Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:42:36.  Memory: start 0001B84C, length 476348.

Command line: Essays.e +1 Es_out


C Essay 1. Beep command and Ratio command, using [] type symbols.

	B [b-a]

	Z xxx = 1/[x+a] * 1/[x+b]

L 1	Id,Ratio,[x+a],[x+b],[b-a]
	Beep 20
	*end
 
xxx = + [b-a]^-1
  * ( [x+a]^-1 - [x+b]^-1 ) + 0.
 

End run. Time 9 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:42:46.  Memory: start 0001B84C, length 476348.


C Essay 2. Ratio command.

	B bma

	Z xxx = xpa^-1 * xpb^-1

L 1	Id,Ratio,xpa,xpb,bma
	*end
 
xxx = + bma^-1
  * ( xpa^-1 - xpb^-1 ) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:42:48.  Memory: start 0001B84C, length 476348.


C Essay 3. Use of .... in front of statements.

	Z xx = a + b*x^3 + c*x^-1

L 1	IF Multi,x^-1
	OR x
L 2	Id,aaa=7
L 3	..IF x^-1
L 4	..Id,x^-1 = [log(B/A)]
	..ENDIF
L 5	Id,x^n~=B^(n+1)/(n+1) - A^(n+1)/(n+1)
	ELSE
L 2	Id,Addfa,(B-A)
	ENDIF
L 7	Al,aaa=7
	*end
 
xx =  + a*B - a*A + 1/4*b*B^4 - 1/4*b*A^4 + c*[log(B/A)] + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:42:51.  Memory: start 0001B84C, length 476348.


C Essay 4. Symbolic integration of x^n from A to B.

	Z xx = a + b*x

L 1	IF NOT x
L 2	Id,Addfa,(B-A)
	ELSE
L 2	Id,x^n~=B^(n+1)/(n+1) - A^(n+1)/(n+1)
	ENDIF

	*end
 
xx =  + a*B - a*A + 1/2*b*B^2 - 1/2*b*A^2 + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:42:53.  Memory: start 0001B84C, length 476348.


C Essay 5. Numbers: Precision, Digits and Rationalization.

	Precision 15
	Rationalization 5
	Digits 3
	Z xx=3.141592654 + 0x12Ab*a + 1/3*ab + 7.1234567E-10*c
	 + 1E15*abc + abc - 1E15*abc
	 + 1E14*abd + abd - 1E14*abd
	*end
 
xx =  + 355/113 + 4779*a + 1/3*ab + .712E-9*c + abd + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:42:56.  Memory: start 0001B84C, length 476348.


C Essay 6. Complex conjugation spinors and gammas.

	I mu=N,nu=N
	V p,q
	Z xx = Conjg( G6(i0,i1)*G(i1,i2,mu)*G(i2,i3,nu)*Ubg(i0,M,p)*Ug(i3,M,q))
L 2	Id,Gammas,"C
	*end
 
xx = + Ubg(i3,M,q)*G(i3,"s,"4,nu,mu,G7)*Ug(i3,M,p) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:42:58.  Memory: start 0001B84C, length 476348.


C Essay 7. Simple G-string.

	I mu=N,nu=N
	Z xx = G(i1,i2,mu)*G(i2,i1,nu)
L 1	Id,Gammas
	*end
 
xx = + 4*D(mu,nu) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:01.  Memory: start 0001B84C, length 476348.


C Essay 8. Gamma command, "C and "A options.

	I mu=N,nu=N
	Z xx = G(i1,i2,mu)*G5(i2,i3)*G(i3,i4,mu)
L 1	Id,Gammas,"C
	Keep xx
	*next
 
xx = + G(i1,"s,"4,mu,G5,mu) + 0.
 
	Z x1=xx
L 2	Id,Gammas
	Keep xx
	*next
 
x1 = + G5(i1)
  * ( - 4 + N_ ) + 0.
 
	Z x2=xx
L 2	Id,Gammas,"A
	*end
 
x2 = + G5(i1)
  * ( - 4 - N_ ) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:03.  Memory: start 0001B84C, length 476348.


C Essay 9. Gamma command, options "I, "W and "P.

	I mu=N,nu=N
	Z xx= G(i1,"s,"4,mu,G5) * F1(mu)
	      + G(i1,"s,"4,mu,nu,G5) * F1(mu,nu)
L 1	Id,Gammas,"I_,"W_,"P_
> P output
	*yep
 
xx = 
 + G(i1,"S,"5,mu,nu)*F1(Dim_4,mu,Dim_4,nu)
 
 - G(i1,"S,"5,mu)*F1(Dim_4,mu)
 
 + G(i1,"s,"_,mu,nu)*G5(i1)*F1(Dim_N_,mu,Dim_N_,nu)
 
 - G(i1,"s,"_,mu)*G(i1,"S,"5,nu)*F1(Dim_N_,mu,Dim_4,nu)
 
 + G(i1,"s,"_,mu)*G5(i1)*F1(Dim_N_,mu)
 
 + G(i1,"s,"_,nu)*G(i1,"S,"5,mu)*F1(Dim_4,mu,Dim_N_,nu) + 0.
 
L 1	Id,Gammas
	*end
 
xx = 
 + G(i1,"S,"5,mu,nu)*F1(Dim_4,mu,Dim_4,nu)
 
 - G(i1,"S,"5,mu)*F1(Dim_4,mu)
 
 + G(i1,"s,"_,mu,nu)*G5(i1)*F1(Dim_N_,mu,Dim_N_,nu)
 
 - G(i1,"s,"_,mu)*G(i1,"S,"5,nu)*F1(Dim_N_,mu,Dim_4,nu)
 
 + G(i1,"s,"_,mu)*G5(i1)*F1(Dim_N_,mu)
 
 + G(i1,"s,"_,nu)*G(i1,"S,"5,mu)*F1(Dim_4,mu,Dim_N_,nu) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:06.  Memory: start 0001B84C, length 476348.


C Essay 10. Gamma command, options "I, "W and "P.

	I mu=N, nu=N, al=N, be=N, ga=N
	Z xx=  { G(i1,i2,mu,ga,nu,al,be,ga)
	      + G(i1,i1,mu,ga,nu,al,be,ga) }*F1(mu,nu,al,be)
L 2	Id,Gammas,"I,"W_,"P_
> P output
	*yep
 
xx = 
 + G(i1,"s,"4,mu,nu,al,be)*F1(mu,nu,al,be)
  * ( - N_ )
 
 - 2*G(i1,"s,"4,mu,be,al,nu)*F1(mu,nu,al,be)
 
 + G(i1,"t,"4,mu,nu,al,be)*F1(mu,nu,al,be)
  * ( 2 - N ) + 0.
 
L 1	Id,Gammas
> P output
	*end
 
xx = 
 + G(i1,"s,"4,mu,nu,al,be)*F1(mu,nu,al,be)
  * ( - N_ )
 
 - 2*G(i1,"s,"4,mu,be,al,nu)*F1(mu,nu,al,be)
 
 + F1(nu,nu,be,be)
  * ( 8 - 4*N )
 
 + F1(al,be,al,be)
  * ( - 8 + 4*N )
 
 + F1(be,al,al,be)
  * ( 8 - 4*N ) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:08.  Memory: start 0001B84C, length 476348.


C Essay 11. Projecting out basic gamma 3- and 1-strings.

	I mu=N, nu=N, al=N, be, b1=N, b2=N, b3=N, b4=N

	Z xx=  { 1/(4*DB(3)) * G(L,"t,"4,mu,nu,al,b1,b2,b3)} * AG(L,b3,b2,b1)
	       + 1/(4*DB(1)) * G(L,"t,"4,mu,nu,al,b1) * AG(L,b1)

L 3	Id,Gammas
L11	Id,Asymm,AG,2,3,4,5,6
	*end
 
xx = 
 + AG(L,mu,nu,al)
 
 + AG(L,mu)*D(nu,al)
 
 - AG(L,nu)*D(mu,al)
 
 + AG(L,al)*D(mu,nu) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:11.  Memory: start 0001B84C, length 476348.


C Essay 12. Projecting out basic gamma 4-, 2- and 0-strings.

	I mu=N, nu=N, al=N, be=N, b1=N, b2=N, b3=N, b4=N

	Z xx = { 1/(4*DB(4)) * G(L,"t,"4,mu,nu,al,be,b1,b2,b3,b4)} * AG(L,b4,b3,b2,b1)
	       + 1/(4*DB(2)) * G(L,"t,"4,mu,nu,al,be,b1,b2) * AG(L,b2,b1)
	       + 1/4 * G(L,"t,"4,mu,nu,al,be) * AG(L)

L 3	Id,Gammas
L11	Id,Asymm,AG,2,3,4,5,6
	*end
 
xx = 
 + AG(L,mu,nu,al,be)
 
 + AG(L,mu,nu)*D(al,be)
 
 - AG(L,mu,al)*D(nu,be)
 
 + AG(L,mu,be)*D(nu,al)
 
 + AG(L,nu,al)*D(mu,be)
 
 - AG(L,nu,be)*D(mu,al)
 
 + AG(L,al,be)*D(mu,nu)
 
 + AG(L)*D(mu,nu)*D(al,be)
 
 - AG(L)*D(mu,al)*D(nu,be)
 
 + AG(L)*D(mu,be)*D(nu,al) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:13.  Memory: start 0001B84C, length 476348.


C Essay 13. Various gamma try-outs.

> P stats
	I mu=N, nu=N, ga=N, la=N, al=N, be=N

	X Gstr(i1,i2,n,mu,nu,la,ga,al,be) =
	  G(i1,n,mu)*G(n,n+1,nu)*G(n+1,n+2,la)*G(n+2,n+3,ga)*G(n+3,n+4,al)*G(n+4,i2,be)

	Z s0 = Gstr(i1,i2,1,mu,mu,la,ga,al,be)
	Z t0 = Gstr(i1,i1,1,mu,mu,la,ga,al,be)
	Z s1 = Gstr(i1,i2,1,mu,nu,mu,ga,al,be)
	Z t1 = Gstr(i1,i1,1,mu,nu,mu,ga,al,be)
	Z s2 = Gstr(i1,i2,1,mu,nu,la,mu,al,be)
	Z t2 = Gstr(i1,i1,1,mu,nu,la,mu,al,be)
	Z s3 = Gstr(i1,i2,1,mu,nu,la,ga,mu,be)
	Z t3 = Gstr(i1,i1,1,mu,nu,la,ga,mu,be)
	Z s4 = Gstr(i1,i2,1,mu,nu,la,ga,al,mu)
	Z t4 = Gstr(i1,i1,1,mu,nu,la,ga,al,mu)

L 3	Id,Gammas
> P output
	*yep

Terms in output 32
Running time 1 sec			Used	Maximum
Generated terms 32 	Input space 	1252 	100000
Equal terms 0     	Output space 	1314 	250000
Cancellations 0   	Nr of expr.  	35 	255
Multiplications 115	String space 	0 	4096
Records written 0 	Merging		0 	0

 
s0 = + G(i1,"s,"4,la,ga,al,be)
  * ( N )
 
t0 = + D(ga,la)*D(al,be)
  * ( 4*N )
 
 + D(ga,al)*D(la,be)
  * ( 4*N )
 
 + D(ga,be)*D(la,al)
  * ( - 4*N )
 
s1 = + G(i1,"s,"4,nu,ga,al,be)
  * ( 2 - N )
 
t1 = 
 + D(nu,ga)*D(al,be)
  * ( 8 - 4*N )
 
 + D(nu,al)*D(ga,be)
  * ( - 8 + 4*N )
 
 + D(nu,be)*D(ga,al)
  * ( 8 - 4*N )
 
s2 = + G(i1,"s,"4,nu,la,al,be)
  * ( N_ )
 
 + 4*G(i1,"s,"4,al,be)*D(nu,la)
 
t2 = + D(nu,la)*D(al,be)
  * ( 16 + 4*N_ )
 
 + D(nu,al)*D(la,be)
  * ( - 4*N_ )
 
 + D(nu,be)*D(la,al)
  * ( 4*N_ )
 
s3 = + G(i1,"s,"4,nu,la,ga,be)
  * ( - N_ )
 
 - 2*G(i1,"s,"4,ga,la,nu,be)
 
t3 = 
 + D(nu,ga)*D(la,be)
  * ( - 8 + 4*N )
 
 + D(nu,la)*D(ga,be)
  * ( 8 - 4*N )
 
 + D(nu,be)*D(ga,la)
  * ( 8 - 4*N )
 
s4 = + G(i1,"s,"4,nu,la,ga,al)
  * ( N_ )
 
 + 2*G(i1,"s,"4,ga,la,nu,al)
 
 + 2*G(i1,"s,"4,al,nu,la,ga)
 
t4 = + D(nu,ga)*D(la,al)
  * ( - 4*N )
 
 + D(nu,la)*D(ga,al)
  * ( 4*N )
 
 + D(nu,al)*D(ga,la)
  * ( 4*N ) + 0.
 
