Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:25:08.  Memory: start 0001B84C, length 476348.

Command line: +1 Tests.e Xax


C Tests 1.  Test of character DS and command Anti.

	G 1
	F F1,F2
	X XX(k)=k-1*a
	T AA: AB_CDBA,EFGH,ABCDBA,AACDAA
	T BB: A=1,F=-3
	G
C Anti,BB
	Z xx=DS(J2;J3;J4;-J2;J3;"C,AA,1:3,5,(F(J2,J3,-J2,-J3,-J4)
	 *DC("F,BB,-1,J2)))
> P output
	*yep
 
xx = + F("B,"A,"B_,"A_,"D_)
 
 + F("B_,"A,"B,"A_,"D_) + 0.
 

C As a consequence of this A_ must be changed to A, because A in table BB.

L 1	Id,Anti,BB
	*end
 
xx = + F("B,"A,"B_,"A,"D_)
 
 + F("B_,"A,"B,"A,"D_) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:25:10.  Memory: start 0001B84C, length 476348.


C Tests 2.  C-formfactors equation test.

	A Pi,N,N_,m,M,M1,M2,M3,x,y
	V p,k
	F C0,Cx,Bx,Ax
	D YY(I) = pDp,pDk,pDk,kDk
	X Y(I,J) = YY(2*I-2+J)
	X Cf1 = -pDp
	X Cf2 = -qDq+pDp

	Z ChR1 = Y(1,1)*C(1,1,m) + Y(1,2)*C(1,2,m) - R1
	Z ChR2 = Y(2,1)*C(1,1,m) + Y(2,2)*C(1,2,m) - R2
	Z Ch24 = C(2,4,m) - R24
	Z ChR3 = Y(1,1)*C(2,1,m) + Y(1,2)*C(2,3,m) - R3
	Z ChR5 = Y(2,1)*C(2,1,m) + Y(2,2)*C(2,3,m) - R5
	Z ChR4 = Y(1,1)*C(2,3,m) + Y(1,2)*C(2,2,m) - R4
	Z ChR6 = Y(2,1)*C(2,3,m) + Y(2,2)*C(2,2,m) - R6

L 4	Id,R1=0.5*(Cf1*C0(m) + B0(qDq,m) - B0(kDk,m))
L 4	Al,R2=0.5*(Cf2*C0(m) + B0(pDp,m) - B0(qDq,m))
L 4	Al,R24 = 1/4*i*Pi^2
	  - 0.5*m^2*C0(m) + 1/4*(B0(kDk,m)-Cf1*C(1,1,m)-Cf2*C(1,2,m))
L 7	Id,R3=0.5*(Cf1*C(1,1,m)+B1(qDq,m)+B0(kDk,m)) - C(2,4,m)
L 7	Al,R4=0.5*(Cf1*C(1,2,m)+B1(qDq,m)-B1(kDk,m))
L 7	Al,R5=0.5*(Cf2*C(1,1,m)+B1(pDp,m)-B1(qDq,m))
L 7	Al,R6=0.5*(Cf2*C(1,2,m)-B1(qDq,m))-C(2,4,m)

L10	Id,C(1,1,m) = 
	 + Det^-1*C0(m)
	  * ( 1/2*pDp*kDk + 1/2*pDk*kDk )
	 
	 - C0(m)
	 
	 + B0(pDp,m)*Det^-1
	  * ( - 1/2*pDk )
	 
	 + B0(kDk,m)*Det^-1
	  * ( - 1/2*kDk )
	 
	 + B0(qDq,m)*Det^-1
	  * ( 1/2*pDk + 1/2*kDk )
	 
L10	Al,C(1,2,m) = 
	 + Det^-1*C0(m)
	  * ( - 1/2*pDp*pDk - 1/2*pDp*kDk )
	 
	 + B0(pDp,m)*Det^-1
	  * ( 1/2*pDp )
	 
	 + B0(kDk,m)*Det^-1
	  * ( 1/2*pDk )
	 
	 + B0(qDq,m)*Det^-1
	  * ( - 1/2*pDp - 1/2*pDk ) + 0.
	 
