-1*aa^8*x*y^10
   + .99136*aa^8*x*y^11 + .3372*aa^8*x*y^13 - .58908E-1*aa^8*x*y^14
   + .3372*aa^8*x*y^15 + .59576*aa^8*x*y^16 + .3372*aa^8*x*y^18
  + .38796*aa^8*x*y^19 + .3372*aa^8*x*y^21 - .47765E+1*aa^8*x^4*y^2
   + .22322E+1*aa^8*x^4*y^3 + .27026E+1*aa^8*x^4*y^4 - .13743E+1*aa^8
  *x^4*y^5 + .30169E+1*aa^8*x^4*y^6 - .15087E+1*aa^8*x^4*y^8
  + .55309*aa^8*x^4*y^9 + .62852E+1*aa^8*x^4*y^10 + .42656*aa^8*x^4
  *y^11 - .22631E+1*aa^8*x^4*y^13 - .34736E+1*aa^8*x^4*y^14
  - .22631E+1*aa^8*x^4*y^15 - .3411E+1*aa^8*x^4*y^16 - .22631E+1*aa^8
  *x^4*y^18 - .57774E+1*aa^8*x^4*y^19 - .22631E+1*aa^8*x^4*y^21
  - .10202E+2*aa^8*x^6*y^2 - .92685E+1*aa^8*x^6*y^3 - .10282E+2*aa^8
  *x^6*y^4 + .40842E+1*aa^8*x^6*y^5 + .42106E+1*aa^8*x^6*y^6
  + .19546E+1*aa^8*x^6*y^8 + .19707E+1*aa^8*x^6*y^9 + .82475E+1*aa^8
  *x^6*y^10 + .16694E+2*aa^8*x^6*y^11 + .31145E+1*aa^8*x^6*y^13
  - .62637E+1*aa^8*x^6*y^14 + .31145E+1*aa^8*x^6*y^15 + .42464E+1*aa^8
  *x^6*y^16 + .31145E+1*aa^8*x^6*y^18 - .22512E+1*aa^8*x^6*y^19
  + .31145E+1*aa^8*x^6*y^21 + 195408045/549755813888*aa^9*del^2*x^4
  *y^2 + 69616827/8796093022208*aa^9*del^2*x^4*y^3 + 69616827/8796093022208
  *aa^9*del^2*x^4*y^4 + .18088E-4*aa^9*del^2*x^4*y^5 - .12808E-3*aa^9
  *del^2*x^4*y^6 - 195408045/549755813888*aa^9*del^2*x^4*y^10
  - .30179E-3*aa^9*del^2*x^4*y^11 + 195408045/549755813888*aa^9*del^2
  *x^4*y^14 + .12016E-3*aa^9*del^2*x^4*y^16 + .28772E-3*aa^9*del^2
  *x^4*y^19 - 65347965/549755813888*aa^9*del^2*x^6*y^2 + .32934E-3
  *aa^9*del^2*x^6*y^3 + .32934E-3*aa^9*del^2*x^6*y^4 - .13683E-3*aa^9
  *del^2*x^6*y^5 + .44508E-4*aa^9*del^2*x^6*y^6 + 65347965/549755813888
  *aa^9*del^2*x^6*y^10 - .27466E-3*aa^9*del^2*x^6*y^11 - 65347965/549755813888
  *aa^9*del^2*x^6*y^14 - .37385E-3*aa^9*del^2*x^6*y^16 - .31084E-3
  *aa^9*del^2*x^6*y^19 + .58579E-1*aa^9*x*y^2 - .87196E-2*aa^9*x*y^3
   - .9554E-2*aa^9*x*y^4 + .70423E-2*aa^9*x*y^5 - .24316E-1*aa^9*x
  *y^6 + .25061E-2*aa^9*x*y^8 - .20958E-2*aa^9*x*y^9 - .61086E-1*aa^9
  *x*y^10 - .35209E-1*aa^9*x*y^11 + .79259E-2*aa^9*x*y^13
  + .47912E-1*aa^9*x*y^14 + .79259E-2*aa^9*x*y^15 + .25323E-1*aa^9
  *x*y^16 + .79259E-2*aa^9*x*y^18 + .50423E-1*aa^9*x*y^19