L 1	Id,Gammas,Trace,i1
L 9	Id,N_=N-4
	Keep s0,t0,s1,t1,s2,t2,s3,t3,s4,t4
	*next

Terms out 32, in 32.

Terms in output 46
Running time 1 sec			Used	Maximum
Generated terms 62 	Input space 	662 	100000
Equal terms 11     	Output space 	1700 	250000
Cancellations 5   	Nr of expr.  	17 	255
Multiplications 167	String space 	0 	4096
Records written 0 	Merging		0 	0

 
s0 = + D(ga,la)*D(al,be)
  * ( 4*N )
 
 + D(ga,al)*D(la,be)
  * ( 4*N )
 
 + D(ga,be)*D(la,al)
  * ( - 4*N )
 
t0 = + D(ga,la)*D(al,be)
  * ( 4*N )
 
 + D(ga,al)*D(la,be)
  * ( 4*N )
 
 + D(ga,be)*D(la,al)
  * ( - 4*N )
 
s1 = 
 + D(nu,ga)*D(al,be)
  * ( 8 - 4*N )
 
 + D(nu,al)*D(ga,be)
  * ( - 8 + 4*N )
 
 + D(nu,be)*D(ga,al)
  * ( 8 - 4*N )
 
t1 = 
 + D(nu,ga)*D(al,be)
  * ( 8 - 4*N )
 
 + D(nu,al)*D(ga,be)
  * ( - 8 + 4*N )
 
 + D(nu,be)*D(ga,al)
  * ( 8 - 4*N )
 
s2 = 
 + D(nu,la)*D(al,be)
  * ( 4*N )
 
 + D(nu,al)*D(la,be)
  * ( 16 - 4*N )
 
 + D(nu,be)*D(la,al)
  * ( - 16 + 4*N )
 
t2 = 
 + D(nu,la)*D(al,be)
  * ( 4*N )
 
 + D(nu,al)*D(la,be)
  * ( 16 - 4*N )
 
 + D(nu,be)*D(la,al)
  * ( - 16 + 4*N )
 
s3 = 
 + D(nu,ga)*D(la,be)
  * ( - 8 + 4*N )
 
 + D(nu,la)*D(ga,be)
  * ( 8 - 4*N )
 
 + D(nu,be)*D(ga,la)
  * ( 8 - 4*N )
 
t3 = 
 + D(nu,ga)*D(la,be)
  * ( - 8 + 4*N )
 
 + D(nu,la)*D(ga,be)
  * ( 8 - 4*N )
 
 + D(nu,be)*D(ga,la)
  * ( 8 - 4*N )
 
s4 = + D(nu,ga)*D(la,al)
  * ( - 4*N )
 
 + D(nu,la)*D(ga,al)
  * ( 4*N )
 
 + D(nu,al)*D(ga,la)
  * ( 4*N )
 
t4 = + D(nu,ga)*D(la,al)
  * ( - 4*N )
 
 + D(nu,la)*D(ga,al)
  * ( 4*N )
 
 + D(nu,al)*D(ga,la)
  * ( 4*N ) + 0.
 

C Results should be all zero.

	Z x0 = s0 - t0
	Z x1 = s1 - t1
	Z x2 = s2 - t2
	Z x3 = s3 - t3
	Z x4 = s4 - t4
	*end

Terms in output 0
Running time 1 sec			Used	Maximum
Generated terms 46 	Input space 	1430 	101016
Equal terms 23     	Output space 	0 	248984
Cancellations 23   	Nr of expr.  	23 	255
Multiplications 148	String space 	0 	4096
Records written 0 	Merging		0 	0

 
x0 = 0.
 
x1 = 0.
 
x2 = 0.
 
x3 = 0.
 
x4 = 0. + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:17.  Memory: start 0001B84C, length 476348.


C Essay 14. Order command.

	Z xx = Fab(4,5,ddd)*Fab(2,3,bbb)*Fab(1,2,aaa)*Fab(3,4,ccc)
	 *Faa(14,15,ddd)*Faa(12,13,bbb)*Faa(11,12,aaa)*Faa(13,14,ccc)
L 1	Id,Order,"C,Faa,Fab
	*next
 
xx = + Fab(1,aaa,bbb,ccc,ddd)*Faa(11,aaa,bbb,ccc,ddd) + 0.
 
	Z xx = Fab(4,5,ddd)*Fab(2,3,bbb)*Fab(1,2,aaa)*Fab(3,4,ccc)
	 *Faa(14,15,ddd)*Faa(12,13,bbb)*Faa(11,12,aaa)*Faa(13,14,ccc)

L 1	Id,Order,Faa,Fab
	*next
 
xx = + Fab(1,aaa)*Fab(1,bbb)*Fab(1,ccc)*Fab(1,ddd)*Faa(11,aaa)*Faa(11,bbb)
  *Faa(11,ccc)*Faa(11,ddd) + 0.
 
	Z xx = Fab(4,5,ddd)*Fab(2,3,bbb)*Fab(1,2,aaa)*Fab(3,4,ccc)
	 *Faa(14,15,ddd)*Faa(12,13,bbb)*Faa(11,12,aaa)*Faa(13,14,ccc)

L 1	Id,Order,90,Faa,Fab
	*end
 
xx = + Fab(91,aaa)*Fab(91,bbb)*Fab(91,ccc)*Fab(91,ddd)*Faa(90,aaa)
  *Faa(90,bbb)*Faa(90,ccc)*Faa(90,ddd) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:19.  Memory: start 0001B84C, length 476348.


C Essay 15. Gamma command, no "S option.

	I mu=N,nu=N,al=N,be=N
	X Sin(i1,i2,mu) = ag*G(i1,i2,mu) + a1*Gi(i1,i2) + a5*G5(i1,i2)
	 + a6*G6(i1,i2) + a7*G7(i1,i2)
	Z xs=Sin(i1,i2,mu)
	Z xd=Sin(i1,i2,mu)*Sin(i2,i3,nu)

L 2	Id,Gammas,"S_
	*end
 
xs = 
 + G(i1,"s,"4,mu)
  * ( ag )
 
 + Gi(i1)
  * ( a1 + a6 + a7 )
 
 + G5(i1)
  * ( a5 + a6 - a7 )
 
xd = 
 + G(i1,"s,"4,mu,nu)
  * ( ag^2 )
 
 + G(i1,"s,"4,mu,G5)
  * ( ag*a5 )
 
 + G(i1,"s,"4,mu,G6)
  * ( ag*a6 )
 
 + G(i1,"s,"4,mu,G7)
  * ( ag*a7 )
 
 + G(i1,"s,"4,mu)
  * ( ag*a1 )
 
 + G(i1,"s,"4,nu)
  * ( ag*a1 )
 
 + G(i1,"s,"4,G5,nu)
  * ( ag*a5 )
 
 + G(i1,"s,"4,G6,nu)
  * ( ag*a6 )
 
 + G(i1,"s,"4,G7,nu)
  * ( ag*a7 )
 
 + Gi(i1)
  * ( 2*a1*a6 + 2*a1*a7 + a1^2 + 2*a5*a6 - 2*a5*a7 + a5^2
  + 2*a6^2 + 2*a7^2 )
 
 + G5(i1)
  * ( 2*a1*a5 + 2*a1*a6 - 2*a1*a7 + 2*a5*a6 + 2*a5*a7 + 2*a6^2
  - 2*a7^2 ) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:22.  Memory: start 0001B84C, length 476348.


C Essay 16. Gamma command, with "S option.

	I mu,nu,al,be
	X Sin(i1,mu) = ag*G(i1,mu) + a1*Gi(i1) + a5*G5(i1)
	 + a6*G6(i1) + a7*G7(i1)
	Z xs=Sin(i1,mu)
	Z xd=Sin(i1,mu)*Sin(i1,nu)
L 2	Id,Gammas
	*end
 
xs = 
 + G(i1,"S,"4,mu)
  * ( ag )
 
 + Gi(i1)
  * ( a1 + a6 + a7 )
 
 + G5(i1)
  * ( a5 + a6 - a7 )
 
xd = 
 + G(i1,"S,"4,mu,nu)
  * ( ag^2 )
 
 + G(i1,"S,"4,mu)
  * ( ag*a1 + ag*a6 + ag*a7 )
 
 + G(i1,"S,"4,nu)
  * ( ag*a1 + ag*a6 + ag*a7 )
 
 + G(i1,"S,"5,mu)
  * ( - ag*a5 - ag*a6 + ag*a7 )
 
 + G(i1,"S,"5,nu)
  * ( ag*a5 + ag*a6 - ag*a7 )
 
 + Gi(i1)
  * ( 2*a1*a6 + 2*a1*a7 + a1^2 + 2*a5*a6 - 2*a5*a7 + a5^2
  + 2*a6^2 + 2*a7^2 )
 
 + G5(i1)
  * ( 2*a1*a5 + 2*a1*a6 - 2*a1*a7 + 2*a5*a6 + 2*a5*a7 + 2*a6^2
  - 2*a7^2 ) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:25.  Memory: start 0001B84C, length 476348.


C Essay 17. Spin summation.

	I mu=N,nu=N,al=N,be=N
	V p,q,k

	Z xx = Ubg(i1,M,p)*G(i1,"S,"7,mu)*Ug(i1,m,q)
	 *Ubg(i2,m,q)*G(i2,"S,"7,al)*Ug(i2,M,p)
	Keep xx
	*next
 
xx = + Ubg(i1,M,p)*G(i1,"S,"7,mu)*Ug(i1,m,q)*Ubg(i2,m,q)*G(i2,"S,"7,al)
  *Ug(i2,M,p) + 0.
 
	Z x1=xx
L 2	Id,Spin,q
	Keep xx
	*next
 
x1 = 
 + Ubg(i1,M,p)*G(i1,"S,"7,mu)*G(i1,q)*G(i1,"S,"7,al)*Ug(i1,M,p)
  * ( - i )
 
 + Ubg(i1,M,p)*G(i1,"S,"7,mu)*Gi(i1)*G(i1,"S,"7,al)*Ug(i1,M,p)
  * ( m ) + 0.
 