L12	Id,C(2,4,m) = 
	 + 1/4*i*Pi^2
	 
	 + Det^-1*C0(m)
	  * ( - 1/4*pDp*pDk*kDk - 1/8*pDp*kDk^2 - 1/8*pDp^2*kDk )
	 
	 + C0(m)
	  * ( - 1/2*m^2 )
	 
	 + B0(pDp,m)*Det^-1
	  * ( 1/8*pDp*pDk + 1/8*pDp*kDk )
	 
	 + B0(kDk,m)*Det^-1
	  * ( 1/8*pDp*kDk + 1/8*pDk*kDk )
	 
	 + 1/4*B0(qDq,m)
	 
	 + B0(qDq,m)*Det^-1
	  * ( - 1/8*pDp*pDk - 1/4*pDp*kDk - 1/8*pDk*kDk ) + 0.
	 
	 
L12	Al,C(2,1,m) = 
	 + i*Pi^2*Det^-1
	  * ( - 1/4*kDk )
	 
	 + Det^-2*C0(m)
	  * ( 3/4*pDp*pDk*kDk^2 + 3/8*pDp*kDk^3 + 3/8*pDp^2*kDk^2 )
	 
	 + Det^-1*C0(m)
	  * ( 1/2*m^2*kDk - pDp*kDk - pDk*kDk - 1/4*kDk^2 )
	 
	 + C0(m)
	 
	 + B0(pDp,m)*Det^-2
	  * ( - 3/8*pDp*pDk*kDk - 3/8*pDp*kDk^2 )
	 
	 + B0(pDp,m)*Det^-1
	  * ( 3/4*pDk + 1/4*kDk )
	 
	 + B0(kDk,m)*Det^-2
	  * ( - 3/8*pDp*kDk^2 - 3/8*pDk*kDk^2 )
	 
	 + B0(kDk,m)*Det^-1
	  * ( kDk )
	 
	 + B0(qDq,m)*Det^-2
	  * ( 3/8*pDp*pDk*kDk + 3/4*pDp*kDk^2 + 3/8*pDk*kDk^2 )
	 
	 + B0(qDq,m)*Det^-1
	  * ( - 3/4*pDk - 5/4*kDk )
	 
L12	Al,C(2,3,m) =
	 + i*Pi^2*Det^-1
	  * ( 1/4*pDk )
	 
	 + Det^-2*C0(m)
	  * ( - 3/8*pDp*pDk*kDk^2 - 3/8*pDp^2*pDk*kDk - 3/4*pDp^2*kDk^2 )
	 
	 + Det^-1*C0(m)
	  * ( - 1/2*m^2*pDk + 1/2*pDp*pDk + pDp*kDk )
	 
	 + B0(pDp,m)*Det^-2
	  * ( 3/8*pDp*pDk*kDk + 3/8*pDp^2*kDk )
	 
	 + B0(pDp,m)*Det^-1
	  * ( - 5/8*pDp )
	 
	 + B0(kDk,m)*Det^-2
	  * ( 3/8*pDp*pDk*kDk + 3/8*pDp*kDk^2 )
	 
	 + B0(kDk,m)*Det^-1
	  * ( - 1/2*pDk - 1/8*kDk )
	 
	 + B0(qDq,m)*Det^-2
	  * ( - 3/4*pDp*pDk*kDk - 3/8*pDp*kDk^2 - 3/8*pDp^2*kDk )
	 
	 + B0(qDq,m)*Det^-1
	  * ( 5/8*pDp + 1/2*pDk + 1/8*kDk )
	 
L12	Al,C(2,2,m) = 
	 + i*Pi^2*Det^-1
	  * ( - 1/4*pDp )
	 