  + .79259E-2*aa^9*x*y^21 - .42558*aa^9*x^4*y^2 - .19625*aa^9*x^4*y^3
   - .20755*aa^9*x^4*y^4 + .68378E-1*aa^9*x^4*y^5 + .18032*aa^9*x^4
  *y^6 + .14085E-1*aa^9*x^4*y^8 + .41741E-1*aa^9*x^4*y^9 + .41149*aa^9
  *x^4*y^10 + .52286*aa^9*x^4*y^11 + .13852E-1*aa^9*x^4*y^13
  - .30239*aa^9*x^4*y^14 + .13852E-1*aa^9*x^4*y^15 + .37703E-1*aa^9
  *x^4*y^16 + .13852E-1*aa^9*x^4*y^18 - .2095*aa^9*x^4*y^19
  + .13852E-1*aa^9*x^4*y^21 + .59854*aa^9*x^6*y^2 - .38438*aa^9*x^6
  *y^3 - .42358*aa^9*x^6*y^4 + .20897*aa^9*x^6*y^5 - .29672*aa^9*x^6
  *y^6 + .10496*aa^9*x^6*y^8 - .26381E-1*aa^9*x^6*y^9 - .7035*aa^9
  *x^6*y^10 - .23917E-2*aa^9*x^6*y^11 + .21444*aa^9*x^6*y^13
  + .47943*aa^9*x^6*y^14 + .21444*aa^9*x^6*y^15 + .51156*aa^9*x^6*y^16
   + .21444*aa^9*x^6*y^18 + .71996*aa^9*x^6*y^19 + .21444*aa^9*x^6
  *y^21 + .58704E-3*aa^10*x*y^2 + .58944E-3*aa^10*x*y^3 + .58944E-3
  *aa^10*x*y^4 - .19718E-3*aa^10*x*y^5 - .20862E-3*aa^10*x*y^6
  - .58704E-3*aa^10*x*y^10 - .11505E-2*aa^10*x*y^11 + .58704E-3*aa^10
  *x*y^14 - .38082E-3*aa^10*x*y^16 + .10259E-3*aa^10*x*y^19
  + .62287E-2*aa^10*x^4*y^2 - .10394E-1*aa^10*x^4*y^3 - .10839E-1*aa^10
  *x^4*y^4 + .47792E-2*aa^10*x^4*y^5 - .28649E-2*aa^10*x^4*y^6
  + .10235E-2*aa^10*x^4*y^8 - 107433375/4398046511104*aa^10*x^4*y^9
   - .72521E-2*aa^10*x^4*y^10 + .69078E-2*aa^10*x^4*y^11 + .24437E-2
  *aa^10*x^4*y^13 + .5539E-2*aa^10*x^4*y^14 + .24437E-2*aa^10*x^4*y^15
   + .1146E-1*aa^10*x^4*y^16 + .24437E-2*aa^10*x^4*y^18 + .11393E-1
  *aa^10*x^4*y^19 + .24437E-2*aa^10*x^4*y^21 + .29619E-1*aa^10*x^6
  *y^2 + .87687E-2*aa^10*x^6*y^3 + .89232E-2*aa^10*x^6*y^4
  - .20335E-2*aa^10*x^6*y^5 - .11481E-1*aa^10*x^6*y^6 - 138128625/2199023255552
  *aa^10*x^6*y^8 - .10165E-2*aa^10*x^6*y^9 - .29557E-1*aa^10*x^6*y^10
   - .33089E-1*aa^10*x^6*y^11 + .82105E-3*aa^10*x^6*y^13 + .25173E-1
  *aa^10*x^6*y^14 + .82105E-3*aa^10*x^6*y^15 + .11688E-2*aa^10*x^6
  *y^16 + .82105E-3*aa^10*x^6*y^18 + .17584E-1*aa^10*x^6*y^19
  + .82105E-3*aa^10*x^6*y^21 + .30855E-3*aa^11*x^4*y^2 + .68702E-5
  *aa^11*x^4*y^3 + .68702E-5*aa^11*x^4*y^4 + .15701E-4*aa^11*x^4*y^5