	Z x1=xx
L 2	Id,Spin,p,q
	*end
 
x1 = 
 - G(i2,"S,"7,mu)*G(i2,q)*G(i2,"S,"7,al)*G(i2,p)
 
 + G(i2,"S,"7,mu)*G(i2,q)*G(i2,"S,"7,al)*Gi(i2)
  * ( - i*M )
 
 + G(i2,"S,"7,mu)*Gi(i2)*G(i2,"S,"7,al)*G(i2,p)
  * ( - i*m )
 
 + G(i2,"S,"7,mu)*Gi(i2)*G(i2,"S,"7,al)*Gi(i2)
  * ( M*m ) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:27.  Memory: start 0001B84C, length 476348.


C Essay 18. Gamma command test.

	I a1=N,a2=N,a3=N,a4=N,a5=N,a6=N
	I b1,b2,b3,b4,b5,b6,b7,b8
	F F1
	V p,q
	S m,m1
	Z x1=Fa(aa,bb)*Fb(aa,bb)*G(1,2,a1,b1,a1,a2,b2,a3)*F1(a2,a3)*Fc(aa,bb)
	Z x2=Fa(aa,bb)*Fb(aa,bb)*G(1,2,a1,b1,a1,a2,b2,a3)*F1(a2,a3)*Ubg(1,m1,q)
	  *Fc(aa,bb)
	Z x3=Fa(aa,bb)*Ug(2,m,p)*Fb(aa,bb)*G(1,2,a1,b1,a1,a2,b2,a3)*F1(a2,a3)
	  *Fc(aa,bb)
	Z x4=Fa(aa,bb)*Ug(2,m,p)*Fb(aa,bb)*G(1,2,a1,b1,a1,a2,b2,a3)*F1(a2,a3)
	  *Ubg(1,m1,q)*Fc(aa,bb)
	Z x5=Fa(aa,bb)*G(3,1,a4)*Fb(aa,bb)*G(1,2,a1,b1,a1,a2,b2,a3)*F1(a2,a3)
	 *G(2,3,a4)*Fc(aa,bb)
L 1	Id,Gammas
	*end
 
x1 = 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"S,"4,b1,a2)*F1(Dim_4,a2,b2)*Fc(aa,bb)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"S,"4,b1,a3)*F1(b2,Dim_4,a3)*Fc(aa,bb)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"S,"4,b1,b2)*F1(Dim_4,a2,Dim_4,a2)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"S,"5,b1,Naa)*F1(Dim_4,a2,Dim_4,a3)*Fc(aa,bb)
  *Epf(a2,a3,b2,Naa)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a2,a3)*G(1,"S,"4,b1,b2)*F1(Dim_N_,a2,Dim_N_,
  a3)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a2)*G(1,"S,"4,a3)*F1(Dim_N_,a2,Dim_4,a3)
  *Fc(aa,bb)*D(b1,b2)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a2)*G(1,"S,"4,b1)*F1(Dim_N_,a2,b2)
  *Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a2)*G(1,"S,"4,b2)*F1(Dim_N_,a2,b1)
  *Fc(aa,bb)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a2)*G(1,"S,"5,Naa)*F1(Dim_N_,a2,Dim_4,a3)
  *Fc(aa,bb)*Epf(a3,b1,b2,Naa)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a3)*G(1,"S,"4,a2)*F1(Dim_4,a2,Dim_N_,a3)
  *Fc(aa,bb)*D(b1,b2)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a3)*G(1,"S,"4,b1)*F1(b2,Dim_N_,a3)
  *Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a3)*G(1,"S,"4,b2)*F1(b1,Dim_N_,a3)
  *Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a3)*G(1,"S,"5,Naa)*F1(Dim_4,a2,Dim_N_,a3)
  *Fc(aa,bb)*Epf(a2,b1,b2,Naa)
  * ( - 2 - N_ )
 
x2 = 
 + Fa(aa,bb)*Fb(aa,bb)*F1(b1,Dim_N_,a3)*Ubg(1,m1,q)*G(1,"s,"_,a3)*G(1,"S,
  "4,b2)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(b2,Naa)*Ubg(1,m1,q)*G(1,"S,"4,b1,Naa)*Fc(aa,bb)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(b2,Dim_N_,a3)*Ubg(1,m1,q)*G(1,"s,"_,a3)*G(1,"S,
  "4,b1)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Naa,b2)*Ubg(1,m1,q)*G(1,"S,"4,b1,Naa)*Fc(aa,bb)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Naa,Dim_N_,a3)*Ubg(1,m1,q)*G(1,"s,"_,a3)
  *G(1,"S,"4,Naa)*Fc(aa,bb)*D(b1,b2)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_N_,a2,b1)*Ubg(1,m1,q)*G(1,"s,"_,a2)*G(1,"S,
  "4,b2)*Fc(aa,bb)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_N_,a2,b2)*Ubg(1,m1,q)*G(1,"s,"_,a2)*G(1,"S,
  "4,b1)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_N_,a2,Naa)*Ubg(1,m1,q)*G(1,"s,"_,a2)
  *G(1,"S,"4,Naa)*Fc(aa,bb)*D(b1,b2)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_N_,a2,Dim_N_,a3)*Ubg(1,m1,q)*G(1,"s,"_,a2,a3)
  *G(1,"S,"4,b1,b2)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_N_,a2,Dim_4,a3)*Ubg(1,m1,q)*G(1,"s,"_,a2)
  *G(1,"S,"5,Naa)*Fc(aa,bb)*Epf(a3,b1,b2,Naa)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_4,a2,Dim_N_,a3)*Ubg(1,m1,q)*G(1,"s,"_,a3)
  *G(1,"S,"5,Naa)*Fc(aa,bb)*Epf(a2,b1,b2,Naa)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_4,a2,Dim_4,a2)*Ubg(1,m1,q)*G(1,"S,"4,b1,b2)
  *Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_4,a2,Dim_4,a3)*Ubg(1,m1,q)*G(1,"S,"5,b1,Naa)
  *Fc(aa,bb)*Epf(a2,a3,b2,Naa)
  * ( - 2 - N_ )
 
x3 = 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"S,"4,b1,a2)*Ug(1,m,p)*F1(Dim_4,a2,b2)*Fc(aa,bb)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"S,"4,b1,a3)*Ug(1,m,p)*F1(b2,Dim_4,a3)*Fc(aa,bb)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"S,"4,b1,b2)*Ug(1,m,p)*F1(Dim_4,a2,Dim_4,a2)
  *Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"S,"5,b1,Naa)*Ug(1,m,p)*F1(Dim_4,a2,Dim_4,a3)
  *Fc(aa,bb)*Epf(a2,a3,b2,Naa)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a2,a3)*G(1,"S,"4,b1,b2)*Ug(1,m,p)
  *F1(Dim_N_,a2,Dim_N_,a3)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a2)*G(1,"S,"4,a3)*Ug(1,m,p)*F1(Dim_N_,a2,
  Dim_4,a3)*Fc(aa,bb)*D(b1,b2)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a2)*G(1,"S,"4,b1)*Ug(1,m,p)*F1(Dim_N_,a2,
  b2)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a2)*G(1,"S,"4,b2)*Ug(1,m,p)*F1(Dim_N_,a2,
  b1)*Fc(aa,bb)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a2)*G(1,"S,"5,Naa)*Ug(1,m,p)*F1(Dim_N_,a2,
  Dim_4,a3)*Fc(aa,bb)*Epf(a3,b1,b2,Naa)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a3)*G(1,"S,"4,a2)*Ug(1,m,p)*F1(Dim_4,a2,
  Dim_N_,a3)*Fc(aa,bb)*D(b1,b2)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a3)*G(1,"S,"4,b1)*Ug(1,m,p)*F1(b2,Dim_N_,
  a3)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a3)*G(1,"S,"4,b2)*Ug(1,m,p)*F1(b1,Dim_N_,
  a3)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*G(1,"s,"_,a3)*G(1,"S,"5,Naa)*Ug(1,m,p)*F1(Dim_4,a2,
  Dim_N_,a3)*Fc(aa,bb)*Epf(a2,b1,b2,Naa)
  * ( - 2 - N_ )
 
x4 = 
 + Fa(aa,bb)*Fb(aa,bb)*F1(b1,Dim_N_,a3)*Ubg(1,m1,q)*G(1,"s,"_,a3)*G(1,"S,
  "4,b2)*Ug(1,m,p)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(b2,Naa)*Ubg(1,m1,q)*G(1,"S,"4,b1,Naa)*Ug(1,m,p)
  *Fc(aa,bb)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(b2,Dim_N_,a3)*Ubg(1,m1,q)*G(1,"s,"_,a3)*G(1,"S,
  "4,b1)*Ug(1,m,p)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Naa,b2)*Ubg(1,m1,q)*G(1,"S,"4,b1,Naa)*Ug(1,m,p)
  *Fc(aa,bb)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Naa,Dim_N_,a3)*Ubg(1,m1,q)*G(1,"s,"_,a3)
  *G(1,"S,"4,Naa)*Ug(1,m,p)*Fc(aa,bb)*D(b1,b2)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_N_,a2,b1)*Ubg(1,m1,q)*G(1,"s,"_,a2)*G(1,"S,
  "4,b2)*Ug(1,m,p)*Fc(aa,bb)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_N_,a2,b2)*Ubg(1,m1,q)*G(1,"s,"_,a2)*G(1,"S,
  "4,b1)*Ug(1,m,p)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_N_,a2,Naa)*Ubg(1,m1,q)*G(1,"s,"_,a2)
  *G(1,"S,"4,Naa)*Ug(1,m,p)*Fc(aa,bb)*D(b1,b2)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_N_,a2,Dim_N_,a3)*Ubg(1,m1,q)*G(1,"s,"_,a2,a3)
  *G(1,"S,"4,b1,b2)*Ug(1,m,p)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_N_,a2,Dim_4,a3)*Ubg(1,m1,q)*G(1,"s,"_,a2)
  *G(1,"S,"5,Naa)*Ug(1,m,p)*Fc(aa,bb)*Epf(a3,b1,b2,Naa)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_4,a2,Dim_N_,a3)*Ubg(1,m1,q)*G(1,"s,"_,a3)
  *G(1,"S,"5,Naa)*Ug(1,m,p)*Fc(aa,bb)*Epf(a2,b1,b2,Naa)
  * ( - 2 - N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_4,a2,Dim_4,a2)*Ubg(1,m1,q)*G(1,"S,"4,b1,b2)
  *Ug(1,m,p)*Fc(aa,bb)
  * ( 2 + N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_4,a2,Dim_4,a3)*Ubg(1,m1,q)*G(1,"S,"5,b1,Naa)
  *Ug(1,m,p)*Fc(aa,bb)*Epf(a2,a3,b2,Naa)
  * ( - 2 - N_ )
 
x5 = 
 + Fa(aa,bb)*Fb(aa,bb)*F1(b1,b2)*Fc(aa,bb)
  * ( - 8*N - 4*N*N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(b2,b1)*Fc(aa,bb)
  * ( - 8*N - 4*N*N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_N_,a2,Dim_N_,a2)*Fc(aa,bb)*D(b1,b2)
  * ( 8*N + 4*N*N_ )
 
 + Fa(aa,bb)*Fb(aa,bb)*F1(Dim_4,a3,Dim_4,a3)*Fc(aa,bb)*D(b1,b2)
  * ( 8*N + 4*N*N_ ) + 0.
 

End run. Time 2 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:31.  Memory: start 0001B84C, length 476348.


C Essay 19. Order command with "C option.