	 + Det^-2*C0(m)
	  * ( 3/4*pDp^2*pDk*kDk + 3/8*pDp^2*kDk^2 + 3/8*pDp^3*kDk )
	 
	 + Det^-1*C0(m)
	  * ( 1/2*m^2*pDp - 1/4*pDp^2 )
	 
	 + B0(pDp,m)*Det^-2
	  * ( - 3/8*pDp^2*pDk - 3/8*pDp^2*kDk )
	 
	 + B0(kDk,m)*Det^-2
	  * ( - 3/8*pDp*pDk*kDk - 3/8*pDp^2*kDk )
	 
	 + B0(kDk,m)*Det^-1
	  * ( 1/4*pDp - 1/4*pDk )
	 
	 + B0(qDq,m)*Det^-2
	  * ( 3/8*pDp*pDk*kDk + 3/8*pDp^2*pDk + 3/4*pDp^2*kDk )
	 
	 + B0(qDq,m)*Det^-1
	  * ( - 1/4*pDp + 1/4*pDk )

L14	Id,B1(x~,m) = -0.5*B0(x,m)

C Det=kDk*pDp-pDk^2
  pDk=0.5*qDq-0.5*kDk-0.5*pDp

L15	Id,qDq=pDp+kDk+2*pDk
L16	Id,Multi,pDk^2=kDk*pDp-Det
	*end
 
ChR1 = 0.
 
ChR2 = 0.
 
Ch24 = 0.
 
ChR3 = 0.
 
ChR5 = 0.
 
ChR4 = 0.
 
ChR6 = 0. + 0.
 

End run. Time 2 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:25:14.  Memory: start 0001B84C, length 476348.


C Tests 3.  Identity among dotproducts.

	V p1,p2,p3,p4,p5,p6,p7,p8,p9,pA,pB,pC,pE,pF,pG,pH
	Z xx = {  p1Dp2*Epf(p3,p4,p5,p6)
		- p1Dp3*Epf(p2,p4,p5,p6)
		- p1Dp4*Epf(p3,p2,p5,p6)
		- p1Dp5*Epf(p3,p4,p2,p6)
		- p1Dp6*Epf(p3,p4,p5,p2) } * Epf(p7,p8,p9,pA)
L 2	Id,Gammas
	*yep

L 1	Id,Numer,p1Dp2,72073513.,p1Dp3,84624678.,p1Dp4,52509276.,p1Dp5,51607603.
L 2	Al,Numer,p1Dp6,97117707.,p1Dp7,56091995.,p1Dp8,86086713.,p1Dp9,35361640.
L 3	Al,Numer,p1DpA,52382708.,p2Dp3,99738370.,p2Dp4,86314985.,p2Dp5,70453871.
L 4	Al,Numer,p2Dp6,114248683.,p2Dp7,71422567.,p2Dp8,111259313.,p2Dp9,53967084.
L 5	Al,Numer,p2DpA,67563860.,p3Dp4,81886836.,p3Dp5,78333162.,p3Dp6,129931642.
L 6	Al,Numer,p3Dp7,73417210.,p3Dp8,114641070.,p3Dp9,53105168.,p3DpA,67662024.
L 7	Al,Numer,p4Dp5,65638463.,p4Dp6,95841513.,p4Dp7,57807475.,p4Dp8,91573602.
L 8	Al,Numer,p4Dp9,48779546.,p4DpA,53427202.,p5Dp6,90443091.,p5Dp7,47695075.
L 9	Al,Numer,p5Dp8,76742276.,p5Dp9,40483748.,p5DpA,45773000.,p6Dp7,89530891.
L10	Al,Numer,p6Dp8,139462170.,p6Dp9,66035460.,p6DpA,69714280.,p7Dp8,83332720.
L11	Id,Numer,p7Dp9,38621796.,p7DpA,45376392.,p8Dp9,60708938.,p8DpA,70447618.
L12	Al,Numer,p9DpA,31692264.
	*end
 
xx = 0. + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:25:17.  Memory: start 0001B84C, length 476348.