   - .11118E-3*aa^11*x^4*y^6 - .30855E-3*aa^11*x^4*y^10 - .26197E-3
  *aa^11*x^4*y^11 + .30855E-3*aa^11*x^4*y^14 + .10431E-3*aa^11*x^4
  *y^16 + .24976E-3*aa^11*x^4*y^19 - .10318E-3*aa^11*x^6*y^2
  + .28589E-3*aa^11*x^6*y^3 + .28589E-3*aa^11*x^6*y^4 - .11878E-3*aa^11
  *x^6*y^5 + .38635E-4*aa^11*x^6*y^6 + .10318E-3*aa^11*x^6*y^10
  - .23842E-3*aa^11*x^6*y^11 - .10318E-3*aa^11*x^6*y^14 - .32452E-3
  *aa^11*x^6*y^16 - .26982E-3*aa^11*x^6*y^19 - .98658E+3*del^2*x*y^2
   - .6203E+3*del^2*x*y^3 - .94178E+3*del^2*x*y^4 - .54091E+3*del^2
  *x*y^5 + .88075E+3*del^2*x*y^6 + .13154E+4*del^2*x*y^8 + .14834E+4
  *del^2*x*y^9 - .32886E+3*del^2*x*y^10 - .37084E+3*del^2*x*y^11
  + .53222E+3*del^2*x*y^13 + .12515E+3*del^2*x*y^14 + .53222E+3*del^2
  *x*y^15 - .13786E+3*del^2*x*y^16 + .53222E+3*del^2*x*y^18
  - .84771E+3*del^2*x*y^19 + .53222E+3*del^2*x*y^21 - .16479E+2*del^2
  *x^4*y^3 + .16479E+2*del^2*x^4*y^4 - .28992E+2*del^2*x^4*y^5
  + .66267E+2*del^2*x^4*y^14 - .13295E+5*del^2*x^6*y^2 - .84252E+4
  *del^2*x^6*y^3 - .12626E+5*del^2*x^6*y^4 - .74056E+4*del^2*x^6*y^5
   + .11869E+5*del^2*x^6*y^6 + .17727E+5*del^2*x^6*y^8 + .1999E+5*del^2
  *x^6*y^9 - .44318E+4*del^2*x^6*y^10 - .49975E+4*del^2*x^6*y^11
  + .71723E+4*del^2*x^6*y^13 + .1952E+4*del^2*x^6*y^14 + .71723E+4
  *del^2*x^6*y^15 - .18578E+4*del^2*x^6*y^16 + .71723E+4*del^2*x^6
  *y^18 - .11424E+5*del^2*x^6*y^19 + .71723E+4*del^2*x^6*y^21
  + .14497E+5*x*y^2 + .91149E+4*x*y^3 + .13839E+5*x*y^4 + .79484E+4
  *x*y^5 - .12942E+5*x*y^6 - .1933E+5*x*y^8 - .21797E+5*x*y^9
  + .48324E+4*x*y^10 + .54493E+4*x*y^11 - .78207E+4*x*y^13
  - .1839E+4*x*y^14 - .78207E+4*x*y^15 + .20257E+4*x*y^16
  - .78207E+4*x*y^18 + .12457E+5*x*y^19 - .78207E+4*x*y^21
  + .24216E+3*x^4*y^3 - .24216E+3*x^4*y^4 + .42602E+3*x^4*y^5
  - .97375E+3*x^4*y^14 + .19537E+6*x^6*y^2 + .1238E+6*x^6*y^3
  + .18553E+6*x^6*y^4 + .10882E+6*x^6*y^5 - .17441E+6*x^6*y^6
  - .26049E+6*x^6*y^8 - .29374E+6*x^6*y^9 + .65122E+5*x^6*y^10
  + .73436E+5*x^6*y^11 - .10539E+6*x^6*y^13 - .28683E+5*x^6*y^14
  - .10539E+6*x^6*y^15 + .27299E+5*x^6*y^16 - .10539E+6*x^6*y^18
  + .16787E+6*x^6*y^19 - .10539E+6*x^6*y^21 + 0.
 

End run. Time 421 sec.