	Z x1 = Fab(4,5,ddd)*Fab(2,3,bbb)*Fab(1,2,aaa)*Fab(3,4,ccc)*
	 (  Faa(12,13,bbb)*Faa(11,12,aaa)*Faa(13,14,ccc)
	  + Faa(12,13,bbb)*Faa(13,14,ccc)*Faa(11,12,aaa)
	  + Faa(11,12,aaa)*Faa(12,13,bbb)*Faa(13,14,ccc)
	  + Faa(11,12,aaa)*Faa(13,14,ccc)*Faa(12,13,bbb)
	  + Faa(13,14,ccc)*Faa(11,12,aaa)*Faa(12,13,bbb)
	  + Faa(13,14,ccc)*Faa(12,13,bbb)*Faa(11,12,aaa) )

L 2	Id,Order,"C,Faa,Fab
	*end
 
x1 = + 6*Fab(1,aaa,bbb,ccc,ddd)*Faa(11,aaa,bbb,ccc) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:33.  Memory: start 0001B84C, length 476348.


C Essay 20. Collecting Gammas and Spinors.

C I aaa=N,bbb=N,ccc=N,ddd=N
	I aaa,bbb,ccc,ddd
	V p
	S m
	B A1,A2,A3,A4,A5
	X Str(i1,i2) =    G(12,13,bbb)*G(i1,12,aaa)*G(13,i2,ccc)
			+ G(12,13,bbb)*G(13,i2,ccc)*G(i1,12,aaa)
			+ G(i1,12,aaa)*G(12,13,bbb)*G(13,i2,ccc)
			+ G(i1,12,aaa)*G(13,i2,ccc)*G(12,13,bbb)
			+ G(13,i2,ccc)*G(i1,12,aaa)*G(12,13,bbb)
			+ G(13,i2,ccc)*G(12,13,bbb)*G(i1,12,aaa)

	Z xx= 	  A1*Str(i1,i2)
		+ A2*Str(i1,i2)*G(i2,i1,ddd)
		+ A2*G(i2,i1,ddd)*Str(i1,i2)
	        + A3*Ubg(i1,m,p)*Str(i1,i2)
		+ A3*Str(i1,i2)*Ubg(i1,m,p)
		+ A4*Ug(i2,m,p)*Str(i1,i2)
		+ A4*Str(i1,i2)*Ug(i2,m,p)
	        + A5*Ug(i2,m,p)*Ubg(i1,m,p)*Str(i1,i2)
	        + A5*Ubg(i1,m,p)*Ug(i2,m,p)*Str(i1,i2)
	        + A5*Ug(i2,m,p)*Str(i1,i2)*Ubg(i1,m,p)
	        + A5*Ubg(i1,m,p)*Str(i1,i2)*Ug(i2,m,p)
	        + A5*Str(i1,i2)*Ug(i2,m,p)*Ubg(i1,m,p)
	        + A5*Str(i1,i2)*Ubg(i1,m,p)*Ug(i2,m,p)
L 2	Id,Gammas,"C
	*end
 
xx = 
 + 6*G(i1,"s,"4,aaa,bbb,ccc)*A1
 
 + 12*G(i1,"s,"4,aaa,bbb,ccc)*Ug(i1,m,p)*A4
 
 + 2*G(i1,"t,"4,aaa,bbb,ccc,ddd)*A2
 
 + 2*G(i1,"t,"4,bbb,ccc,ddd,aaa)*A2
 
 + 2*G(i1,"t,"4,ccc,ddd,aaa,bbb)*A2
 
 + 6*G(i1,"t,"4,ddd,aaa,bbb,ccc)*A2
 
 + 12*Ubg(i1,m,p)*G(i1,"s,"4,aaa,bbb,ccc)*A3
 
 + 36*Ubg(i1,m,p)*G(i1,"s,"4,aaa,bbb,ccc)*Ug(i1,m,p)*A5 + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:36.  Memory: start 0001B84C, length 476348.


C Essay 21. Order command with various options.

	Z xx=Fa(aa,ab)*F1(2,3,bb)*Fb(aa,ab)*F1(1,2,aa)*F1(3,4,cc)*Fc(aa,ab)
	Keep xx
	*next
 
xx = + Fa(aa,ab)*F1(2,3,bb)*Fb(aa,ab)*F1(1,2,aa)*F1(3,4,cc)*Fc(aa,ab) + 0.
 
	Z x1=xx
L 2	Id,Order,F1
	Keep xx
	*next
 
x1 = + Fa(aa,ab)*Fb(aa,ab)*F1(1,aa)*F1(1,bb)*F1(1,cc)*Fc(aa,ab) + 0.
 
	Z x1=xx
L 2	Id,Order,0,F1
	Keep xx
	*next
 
x1 = + Fa(aa,ab)*Fb(aa,ab)*F1(aa)*F1(bb)*F1(cc)*Fc(aa,ab) + 0.
 
	Z x1=xx
L 2	Id,Order,10,F1
	Keep xx
	*next
 
x1 = + Fa(aa,ab)*Fb(aa,ab)*F1(10,aa)*F1(10,bb)*F1(10,cc)*Fc(aa,ab) + 0.
 
	Z x1=xx
L 2	Id,Order,"C,F1
	Keep xx
	*next
 
x1 = + Fa(aa,ab)*Fb(aa,ab)*F1(1,aa,bb,cc)*Fc(aa,ab) + 0.
 
	Z x1=xx
L 2	Id,Order,0,"C,F1
	Keep xx
	*next
 
x1 = + Fa(aa,ab)*Fb(aa,ab)*F1(aa,bb,cc)*Fc(aa,ab) + 0.
 
	Z x1=xx
L 2	Id,Order,10,"C,F1
	*end
 
x1 = + Fa(aa,ab)*Fb(aa,ab)*F1(10,aa,bb,cc)*Fc(aa,ab) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:39.  Memory: start 0001B84C, length 476348.


C Essay 22. Some simple N-dimensional traces.

> P stats
	I a1=N,a2=N,a3=N,a4=N,a5=N,a6=N
	I b1,b2,b3,b4,b5,b6,b7,b8
	V p
	Z x1 = G(1,"t,"4,a1,a2,a3,a4,a1,a2,a3,a4)
	Z x2 = G(1,"t,"4,a1,b2,b3,b4,a1,b2,b3,b4)
L 1	Id,Gammas
L 9	Id,N=N_+4
	*end

Terms in output 7
Running time 1 sec			Used	Maximum
Generated terms 18 	Input space 	598 	100000
Equal terms 11     	Output space 	174 	250000
Cancellations 0   	Nr of expr.  	13 	255
Multiplications 88	String space 	0 	4096
Records written 0 	Merging		0 	0

 
x1 =  - 512 - 448*N_ - 80*N_^2 + 16*N_^3 + 4*N_^4
 
x2 =  - 512 - 64*N_ + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:42.  Memory: start 0001B84C, length 476348.


C Essay 23. Various traces and strings.

	I al=N, be=N, mu, nu

	Z x0=
	 + a0s*G(1,"s,"4)
	 + a0t*G(1,"t,"4)
	 + a0s_*G(1,"s,"_)
	 + a0t_*G(1,"t,"_)

	 + a0S*G(1,"s,"4,Gi) + a05S*G(1,"s,"4,G5)
	 + a06S*G(1,"s,"4,G6) + a07S*G(1,"s,"4,G7)

	 + a0T*G(1,"t,"4,Gi) + a05T*G(1,"t,"4,G5)
	 + a06T*G(1,"t,"4,G6) + a07T*G(1,"t,"4,G7)

	Z x1=
	 + F1(al)*{
	 + a1s*G(1,"s,"4,al)
	 + a1t*G(1,"t,"4,al)
	 + a1s_*G(1,"s,"_,al)
	 + a1t_*G(1,"t,"_,al) }

	 + a1S*G(1,"s,"4,Gi,mu) + a15S*G(1,"s,"4,G5,mu)
	 + a16S*G(1,"s,"4,G6,mu) + a17S*G(1,"s,"4,G7,mu)

	 + a1T*G(1,"t,"4,Gi,mu) + a15T*G(1,"t,"4,G5,mu)
	 + a16T*G(1,"t,"4,G6,mu) + a17T*G(1,"t,"4,G7,mu)

	Z x2=
	 + F2(al,be)*{
	 + a2s*G(1,"s,"4,al,be)
	 + a2t*G(1,"t,"4,al,be)
	 + a2s_*G(1,"s,"_,al,be)
	 + a2t_*G(1,"t,"_,al,be) }

	 + a2S*G(1,"s,"4,Gi,mu,nu) + a25S*G(1,"s,"4,G5,mu,nu)
	 + a26S*G(1,"s,"4,G6,mu,nu) + a27S*G(1,"s,"4,G7,mu,nu)

	 + a2T*G(1,"t,"4,Gi,mu,nu) + a25T*G(1,"t,"4,G5,mu,nu)
	 + a26T*G(1,"t,"4,G6,mu,nu) + a27T*G(1,"t,"4,G7,mu,nu)

L 2	Id,Gammas,1:"S_

	*end
 
x0 = 
  + 4*a0t + a0s_ + a0t_ + 4*a0T + 4*a06T + 4*a07T
 
 + Gi(1)
  * ( a0s + a0S + a06S + a07S )
 
 + G5(1)
  * ( a05S + a06S - a07S )
 
x1 = 
 + G(1,"S,"4,mu)
  * ( a1S + a16S + a17S )
 
 + G(1,"S,"5,mu)
  * ( a15S + a16S - a17S )
 
 + F1(al)*G(1,"s,"4,al)
  * ( a1s )
 
 + F1(al)*G(1,"s,"_,al)
  * ( a1s_ )
 
x2 = 
 + D(mu,nu)
  * ( 4*a2T + 4*a26T + 4*a27T )
 
 + G(1,"S,"4,mu,nu)
  * ( a2S + a26S + a27S )
 
 + G(1,"S,"5,mu,nu)
  * ( a25S + a26S - a27S )
 
 + F2(al,al)
  * ( 4*a2t )
 
 + F2(al,be)*G(1,"s,"4,al,be)
  * ( a2s )
 
 + F2(al,be)*G(1,"s,"_,al,be)
  * ( a2s_ )
 
 + F2(Dim_N_,al,Dim_N_,al)
  * ( a2t_ ) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:45.  Memory: start 0001B84C, length 476348.


C Essay 24. DC function. Symmetrized Id argument.

> P lists
	X XAX_(I1,I2,K1,K2,L1,L2): Fchar(I1,I2,K1,K2,L1,L2)
	T AP: A,Z
	Z xx=AX_X("A,"A_,"Y,"Y_,"X,"X_) + ~YAY_~K
	 + a1*DC("P,AP,-3,"A_,"A,"B,"A,"B)
	 + a2*DC("P,AP,3,"A_,"A,"B,"A,"B)
	 + a3*DC("P,AP,-7,"A,"Z_,"A,"B,"Z,"A_,"C,"B,"Z,"C,"D)
	 + a7*DC("P,AP,-1,"A,"A,"B,"A,"B,"B,"A)
	 + a8*DC("P,AP,-1,"A_,"A,"A,"B,"A,"B,"B,"A)
	 + a9*DC("P,AP,-1,"A_,"A,"A,"A,"B,"A,"B,"B,"A)
	 + a10*DC("P,AP,-1,"A_,"A,"A,"A,"A,"B,"A,"B,"B,"A)
	 + a11*DC("P,AP,-1,"A_,"A,"A,"A,"A,"A,"B,"A,"B,"B,"A)
	 + a12*DC("P,AP,-1,"A_,"A,"A,"A,"A,"A,"A,"B,"A,"B,"B,"A)
	 + bb1*(6*2)^-3 + bb2*(6*2)^3+ bb3*(6*6*2*2)^-7
	 + c4*24*(b4 + 5*(b5 + 6*(b6 + 7*(b7+8*(bb8+9*bb9)))))*6
	 + c8*40320*(b8+ 9*(b9 + 10*(b10 + 11*(b11+12*(b12+13*b13)))))
L 7	Id,~YAY_~K: 24*aaa
	*end


A i=i, AY_YK, a1, a2, a3, a7, a8, a9, a10, a11, a12, bb1, bb2, bb3, 
  c4, c8, b4, b8, b5, b9, b6, b10, b7, b11, bb8, bb9, b12, b13, aaa

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, Fchar

E AX_X=X1, AP=T0
 
xx = 
  + 1/1728*a1 + 1728*a2 + .77887E-15*a3 + 1/144*a7 + 1/720*a8
  + 1/4320*a9 + 1/30240*a10 + 1/241920*a11 + 1/2177280*a12
  + 1/1728*bb1 + 1728*bb2 + .77887E-15*bb3 + 144*c4*b4 + 720*c4*b5
   + 4320*c4*b6 + 30240*c4*b7 + 241920*c4*bb8 + 2177280*c4*bb9
  + 40320*c8*b8 + 362880*c8*b9 + 3628800*c8*b10 + 39916800*c8*b11
  + 479001600*c8*b12 + 6227020800*c8*b13 + 24*aaa
 
 + Fchar("X,"X_,"A,"A_,"Y,"Y_) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:47.  Memory: start 0001B84C, length 476348.