C Tests 4. Simple freeze example.

	Common AA1,AA2
	Z AA1=x1*(ax1+ay1)+x2*(bx1+by2)
	Z AA2=y1*(ax1+ay1)+y2*(bx1+by2)
	B x1,x2,y1,y2
	*begin
 
AA1 = + x1
  * ( ax1 + ay1 )
 
 + x2
  * ( bx1 + by2 )
 
AA2 = + y1
  * ( ax1 + ay1 )
 
 + y2
  * ( bx1 + by2 ) + 0.
 

Begin. Time 1 sec.
	Freeze AA1,AA2
> P output
	*begin

Begin. Time 1 sec.
	Z AA1=AA1
	Z AA2=AA2
> P output
> P lists
	*yep


A i=i

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 AA1=CF: 2, AA2=CF: 2, A_A1=C, A_A2=C


A i=i, x1, x2, ax1, ay1, bx1, by2, y1, y2

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 AA1=CF: 2, AA2=CF: 2, A_A1=C, A_A2=C
 
AA1 = + DF(AA1,1)
  * ( x1 )
 
 + DF(AA1,2)
  * ( x2 )
 
AA2 = + DF(AA2,1)
  * ( y1 )
 
 + DF(AA2,2)
  * ( y2 ) + 0.
 
L 1	Id,Expand,AA1
L 2	Id,Expand,AA2
	*end


A i=i, x1, x2, ax1, ay1, bx1, by2, y1, y2

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 AA1=CF: 2, AA2=CF: 2, A_A1=C, A_A2=C
 
AA1 =  + x1*ax1 + x1*ay1 + x2*bx1 + x2*by2
 
AA2 =  + ax1*y1 + ay1*y1 + bx1*y2 + by2*y2 + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:25:21.  Memory: start 0001B84C, length 476348.


C Tests 5.  Freeze example involving many (261) subfiles.

> P lists
> P stats
	A x
	*fix


A i=i, x

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

Begin. Time 1 sec.
	B x,xx
	Common xfile,yfile
	Z xfile=DS(J1,-4,126,(x^J1*y^J1))
	 + DS(J2,-4,126,(xx^J2*y^J2))
> P noutput
	*begin


A i=i, x, xx, y

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 xfile=C, yfile=C

Terms in output 261
Running time 1 sec			Used	Maximum
Generated terms 262 	Input space 	3164 	100000
Equal terms 1     	Output space 	10392 	250000
Cancellations 0   	Nr of expr.  	13 	255
Multiplications 1050	String space 	0 	4096
Records written 0 	Merging		0 	0


Begin. Time 2 sec.
	Z yfile=xfile
	*begin


A i=i, x

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 xfile=C, yfile=C

Terms in output 261
Running time 2 sec			Used	Maximum
Generated terms 261 	Input space 	204 	100000
Equal terms 0     	Output space 	7232 	250000
Cancellations 0   	Nr of expr.  	11 	255
Multiplications 1045	String space 	0 	4096
Records written 2 	Merging		0 	0



A i=i, x, xx, y

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 xfile=C, yfile=C

Begin. Time 2 sec.
	Freeze xfile
	Z xx2=xfile - yfile
L 2	Id,Expand,xfile
	*end


A i=i, x, xx, y

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 xfile=CF: 261, yfile=C, x_file=C

Terms in output 0
Running time 36 sec			Used	Maximum
Generated terms 522 	Input space 	334 	100000
Equal terms 261     	Output space 	0 	250000
Cancellations 261   	Nr of expr.  	14 	255
Multiplications 3134	String space 	0 	4096
Records written 533 	Merging		0 	0



A i=i, x, xx, y

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 xfile=CF: 261, yfile=C, x_file=C

End run. Time 36 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:25:58.  Memory: start 0001B84C, length 476348.


C Tests 6. Reproduces the last equation in Gammatrica.