C Essay 25. The All command.

> P lists
	V p,q
	F F
	I mu=N,nu=N

	Z xx=3*pDp^2*pDq^3*F1(p,p,q,p)*p(mu)*q(nu)

L 1	Id,All,p,N,F
L 2	Id,F(i1~,i2~,i3~,i4~,i5~,i6~,i7~,i8~,i9~,i10~,i11~)=
	 F(i1,i2,i3,i6,i7,i8,i9,i10,i11)*D(i4,i5)
	*end


I mu=N, nu=N

V p, q

A i=i, N, N_

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, F1
 
xx = + F1(Naa,Nab,q,Nac)*F(mu,Nad,Nad,q,q,q,Naa,Nab,Nac)*q(nu)
  * ( 3*N ) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:50.  Memory: start 0001B84C, length 476348.


C Essay 26. An N-dimensional trace.

	I mu1=N,mu2=N,mu3=N,mu4=N,mu5=N,mu6=N,mu7=N,mu8=N
	S N,N_
	F F1,F2,F3,F4
	V P

	Z xx=G(i1,1,mu1)*G(1,2,mu2)*G(2,3,mu3)*G(3,4,mu4)*G(4,5,mu5)
	 *G(5,6,mu6)*G(6,7,mu1)*G(7,8,mu2)*G(8,9,mu3)*G(9,10,mu4)*G(10,11,mu5)
	 *G(11,i1,mu6)
	 -2*a4*4*4^5
	Sum,mu1,mu2,mu3,mu4,mu5,mu6,mu7,mu8
L 1	Id,Gammas,"C
> P output
	*yep
 
xx =  - 8192*a4
 
 + G(i1,"t,"4,Naa,Nab,Nac,Nad,Nae,Naf,Naa,Nab,Nac,Nad,Nae,Naf) + 0.
 
L 1	Id,Gammas
> P output
L 9	Id,N=N_+4
	*end
 
xx = 
  - 8192 - 9728*N_ - 2560*N_^2 + 800*N_^3 + 400*N_^4 + 24*N_^5
  - 4*N_^6 - 8192*a4 + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:53.  Memory: start 0001B84C, length 476348.


C Essay 27. A product of two N_dimensional traces.

	I mu1=N,mu2=N,mu3=N,mu4=N,mu5=N,mu6=N,mu7=N,mu8=N
	S N,N_
	F F1,F2,F3,F4
	V P

	Z xx=G(i1,1,mu1)*G(1,2,mu2)*G(2,3,mu3)*G(3,4,mu4)*G(4,5,mu5)
	 *G(5,i1,mu6)*G(i2,7,mu1)*G(7,8,mu2)*G(8,9,mu3)*G(9,10,mu4)*G(10,11,mu5)
	 *G(11,i2,mu6)

	Sum,mu1,mu2,mu3,mu4,mu5,mu6,mu7,mu8
L 1	Id,Gammas,"C
> P output
	*yep
 
xx = + G(i1,"t,"4,Naa,Nab,Nac,Nad,Nae,Naf)*G(i2,"t,"4,Naa,Nab,Nac,Nad,Nae,
  Naf) + 0.
 
L 1	Id,Gammas
L 9	Id,N=N_+4
	*end
 
xx =  + 8704 + 7936*N_ + 2400*N_^2 + 240*N_^3 + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:43:56.  Memory: start 0001B84C, length 476348.


C Essay 28. Various N-dimensional traces.

	I mu1=N,mu2=N,mu3=N,mu4=N,mu5=N,mu6=N,mu7=N,mu8=N
	S N,N_
	F F1,F2,F3,F4
	V P
	B Tr4,Tr6,t00,t11,t000,t011,t020,t121,t222
	 ,Tr8,t0000,t0011,t0020,t0121,t0222,t0231,t1111,t1221,t1322,t2332,t3333
	Z xx=
	 Tr4*{t00*G(i1,1,mu1)*G(1,2,mu1)*G(2,3,mu2)*G(3,i1,mu2)
	 + t11*G(i1,1,mu1)*G(1,2,mu2)*G(2,3,mu1)*G(3,i1,mu2) }
	 +
	 Tr6*{
	   t000*G(i1,1,mu1)*G(1,2,mu1)*G(2,3,mu2)*G(3,4,mu2)*G(4,5,mu3)*G(5,i1,mu3)
	 + t011*G(i1,1,mu1)*G(1,2,mu1)*G(2,3,mu2)*G(3,4,mu3)*G(4,5,mu2)*G(5,i1,mu3)
	 + t020*G(i1,1,mu1)*G(1,2,mu1)*G(2,3,mu2)*G(3,4,mu3)*G(4,5,mu3)*G(5,i1,mu2)
	 + t121*G(i1,1,mu1)*G(1,2,mu2)*G(2,3,mu1)*G(3,4,mu3)*G(4,5,mu2)*G(5,i1,mu3)
	 + t222*G(i1,1,mu1)*G(1,2,mu2)*G(2,3,mu3)*G(3,4,mu1)*G(4,5,mu2)*G(5,i1,mu3)
	  }
	 + Tr8*{
	   t0000*G(i1,1,mu1)*G(1,2,mu1)*G(2,3,mu2)*G(3,4,mu2)*G(4,5,mu3)*G(5,6,mu3)
	  *G(6,7,mu4)*G(7,i1,mu4)
	 +  t0011*G(i1,1,mu1)*G(1,2,mu1)*G(2,3,mu2)*G(3,4,mu2)*G(4,5,mu3)*G(5,6,mu4)
	  *G(6,7,mu3)*G(7,i1,mu4)
	 + t0020*G(i1,1,mu1)*G(1,2,mu1)*G(2,3,mu2)*G(3,4,mu2)*G(4,5,mu3)*G(5,6,mu4)
	  *G(6,7,mu4)*G(7,i1,mu3)
	 + t0121*G(i1,1,mu1)*G(1,2,mu1)*G(2,3,mu2)*G(3,4,mu3)*G(4,5,mu2)*G(5,6,mu4)
	  *G(6,7,mu3)*G(7,i1,mu4)
	 + t0222*G(i1,1,mu1)*G(1,2,mu1)*G(2,3,mu2)*G(3,4,mu3)*G(4,5,mu4)*G(5,6,mu2)
	  *G(6,7,mu3)*G(7,i1,mu4)
	 + t0231*G(i1,1,mu1)*G(1,2,mu1)*G(2,3,mu2)*G(3,4,mu3)*G(4,5,mu4)*G(5,6,mu2)
	  *G(6,7,mu4)*G(7,i1,mu3)
	 + t1111*G(i1,1,mu1)*G(1,2,mu2)*G(2,3,mu1)*G(3,4,mu2)*G(4,5,mu3)*G(5,6,mu4)
	  *G(6,7,mu3)*G(7,i1,mu4)
	 + t1221*G(i1,1,mu1)*G(1,2,mu2)*G(2,3,mu1)*G(3,4,mu3)*G(4,5,mu2)*G(5,6,mu4)
	  *G(6,7,mu3)*G(7,i1,mu4)
	 + t1322*G(i1,1,mu1)*G(1,2,mu2)*G(2,3,mu1)*G(3,4,mu3)*G(4,5,mu4)*G(5,6,mu2)
	  *G(6,7,mu3)*G(7,i1,mu4)
	 + t2332*G(i1,1,mu1)*G(1,2,mu2)*G(2,3,mu3)*G(3,4,mu1)*G(4,5,mu4)*G(5,6,mu2)
	  *G(6,7,mu3)*G(7,i1,mu4)
	 + t3333*G(i1,1,mu1)*G(1,2,mu2)*G(2,3,mu3)*G(3,4,mu4)*G(4,5,mu1)*G(5,6,mu2)
	  *G(6,7,mu3)*G(7,i1,mu4)
	 }
	Sum,mu1,mu2,mu3,mu4,mu5,mu6,mu7,mu8

L 2	Id,Gammas
> P stats
L10	Id,N_=N-4
> P output
	*yep

Terms in output 45
Running time 1 sec			Used	Maximum
Generated terms 77 	Input space 	2330 	100000
Equal terms 32     	Output space 	1350 	250000
Cancellations 0   	Nr of expr.  	15 	255
Multiplications 382	String space 	0 	4096
Records written 0 	Merging		0 	0

 
xx = 
 + Tr4*t00
  * ( 4*N^2 )
 
 + Tr4*t11
  * ( 8*N - 4*N^2 )
 
 + Tr6*t000
  * ( 4*N^3 )
 
 + Tr6*t011
  * ( 8*N^2 - 4*N^3 )
 
 + Tr6*t020
  * ( 4*N^3 )
 
 + Tr6*t121
  * ( 16*N - 16*N^2 + 4*N^3 )
 
 + Tr6*t222
  * ( - 16*N + 24*N^2 - 4*N^3 )
 
 + Tr8*t0000
  * ( 4*N^4 )
 
 + Tr8*t0011
  * ( 8*N^3 - 4*N^4 )
 
 + Tr8*t0020
  * ( 4*N^4 )
 
 + Tr8*t0121
  * ( 16*N^2 - 16*N^3 + 4*N^4 )
 
 + Tr8*t0222
  * ( - 16*N^2 + 24*N^3 - 4*N^4 )
 
 + Tr8*t0231
  * ( 16*N^2 - 16*N^3 + 4*N^4 )
 
 + Tr8*t1111
  * ( 16*N^2 - 16*N^3 + 4*N^4 )
 
 + Tr8*t1221
  * ( 32*N - 48*N^2 + 24*N^3 - 4*N^4 )
 
 + Tr8*t1322
  * ( - 32*N + 64*N^2 - 32*N^3 + 4*N^4 )
 
 + Tr8*t2332
  * ( 64*N - 96*N^2 + 40*N^3 - 4*N^4 )
 
 + Tr8*t3333
  * ( - 64*N + 112*N^2 - 48*N^3 + 4*N^4 ) + 0.
 
	B Tr4,Tr6,t00,t11,t000,t011,t020,t121,t222
	 ,Tr8,t0000,t0011,t0020,t0121,t0222,t0231,t1111,t1221,t1322,t2332,t3333
L 1	Id,N=4
	*end

Terms out 45, in 45.

Terms in output 18
Running time 1 sec			Used	Maximum
Generated terms 45 	Input space 	176 	100000
Equal terms 27     	Output space 	720 	250000
Cancellations 0   	Nr of expr.  	12 	255
Multiplications 254	String space 	0 	4096
Records written 0 	Merging		0 	0

 
xx = 
 + 64*Tr4*t00
 
 - 32*Tr4*t11
 
 + 256*Tr6*t000
 
 - 128*Tr6*t011
 
 + 256*Tr6*t020
 
 + 64*Tr6*t121
 
 + 64*Tr6*t222
 
 + 1024*Tr8*t0000
 
 - 512*Tr8*t0011
 
 + 1024*Tr8*t0020
 
 + 256*Tr8*t0121
 
 + 256*Tr8*t0222
 
 + 256*Tr8*t0231
 
 + 256*Tr8*t1111
 
 - 128*Tr8*t1221
 
 - 128*Tr8*t1322
 
 + 256*Tr8*t2332
 
 - 512*Tr8*t3333 + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:00.  Memory: start 0001B84C, length 476348.


C Essay 29. Test of IF etc. statements.

	B A1,B1,A2,B2,A3,B3,A4,B4

	Z xx=a*b + a + b + c

L 1	IF a
	AND b
L 2	Id,Addfa,A1
	ELSE
L 2	Id,Addfa,B1
	ENDIF

L 3	IF NOT a
	OR b
L 4	Id,Addfa,A2
	ELSE
L 4	Id,Addfa,B2
	ENDIF

L 5	IF a
	OR NOT b
L 6	Id,Addfa,A3
	ELSE
L 6	Id,Addfa,B3
	ENDIF

L 7	IF a
	AND NOT b
L 8	Id,Addfa,A4
	ELSE
L 8	Id,Addfa,B4
	ENDIF

C Output must be:
C   A1*A2*A3*B4  * ( a*b ) + B1*A2*A3*B4 * ( c )
C + B1*A2*B3*B4 * ( b )    + B1*B2*A3*A4 * ( a )
	*end
 
xx = 
 + A1*A2*A3*B4
  * ( a*b )
 
 + B1*A2*A3*B4
  * ( c )
 
 + B1*A2*B3*B4
  * ( b )
 
 + B1*B2*A3*A4
  * ( a ) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:02.  Memory: start 0001B84C, length 476348.


C Essay 30. All command and Gamma matrices.

	I al,be,mu,nu
	A N,N_
	V p,k
	F F,F20,F22

	Z xx = G(1,1,al,be,p,al,be,p)

L 1	Id,All,p,N,F
L 2	Id,F(i1~,i2~) = D(i1,i2)*F20(k) + k(i1)*k(i2)*F22(k)

L 3	Id,Gammas
	*end
 
xx = + F20(k)
  * ( 64 - 32*N_ )
 
 + F22(k)
  * ( 16*kDk ) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:05.  Memory: start 0001B84C, length 476348.


C Essay 31. All command with function as argument.

	I al,be,mu,nu
	A N,N_
	V p,k
	F F,F20,F22

	Z xx = G(1,1,al,be,p,al,be,p)

L 1	Id,All,G,N,F
	*end
 
xx = + G(1,1,al,be,Naa,al,be,Nab)*F(p,p,Naa,Nab) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:08.  Memory: start 0001B84C, length 476348.


C Essay 32. All with G-function as argument and Gamma, Ndotpr commands.

	F F1
	I mu,nu,al=N,be=N,ga=N,de=N
	V p,q,k,l
	Z ft = G(1,1,k,G5,p,q,l,G5,q,p)
L 1	Id,All,G,N,F1
> P output
	*yep
 
ft = + G(1,1,Naa,G5,Nab,Nac,Nad,G5,Nae,Naf)*F1(k,p,q,l,q,p,Naa,Nab,Nac,Nad,
  Nae,Naf) + 0.
 
L 1	Id,Gammas
> P output
	*yep
 
ft = 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_N_,Nac,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_4,Nac,
  Dim_4,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nab,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nac,
  Dim_N_,Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_N_,Nab,
  Dim_4,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_4,Nac,
  Dim_N_,Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_N_,Nac,
  Dim_4,Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_4,Nab,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nab,Dim_N_,Nac,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nab,Dim_4,Nac,Dim_4,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Nab,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Nac,Dim_4,
  Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nac,
  Dim_N_,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Naa,Dim_N_,Nab,Dim_4,Nac,
  Dim_4,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Naa,Dim_N_,Nac,Dim_N_,Nab,
  Dim_N_,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Naa,Dim_N_,Nac,Dim_N_,Nac,
  Dim_N_,Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Naa,Dim_4,Nac,Dim_N_,Nab,
  Dim_4,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Naa,Dim_4,Nac,Dim_4,Nac,
  Dim_N_,Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_N_,Naa,Dim_N_,Nac,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_N_,Naa,Dim_4,Nac,
  Dim_4,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Naa,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nac,
  Dim_N_,Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_4,Nac,Dim_N_,Naa,
  Dim_4,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_4,Nac,Dim_4,Nac,
  Dim_N_,Naa)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Naa,Dim_N_,Nab,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Naa,Dim_N_,Nac,
  Dim_N_,Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nab,Dim_N_,Naa,
  Dim_N_,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nab,Dim_N_,Nac,
  Dim_N_,Naa)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nac,Dim_N_,Naa,
  Dim_N_,Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nac,Dim_N_,Nab,
  Dim_N_,Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_N_,Naa,Dim_N_,Nab,
  Dim_4,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_N_,Naa,Dim_4,Nac,
  Dim_N_,Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_N_,Nab,Dim_N_,Naa,
  Dim_4,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_N_,Nab,Dim_4,Nac,
  Dim_N_,Naa)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_4,Nac,Dim_N_,Naa,
  Dim_N_,Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_4,Nac,Dim_N_,Nab,
  Dim_N_,Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Naa,Dim_N_,Nac,Dim_N_,Nac,
  Dim_4,Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Naa,Dim_N_,Nac,Dim_4,Nab,
  Dim_N_,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Nac,
  Dim_N_,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Naa,Dim_4,Nac,Dim_4,Nab,Dim_4,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Naa,Dim_4,Nac,Dim_4,Nac,Dim_4,
  Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_N_,Naa,Dim_N_,Nac,
  Dim_4,Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_N_,Naa,Dim_4,Nab,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_N_,Nac,Dim_N_,Naa,
  Dim_4,Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_N_,Nac,Dim_4,Nab,
  Dim_N_,Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_4,Nab,Dim_N_,Naa,
  Dim_N_,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_4,Nab,Dim_N_,Nac,
  Dim_N_,Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nab,Dim_N_,Naa,Dim_N_,Nac,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nab,Dim_N_,Naa,Dim_4,Nac,Dim_4,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nab,Dim_N_,Nac,Dim_N_,Naa,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nab,Dim_N_,Nac,Dim_N_,Nac,
  Dim_N_,Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nab,Dim_4,Nac,Dim_N_,Naa,Dim_4,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nab,Dim_4,Nac,Dim_4,Nac,Dim_N_,
  Naa)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nac,Dim_N_,Naa,Dim_4,Nab,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nac,Dim_N_,Naa,Dim_4,Nac,Dim_4,
  Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Nab,Dim_N_,Naa,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Nab,Dim_4,Nac,Dim_N_,
  Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Nac,Dim_N_,Naa,Dim_4,
  Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Nac,Dim_4,Nab,Dim_N_,
  Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nac,
  Dim_4,Naa)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_N_,Nac,Dim_4,Naa,
  Dim_N_,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_4,Naa,Dim_N_,Nac,
  Dim_N_,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_4,Naa,Dim_4,Nac,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_4,Nac,Dim_4,Naa,Dim_4,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_4,Nac,Dim_4,Nac,Dim_4,
  Naa)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nab,Dim_N_,Nac,
  Dim_4,Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nab,Dim_4,Naa,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nac,Dim_N_,Nab,
  Dim_4,Naa)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nac,Dim_4,Naa,
  Dim_N_,Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_4,Naa,Dim_N_,Nab,
  Dim_N_,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_4,Naa,Dim_N_,Nac,
  Dim_N_,Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nac,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_4,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_4,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_4,Naa,Dim_N_,Nac,Dim_N_,Nab,
  Dim_N_,Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_4,Naa,Dim_N_,Nac,Dim_N_,Nac,
  Dim_N_,Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_4,Naa,Dim_4,Nac,Dim_N_,Nab,Dim_4,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_4,Naa,Dim_4,Nac,Dim_4,Nac,Dim_N_,
  Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_N_,Nab,Dim_4,Naa,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_N_,Nab,Dim_4,Nac,Dim_4,
  Naa)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_4,Naa,Dim_N_,Nab,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_4,Naa,Dim_4,Nac,Dim_N_,
  Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_4,Nac,Dim_N_,Nab,Dim_4,
  Naa)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_4,Nac,Dim_4,Naa,Dim_N_,
  Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_N_,Nac,
  Dim_N_,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_4,Nac,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nab,
  Dim_N_,Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nac,Dim_N_,Nac,
  Dim_N_,Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_N_,Nab,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Naa,Dim_N_,Nab,Dim_4,Nac,Dim_4,Nac,Dim_N_,
  Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_N_,Nac,Dim_4,
  Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_4,Nab,Dim_N_,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Naa,Dim_4,Nab,Dim_4,Nab,Dim_N_,Nac,Dim_N_,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Naa,Dim_4,Nab,Dim_4,Nab,Dim_4,Nac,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Nab,Dim_4,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Nac,Dim_4,
  Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_N_,Nac,Dim_4,Naa,Dim_4,
  Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_N_,Nac,Dim_4,Nab,Dim_4,
  Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_4,Naa,Dim_N_,Nac,Dim_4,
  Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_4,Naa,Dim_4,Nab,Dim_N_,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_4,Nab,Dim_N_,Nac,Dim_4,
  Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_4,Nab,Dim_4,Naa,Dim_N_,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Naa,Dim_N_,Nac,Dim_N_,Nac,Dim_4,
  Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Naa,Dim_N_,Nac,Dim_4,Nab,Dim_N_,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Naa,Dim_4,Nab,Dim_N_,Nac,Dim_N_,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Naa,Dim_4,Nac,Dim_4,Nab,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Naa,Dim_4,Nac,Dim_4,Nac,Dim_4,
  Nab)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Nab,Dim_N_,Nac,Dim_N_,Nac,Dim_4,
  Naa)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Nab,Dim_N_,Nac,Dim_4,Naa,Dim_N_,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Nab,Dim_4,Naa,Dim_N_,Nac,Dim_N_,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Nab,Dim_4,Naa,Dim_4,Nac,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Nab,Dim_4,Nac,Dim_4,Naa,Dim_4,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Nab,Dim_4,Nac,Dim_4,Nac,Dim_4,
  Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Naa,Dim_4,Nab,Dim_4,
  Nac)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Naa,Dim_4,Nac,Dim_4,
  Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Nab,Dim_4,Naa,Dim_4,
  Nac)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Nab,Dim_4,Nac,Dim_4,
  Naa)
 
 + 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Nac,Dim_4,Naa,Dim_4,
  Nab)
 
 - 4*F1(k,p,q,l,q,p,Dim_4,Naa,Dim_4,Nab,Dim_4,Nac,Dim_4,Nac,Dim_4,Nab,Dim_4,
  Naa) + 0.
 