	I m1=N,m2=N,m3=N,m4=N,m5=N,m6=N,m7=N,m8=N,m9=N,mA=N
	A M

	Z xx =
	 G(1,"t,"4,m1,m2,m3,m4,m5,m6,m7,m8,m9,mA,m1,m2,m3,m4,m5,m6,m7,m8,m9,mA)

L 1	Id,Gammas
> P stats
	*yep

Terms in output 35
Running time 12 sec			Used	Maximum
Generated terms 8192 	Input space 	1406 	100000
Equal terms 8111     	Output space 	0 	250000
Cancellations 46   	Nr of expr.  	14 	255
Multiplications 42759	String space 	0 	4096
Records written 0 	Merging		0 	0


Terms in output 36
Running time 17 sec			Used	Maximum
Generated terms 10825 	Input space 	1406 	100000
Equal terms 10740     	Output space 	870 	250000
Cancellations 49   	Nr of expr.  	14 	255
Multiplications 57855	String space 	0 	4096
Records written 0 	Merging		0 	0

L 1	Id,N_=N-4
L 2	Id,N=M
	*yep

Terms out 36, in 36.

Terms in output 10
Running time 18 sec			Used	Maximum
Generated terms 846 	Input space 	358 	100000
Equal terms 836     	Output space 	240 	250000
Cancellations 0   	Nr of expr.  	19 	255
Multiplications 10995	String space 	0 	4096
Records written 0 	Merging		0 	0

L 1	Id,M=N_
	*yep

Terms out 10, in 10.

Terms in output 10
Running time 18 sec			Used	Maximum
Generated terms 10 	Input space 	220 	100000
Equal terms 0     	Output space 	240 	250000
Cancellations 0   	Nr of expr.  	18 	255
Multiplications 85	String space 	0 	4096
Records written 0 	Merging		0 	0

L 1	Id,Addfa,(1/N_/4)
L 3	Id,N_=N-4
	*end

Terms out 10, in 10.

Terms in output 10
Running time 19 sec			Used	Maximum
Generated terms 1023 	Input space 	362 	100000
Equal terms 1013     	Output space 	236 	250000
Cancellations 0   	Nr of expr.  	18 	255
Multiplications 9276	String space 	0 	4096
Records written 0 	Merging		0 	0

 
xx = 
  + 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 19 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:26:20.  Memory: start 0001B84C, length 476348.


C Tests 7.  Lehmann parameters.

	F ln
	B s
	Z AVY(s,t,u) = - 1/36*s*t - 1/36*t^2 + 5/144*s^2 + 9/32*s^2*B0
	 + 1/32*gu^2*s^2*B0
	 - 1/32*s^2*(1+gup^2)*(ln(s) - ln(m2))
	 - (1/96*s*t + 1/48*t^2)*(ln(t)-ln(m2))
	 - (1/96*s*u + 1/48*u^2)*(ln(u)-ln(m2))

	Z AL(s,t,u) = C*{3*s^2*(ln(s) - a1 - ln(m2))
	 + t*(t-u)*(ln(t) - a2 - ln(m2))
	 + u*(u-t)*(ln(u) - a2 - ln(m2))}

C Relation between a1, a2 and Lehman's alfa1, alfa2:
 ax = - ln(alfax*m^2)
 Note that this makes ln(s) - a1 - ln(m^2) = ln(alfa1*s).
 The coefficients beta1 and beta2 are defined by:
 betax = - ln(alfax*Cp), with Cp = 16*Pi^2*Fpi^2 and Fpi = 92 MeV,
 as deduced from PCAC.
 The critical quantity is
 x = 1/2*(beta2-beta1-1/9) = 1/2*(a2-a1-1/9)
 Note that the quantity Cp is irrelevant here.