L 1	Id,Ndotpr,F1
> P output
	*yep
 
ft = 
  + 16*pk_*ql_*pq_ - 8*pk_*qq_*pl_ + 8*pk_*pl_*qq4 - 8*ql_*qk_*pp_
   + 8*ql_*qk_*pp4 + 16*pq_*pq4*kl_ - 16*pq_*pq4*kl4 + 16*pq_*pl4*qk4
   - 16*pq4*pl_*qk_ - 16*pq4*ql4*pk4 - 8*qq_*pl4*pk4 + 4*qq_*pp_*kl_
   - 4*qq_*pp_*kl4 - 4*qq_*kl_*pp4 + 4*qq_*pp4*kl4 + 8*pl4*qq4*pk4
   - 8*ql4*pp_*qk4 + 8*ql4*pp4*qk4 - 4*qq4*pp_*kl_ + 4*qq4*pp_*kl4
   + 4*qq4*kl_*pp4 - 4*qq4*pp4*kl4 + 0.
 
> P lists
	*end


I mu, nu, al=N, be=N, ga=N, de=N

V p, q, k, l

A i=i, N, N_, pk_, ql_, pq_, pq4, qq_, pl_, pl4, ql4, qq4, qk_, pp_, 
  kl_, pp4, pk4, qk4, kl4

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
 
ft = 
  + 16*pk_*ql_*pq_ - 8*pk_*qq_*pl_ + 8*pk_*pl_*qq4 - 8*ql_*qk_*pp_
   + 8*ql_*qk_*pp4 + 16*pq_*pq4*kl_ - 16*pq_*pq4*kl4 + 16*pq_*pl4*qk4
   - 16*pq4*pl_*qk_ - 16*pq4*ql4*pk4 - 8*qq_*pl4*pk4 + 4*qq_*pp_*kl_
   - 4*qq_*pp_*kl4 - 4*qq_*kl_*pp4 + 4*qq_*pp4*kl4 + 8*pl4*qq4*pk4
   - 8*ql4*pp_*qk4 + 8*ql4*pp4*qk4 - 4*qq4*pp_*kl_ + 4*qq4*pp_*kl4
   + 4*qq4*kl_*pp4 - 4*qq4*pp4*kl4 + 0.
 

End run. Time 2 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:12.  Memory: start 0001B84C, length 476348.


C Essay 33. All with G-function as argument and Gamma, Ndotpr commands.

	F F1
	I mu,nu
	V p,q
	A N,N_
	Z ft = G(1,1,mu,G5,p,nu,G5,q)
L 1	Id,All,G,N,F1
C P output
C *yep
L 2	Id,Gammas,"A
C P output
C *yep
L10	Id,Ndotpr,F1
C P output
C *yep
C P lists
	*end
 
ft = + 4*p(mu)*q(nu)
 
 + 4*q(mu)*p(nu)
 
 + D(mu,nu)
  * ( - 4*pq_ - 4*pq4 ) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:15.  Memory: start 0001B84C, length 476348.


C Essay 34. Epf function reduction.

	I Naa
	V P,K,W2
	Z xx= Epf(Naa,P,K,W2)*Epf(Naa,P,K,W2)
L 1	Id,Trick
	*end
 
xx =  + PDP*KDK*W2DW2 - PDP*KDW2^2 + 2*PDK*PDW2*KDW2 - PDK^2*W2DW2
   - PDW2^2*KDK + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:18.  Memory: start 0001B84C, length 476348.


C Essay 35. Mixed N- and 4-dimensional traces.

	I mu,nu,al=N,be=N,ga=N,de=N
	V p,q
	Z ft1 = G(1,mu)*G5(1)*G(1,al)*G(1,be)*G(1,nu)*G5(1)*G(1,be)*G(1,al) 
	Z ft2 = G(1,mu)*G5(1)*G(1,nu)*G5(1) 
	Z ft1 = G(1,mu)*G5(1)*G(1,al)*G(1,be)*G(1,nu)*G5(1)*G(1,al)*G(1,be) 
L 1	Id,Gammas,Trace,1
	*end
 
ft1 = + D(mu,nu)
  * ( - 16 + 16*N_ - 4*N_^2 )
 
ft2 = - 4*D(mu,nu)
 
ft1 = + D(mu,nu)
  * ( - 16 - 24*N_ + 4*N_^2 ) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:21.  Memory: start 0001B84C, length 476348.


C Essay 36. A trace of 10 gammas.

> P stats
	I a1,a2,a3,a4,a5,a6
	I b1,b2,b3,b4,b5,b6,b7,b8
	V p
	Z xx = G(1,"T,"4,a1,a2,a3,a4,a5,p,b1,b2,b3,p)
L 1	Id,Gammas
> P noutp
	*end

Terms in output 258
Running time 1 sec			Used	Maximum
Generated terms 306 	Input space 	860 	100000
Equal terms 42     	Output space 	14518 	250000
Cancellations 6   	Nr of expr.  	14 	255
Multiplications 1887	String space 	0 	4096
Records written 0 	Merging		0 	0


End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:24.  Memory: start 0001B84C, length 476348.


C Essay 37. Traces and Ndotpr command.

	F F1
	I mu,nu,al=N,be=N,ga=N,de=N
	V p,q,k,P,Q,K
	Z ft = G(1,1,p,G5,q,k,P,G5,Q,K)
	Z fp = G(1,1,q,k,P,G5,Q,K,p,G5)
L 1	Id,All,G,N,F1
L 2	Id,Gammas,"A
L10	Id,Ndotpr,F1
> P stats
	*yep

Terms in output 240
Running time 2 sec			Used	Maximum
Generated terms 240 	Input space 	936 	100000
Equal terms 0     	Output space 	6264 	250000
Cancellations 0   	Nr of expr.  	17 	255
Multiplications 2724	String space 	0 	4096
Records written 0 	Merging		0 	0

L 1	Id,pq_=pDq-pq4
L 1	Al,kP_=kDP-kP4
L 1	Al,QK_=QDK-QK4
L 1	Al,pk_=pDk-pk4
L 1	Al,qP_=qDP-qP4
L 1	Al,pP_=pDP-pP4
L 1	Al,qk_=qDk-qk4
L 2	Id,pQ_=pDQ-pQ4
L 2	Al,PK_=PDK-PK4
L 2	Al,pK_=pDK-pK4
L 2	Al,PQ_=PDQ-PQ4
L 2	Al,kQ_=kDQ-kQ4
L 2	Al,qQ_=qDQ-qQ4
L 2	Al,kK_=kDK-kK4
L 2	Al,qK_=qDK-qK4
	Keep ft,fp
	*next

Terms out 240, in 240.

Terms in output 30
Running time 2 sec			Used	Maximum
Generated terms 810 	Input space 	1008 	100000
Equal terms 390     	Output space 	804 	250000
Cancellations 390   	Nr of expr.  	25 	255
Multiplications 2784	String space 	0 	4096
Records written 0 	Merging		0 	0

 
ft = 
  - 4*pDq*kDP*QDK + 4*pDq*kDQ*PDK - 4*pDq*kDK*PDQ + 4*pDk*qDP*QDK
  - 4*pDk*qDQ*PDK + 4*pDk*qDK*PDQ - 4*pDP*qDk*QDK + 4*pDP*qDQ*kDK
  - 4*pDP*qDK*kDQ + 4*pDQ*qDk*PDK - 4*pDQ*qDP*kDK + 4*pDQ*qDK*kDP
  - 4*pDK*qDk*PDQ + 4*pDK*qDP*kDQ - 4*pDK*qDQ*kDP
 
fp = 
  - 4*pDq*kDP*QDK + 4*pDq*kDQ*PDK - 4*pDq*kDK*PDQ + 4*pDk*qDP*QDK
  - 4*pDk*qDQ*PDK + 4*pDk*qDK*PDQ - 4*pDP*qDk*QDK + 4*pDP*qDQ*kDK
  - 4*pDP*qDK*kDQ + 4*pDQ*qDk*PDK - 4*pDQ*qDP*kDK + 4*pDQ*qDK*kDP
  - 4*pDK*qDk*PDQ + 4*pDK*qDP*kDQ - 4*pDK*qDQ*kDP + 0.
 
	Z xx=ft-fp
> P stats
	*end

Terms in output 0
Running time 3 sec			Used	Maximum
Generated terms 30 	Input space 	590 	100400
Equal terms 15     	Output space 	0 	249600
Cancellations 15   	Nr of expr.  	11 	255
Multiplications 92	String space 	0 	4096
Records written 0 	Merging		0 	0

 
xx = 0. + 0.
 

End run. Time 3 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:29.  Memory: start 0001B84C, length 476348.


C Essay 38. Trace and Ndotpr command.

> P stats
	I mu,nu,al=N,be=N,ga=N,de=N
	V p,q
	Z ft = G(1,1,mu,G5,al,be,nu,G5,ga,de) * F1(al,be,ga,de)
L 1	Id,Trick,Trace,1
> P output
	Sum al,be,ga,de
	*yep

Terms in output 36
Running time 0 sec			Used	Maximum
Generated terms 36 	Input space 	662 	100000
Equal terms 0     	Output space 	1872 	250000
Cancellations 0   	Nr of expr.  	14 	255
Multiplications 336	String space 	0 	4096
Records written 0 	Merging		0 	0

 
ft = 
 - 4*F1(mu,nu,Dim_N_,Naa,Dim_N_,Naa)
 
 - 4*F1(mu,nu,Dim_4,Naa,Dim_4,Naa)
 
 + 4*F1(mu,Dim_N_,Naa,nu,Dim_N_,Naa)
 
 - 4*F1(mu,Dim_N_,Naa,Dim_N_,Naa,nu)
 
 - 4*F1(mu,Dim_4,Naa,nu,Dim_4,Naa)
 
 + 4*F1(mu,Dim_4,Naa,Dim_4,Naa,nu)
 
 + 4*F1(nu,mu,Dim_N_,Naa,Dim_N_,Naa)
 
 + 4*F1(nu,mu,Dim_4,Naa,Dim_4,Naa)
 
 + 4*F1(nu,Dim_N_,Naa,mu,Dim_N_,Naa)
 
 - 4*F1(nu,Dim_N_,Naa,Dim_N_,Naa,mu)
 
 - 4*F1(nu,Dim_4,Naa,mu,Dim_4,Naa)
 
 + 4*F1(nu,Dim_4,Naa,Dim_4,Naa,mu)
 
 - 4*F1(Dim_N_,Naa,mu,nu,Dim_N_,Naa)
 
 + 4*F1(Dim_N_,Naa,mu,Dim_N_,Naa,nu)
 
 - 4*F1(Dim_N_,Naa,nu,mu,Dim_N_,Naa)
 
 + 4*F1(Dim_N_,Naa,nu,Dim_N_,Naa,mu)
 
 + 4*F1(Dim_N_,Naa,Dim_N_,Naa,mu,nu)
 
 - 4*F1(Dim_N_,Naa,Dim_N_,Naa,nu,mu)
 
 - 4*F1(Dim_N_,Naa,Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nab)*D(mu,nu)
 
 - 4*F1(Dim_N_,Naa,Dim_N_,Naa,Dim_4,Nab,Dim_4,Nab)*D(mu,nu)
 
 + 4*F1(Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Naa,Dim_N_,Nab)*D(mu,nu)
 
 - 4*F1(Dim_N_,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_N_,Naa)*D(mu,nu)
 
 - 4*F1(Dim_N_,Naa,Dim_4,Nab,Dim_N_,Naa,Dim_4,Nab)*D(mu,nu)
 
 + 4*F1(Dim_N_,Naa,Dim_4,Nab,Dim_4,Nab,Dim_N_,Naa)*D(mu,nu)
 
 + 4*F1(Dim_4,Naa,mu,nu,Dim_4,Naa)
 
 - 4*F1(Dim_4,Naa,mu,Dim_4,Naa,nu)
 
 + 4*F1(Dim_4,Naa,nu,mu,Dim_4,Naa)
 
 - 4*F1(Dim_4,Naa,nu,Dim_4,Naa,mu)
 
 + 4*F1(Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nab,Dim_4,Naa)*D(mu,nu)
 
 - 4*F1(Dim_4,Naa,Dim_N_,Nab,Dim_4,Naa,Dim_N_,Nab)*D(mu,nu)
 
 + 4*F1(Dim_4,Naa,Dim_4,Naa,mu,nu)
 
 - 4*F1(Dim_4,Naa,Dim_4,Naa,nu,mu)
 
 - 4*F1(Dim_4,Naa,Dim_4,Naa,Dim_N_,Nab,Dim_N_,Nab)*D(mu,nu)
 
 - 4*F1(Dim_4,Naa,Dim_4,Naa,Dim_4,Nab,Dim_4,Nab)*D(mu,nu)
 
 + 4*F1(Dim_4,Naa,Dim_4,Nab,Dim_4,Naa,Dim_4,Nab)*D(mu,nu)
 
 - 4*F1(Dim_4,Naa,Dim_4,Nab,Dim_4,Nab,Dim_4,Naa)*D(mu,nu) + 0.
 