	Keep AVY,AL

L 3	Id,u=-s-t

	*next
 
AVY(s,t,u) = 
  - 1/36*t^2
 
 + s
  * ( - 1/36*t )
 
 + s^2
  * ( 5/144 + 9/32*B0 + 1/32*B0*gu^2 )
 
 + ln(m2)
  * ( 1/24*t^2 )
 
 + ln(m2)*s
  * ( 1/24*t )
 
 + ln(m2)*s^2
  * ( 1/24 + 1/32*gup^2 )
 
 + ln(s)*s^2
  * ( - 1/32 - 1/32*gup^2 )
 
 + ln(t)
  * ( - 1/48*t^2 )
 
 + ln(t)*s
  * ( - 1/96*t )
 
 + ln(u)
  * ( - 1/48*t^2 )
 
 + ln(u)*s
  * ( - 1/32*t )
 
 - 1/96*ln(u)*s^2
 
AL(s,t,u) = 
  - 4*t^2*C*a2
 
 + s
  * ( - 4*t*C*a2 )
 
 + s^2
  * ( - 3*C*a1 - C*a2 )
 
 + ln(m2)
  * ( - 4*t^2*C )
 
 + ln(m2)*s
  * ( - 4*t*C )
 
 + ln(m2)*s^2
  * ( - 4*C )
 
 + ln(s)*s^2
  * ( 3*C )
 
 + ln(t)
  * ( 2*t^2*C )
 
 + ln(t)*s
  * ( t*C )
 
 + ln(u)
  * ( 2*t^2*C )
 
 + ln(u)*s
  * ( 3*t*C )
 
 + ln(u)*s^2
  * ( C ) + 0.
 

	Z diff= AVY(s,t,u) - AL(s,t,u)

	Z x = 1/2*(a2-a1-1/9)

L 2	Id,u=-s-t
L 2	Al,C=-1/96
L 2	Al,a1=32*( 5/144 + 9/32*B0 + 1/32*B0*gu^2 + 1/144 )
L 2	Al,a2=-24/36

	Keep AVY,AL,x

	*next
 
diff = + ln(m2)
  * ( 1/32*s^2*gup^2 )
 
 + ln(s)
  * ( - 1/32*s^2*gup^2 )
 
x =  - 19/18 - 9/2*B0 - 1/2*B0*gu^2 + 0.
 
	Z I0d = 3*AL(s,t,u) + AL(u,s,t) + AL(t,u,s)
	Z I1d = AL(u,s,t) - AL(t,u,s)
	Z I2d = AL(u,s,t) + AL(t,u,s)

L 2	Id,u=-s-t
L 2	Al,C=-1/96

	Keep x
	*next
 
I0d = 
  + 1/16*s*t*a1 + 7/48*s*t*a2 + 1/8*s^2*a1 + 1/12*s^2*a2 + 1/16*t^2
  *a1 + 7/48*t^2*a2
 
 + ln(m2)
  * ( 5/24*s*t + 5/24*s^2 + 5/24*t^2 )
 
 + ln(s)
  * ( - 1/8*s^2 )
 
 + ln(t)
  * ( - 1/48*s*t - 5/48*t^2 )
 
 + ln(u)
  * ( - 3/16*s*t - 1/12*s^2 - 5/48*t^2 )
 
I1d = 
  + 1/16*s*t*a1 - 1/16*s*t*a2 + 1/32*s^2*a1 - 1/32*s^2*a2
 
 + ln(s)
  * ( 1/48*s*t + 1/96*s^2 )
 
 + ln(t)
  * ( 1/96*s*t + 1/48*t^2 )
 
 + ln(u)
  * ( - 1/32*s*t - 1/96*s^2 - 1/48*t^2 )
 
I2d = 
  + 1/16*s*t*a1 + 1/48*s*t*a2 + 1/32*s^2*a1 + 5/96*s^2*a2
  + 1/16*t^2*a1 + 1/48*t^2*a2
 
 + ln(m2)
  * ( 1/12*s*t + 1/12*s^2 + 1/12*t^2 )
 
 + ln(s)
  * ( - 1/32*s^2 )
 
 + ln(t)
  * ( 1/96*s*t - 1/24*t^2 )
 
 + ln(u)
  * ( - 3/32*s*t - 5/96*s^2 - 1/24*t^2 ) + 0.
 