L 1	Id,Ndotpr,F1,p,q,q,p
> P output
	*yep

Terms out 36, in 36.

Terms in output 11
Running time 1 sec			Used	Maximum
Generated terms 36 	Input space 	154 	100000
Equal terms 19     	Output space 	352 	250000
Cancellations 6   	Nr of expr.  	7 	255
Multiplications 108	String space 	0 	4096
Records written 0 	Merging		0 	0

 
ft = 
 + p(mu)*p(nu)
  * ( - 8*qq_ + 8*qq4 )
 
 + p(mu)*q(nu)
  * ( - 16*pq4 )
 
 + q(mu)*p(nu)
  * ( 16*pq_ )
 
 + q(mu)*q(nu)
  * ( - 8*pp_ + 8*pp4 )
 
 + D(mu,nu)
  * ( - 16*pq_*pq4 - 4*qq_*pp_ + 4*qq_*pp4 + 4*qq4*pp_ - 4*qq4*pp4 ) + 0.
 
> P lists
	*end


I mu, nu

V p, q

A i=i, N, N_, pq_, pq4, qq_, qq4, pp_, pp4

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

Terms out 11, in 11.

Terms in output 11
Running time 1 sec			Used	Maximum
Generated terms 11 	Input space 	84 	100000
Equal terms 0     	Output space 	352 	250000
Cancellations 0   	Nr of expr.  	6 	255
Multiplications 22	String space 	0 	4096
Records written 0 	Merging		0 	0

 
ft = 
 + p(mu)*p(nu)
  * ( - 8*qq_ + 8*qq4 )
 
 + p(mu)*q(nu)
  * ( - 16*pq4 )
 
 + q(mu)*p(nu)
  * ( 16*pq_ )
 
 + q(mu)*q(nu)
  * ( - 8*pp_ + 8*pp4 )
 
 + D(mu,nu)
  * ( - 16*pq_*pq4 - 4*qq_*pp_ + 4*qq_*pp4 + 4*qq4*pp_ - 4*qq4*pp4 ) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:32.  Memory: start 0001B84C, length 476348.


C Essay 39. Gamma with "A option

> P stats
	I mu,nu,al=N,be=N,ga=N,de=N
	V p,q
	Z ft1 = G(1,1,mu,G5,al,be,nu,G5,be,al) 
	Z ft2 = G(1,1,mu,G5,nu,G5) 
	Z ft3 = G(1,1,mu,G5,al,be,nu,G5,al,be) 
	Z ft1p = G(2,2,mu,G5,al,be,nu,G5,be,al) 
	Z ft2p = G(2,2,mu,G5,nu,G5) 
	Z ft3p = G(2,2,mu,G5,al,be,nu,G5,al,be) 
L 1	Id,Gammas,1:"A,2
	*end

Terms in output 14
Running time 0 sec			Used	Maximum
Generated terms 20 	Input space 	652 	100000
Equal terms 5     	Output space 	416 	250000
Cancellations 1   	Nr of expr.  	17 	255
Multiplications 150	String space 	0 	4096
Records written 0 	Merging		0 	0

 
ft1 = + D(mu,nu)
  * ( - 16 - 16*N_ - 4*N_^2 )
 
ft2 = - 4*D(mu,nu)
 
ft3 = + D(mu,nu)
  * ( - 16 + 8*N_ + 4*N_^2 )
 
ft1p = + D(mu,nu)
  * ( - 16 + 16*N_ - 4*N_^2 )
 
ft2p = - 4*D(mu,nu)
 
ft3p = + D(mu,nu)
  * ( - 16 - 24*N_ + 4*N_^2 ) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:35.  Memory: start 0001B84C, length 476348.


C Essay 40. Overflow.

	Overflow off
	Z xx= + a1^120*a1^10 + a2^-120*a2^-10
	*end
 
xx =  + a1^127 + a2^-128 + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:37.  Memory: start 0001B84C, length 476348.


C Essay 41. Miscellaneous gamma tests.

	A N,N_
	V P
	I MU=N,s1,s2,s3
	*fix

Begin. Time 1 sec.
	Z aa0=G(s1,s1,MU,P,G6)*G(s2,s3,MU,G6)
	Z aa1=G(s1,s1,MU,P,G5)*G(s2,s3,MU,G6)
	     +G(s1,s1,MU,P)*G(s2,s3,MU,G6)
L 1	Id,Gammas
> P output
	*next
 
aa0 = + 4*G(s2,"S,"4,P)
 
 - 4*G(s2,"S,"5,P)
 
aa1 = + 4*G(s2,"S,"4,P)
 
 - 4*G(s2,"S,"5,P) + 0.
 
	Z aa2=G(s2,s3,MU,G6)*G(s1,s1,MU,P,G6)
L 1	Id,Gammas
	*end
 
aa2 = + 4*G(s2,"S,"4,P)
 
 - 4*G(s2,"S,"5,P) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:40.  Memory: start 0001B84C, length 476348.


C Essay 42. Miscellaneous gamma tests.

	A N,N_
	I mu,nu,la,ga
	I s3
	Z xx2=G(s3,s3,ga,mu)
L 1	Id,Gammas
	Keep xx2
	*next
 
xx2 = + 4*D(mu,ga) + 0.
 
> P list
	A aa
	Z xxp=aa*xx2
	*end


I mu, nu, la, ga, s3

A i=i, N, N_, aa

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

E xx2
 
xxp = + D(mu,ga)
  * ( 4*aa ) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:43.  Memory: start 0001B84C, length 476348.


C Essay 43. Miscellaneous gamma tests.

	A N,N_
	I mu=N,nu=N,la,si
	Z xx=G(1,2,mu)*G(3,3,mu,nu,la,si)*fff(nu)
L 1	Id,Gammas
	*end
 
xx = 
 + 4*G(1,"S,"4,nu)*fff(Dim_4,nu)*D(la,si)
 
 - 4*G(1,"S,"4,la)*fff(si)
 
 + 4*G(1,"S,"4,si)*fff(la)
 
 + 4*G(1,"s,"4,Dim_N_,nu)*fff(Dim_N_,nu)*D(la,si) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:46.  Memory: start 0001B84C, length 476348.


C Essay 44. Miscellaneous gamma tests.

C Needs two gamma commands if results from one are to become
  implemented in the other.

	I mu,nu,ga
	Z xx=G(1,2,mu,nu)*G(3,3,mu,nu)
L 1	Id,Gammas
	*end
 
xx = + 4*G(1,"S,"4,mu,mu) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:48.  Memory: start 0001B84C, length 476348.


C Essay 45. Miscellaneous gamma tests.

	A N,N_
	I mu,nu
	Z xx=G(3,4,mu,nu)
	Z xy=G(1,2,mu,nu)
L 1	Id,Gammas,1:"C,3:"U,"A_,"S_,"I_,"P_,"W_,"i_
	*end
 
xx = + G(3,"S,"4,mu,nu)
 
xy = + G(1,"s,"4,mu,nu) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:51.  Memory: start 0001B84C, length 476348.


C Essay 46. Numerical 'common" files.

	Rat 0
	Common xx
	Z xx=1/4*3/17*56
	*next
 
xx =  + .24706E+1 + 0.
 

C This works only if xx integer < 2^29.

	Z cc=a/{xx}
	*end

*
*** Level 0 error # 138:
 Non-numeric expression in brackets with negative exponent.
***

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:54.  Memory: start 0001B84C, length 476348.


C Essay 47. Numerical "next" files.

	Rat 0
	Z xx=1/4*3/17*56
	Keep xx
	*next
 
xx =  + .24706E+1 + 0.
 
	Z cc=a/{xx}
	*end
 
cc =  + .40476*a + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:57.  Memory: start 0001B84C, length 476348.


C Essay 48. Miscellaneous gamma tests.

	A N,N_
	I mu,nu
	Z xx=G(1,2,mu,mu,nu)
L 1	Id,Gammas,"C
	*end
 
xx = + 4*G(1,"s,"4,nu) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:44:59.  Memory: start 0001B84C, length 476348.


C Essay 49. Miscellaneous gamma tests.

	I mu1=N,mu2=N,mu3=N,mu4=N
	*fix

Begin. Time 1 sec.

	Z aa1=G(3,4,mu1,mu2,mu3,mu4)*G(1,1,mu1,mu2,mu3,mu4)
L 1	Id,Gammas,"U
L 9	Id,Gammas
L17	Id,N_=N-4
	*end
 
aa1 = + Gi(3)
  * ( - 8*N + 12*N^2 ) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:45:02.  Memory: start 0001B84C, length 476348.


C Essay 50. Miscellaneous gamma tests.

	I mu5,mu1=N,mu2=N,mu3=N,mu4=N
	*fix

Begin. Time 1 sec.

	Z aa=Epf(mu1,mu2,mu3,mu4)*G(1,1,mu1,mu2,mu3,mu4,G5)
L 1	Id,Gammas
	*end
 
aa =  + 96 + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:45:05.  Memory: start 0001B84C, length 476348.


C Essay 51. Miscellaneous gamma tests.

	I mu1=N,mu2=N,mu3=N,mu4=N      
	*fix

Begin. Time 0 sec.
	Z aa2=G(1,1,mu1,mu2,G6)*G(3,4,mu1,mu2)
L 1	Id,Gammas
	*end
 
aa2 = + Gi(3)
  * ( 16 + 4*N_ ) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:45:08.  Memory: start 0001B84C, length 476348.


C Essay 52. Miscellaneous gamma tests.

	I mu1=N,mu2=N,mu3=N,mu4=N      
	*fix

Begin. Time 0 sec.

	Z aa0=G(3,4,mu1,mu2,mu3,mu4,G5)*G(1,1,mu1,mu2,mu3,mu4,G5)
L 1	Id,Gammas						
	*end
 
aa0 = + 96*Gi(3) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:45:11.  Memory: start 0001B84C, length 476348.


C Essay 53. Freeze test with Excl on B-line.

> P ni

Begin. Time 0 sec.
 
aa = 
  + gam(s1,s2,AL)*gam(s2,s3,MU)*NOM(K,XM) + gam(s1,s2,BE)*gam(s2,s3,GA)
  *NOM(K,XM)
 
 + x
  * ( - gam(s1,s2,AL)*gam(s2,s3,MU)*NOM(K,XM) - gam(s1,s2,BE)*gam(s2,s3,GA)
  *NOM(K,XM) ) + 0.
 

Begin. Time 0 sec.
> P ou
 
cc = + DF(aa,1)
 
 + DF(aa,2)
  * ( x ) + 0.
 

End run. Time 0 sec.