	Z x=x

L 2	Id,B0 = Pi/sqrt3 - 2

> P output
	*yep
 
x =  + 143/18 + gu^2 - 1/2*gu^2*Pi*sqrt3^-1 - 9/2*Pi*sqrt3^-1 + 0.
 

	N R0
L 1	Id,Numer,Pi,3.141592654,sqrt3,1.732050808

	*end
 
x =  - .21765 + .931E-1*gu^2 + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:26:23.  Memory: start 0001B84C, length 476348.


C Tests 8.  Milgram's use of numerics for function args.

	Z test=MAXS(-1,0,-1)
L 1	Id,MAXS(MA0~,MA1~,MA2~)=
	 MXFS(
	  	(  MA0*DT(MA0-MA1,MA0-MA2)
	   	+ MA1*DT(MA1-MA0,MA1-MA2)
	   	+ MA2*DT(MA2-MA0,MA2-MA1)
	   	- MA0*DK(MA0,MA1)*DT(MA0-MA2)
	   	- MA1*DK(MA1,MA2)*DT(MA1-MA0)
	   	- MA2*DK(MA2,MA0)*DT(MA2-MA1)
	   	+ MA0*DT(MA0-MA1,MA1-MA2,MA2-MA0)
		)
	 	*DT( MA0*DT(MA0-MA1,MA0-MA2)
	    		+ MA1*DT(MA1-MA0,MA1-MA2)
	    		+ MA2*DT(MA2-MA0,MA2-MA1)
	    		- MA0*DK(MA0,MA1)*DT(MA0-MA2)
	    		- MA1*DK(MA1,MA2)*DT(MA1-MA0)
	    		- MA2*DK(MA2,MA0)*DT(MA2-MA1)
	    		+ MA0*DT(MA0-MA1,MA1-MA2,MA2-MA0)
			)
	 	- DT( -1-	(
			MA0*DT(MA0-MA1,MA0-MA2)+MA1*DT(MA1-MA0,MA1-MA2)
	         	+MA2*DT(MA2-MA0,MA2-MA1)
	         	-MA0*DK(MA0,MA1)*DT(MA0-MA2)
	         	-MA1*DK(MA1,MA2)*DT(MA1-MA0)
	         	-MA2*DK(MA2,MA0)*DT(MA2-MA1)
	         	+MA0*DT(MA0-MA1,MA1-MA2,MA2-MA0)
				 )
			)
	    )
	*end
 
test = + MXFS(0) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:26:25.  Memory: start 0001B84C, length 476348.


C Tests 9.  Milgram's use of numerics for function args. Alternative.

	Z test=MAXS(-1,0,-1)
L 1	Id,MAXS(MA0~,MA1~,MA2~)=MXFS1(MA0,MA1,MA2,MA1-MA0,MA2-MA0,MA2-MA1)
L 3	Id,MXFS1(MA0~,MA1~,MA2~,MA10~,MA20~,MA21~)
	 = MXFS2(  MA0*DT(-MA10,-MA20)
	   	+ MA1*DT(MA10,-MA21)
	   	+ MA2*DT(MA20,MA21)
	   	- MA0*DK(MA0,MA1)*DT(-MA20)
	   	- MA1*DK(MA1,MA2)*DT(MA10)
	   	- MA2*DK(MA2,MA0)*DT(MA21)
	   	+ MA0*DT(-MA10,-MA21,MA20)
		,
		 MA0*DT(-MA10,-MA20)
	    	+ MA1*DT(MA10,-MA21)
	    	+ MA2*DT(MA20,MA21)
	    	- MA0*DK(MA0,MA1)*DT(-MA20)
	    	- MA1*DK(MA1,MA2)*DT(MA10)
	    	- MA2*DK(MA2,MA0)*DT(MA21)
	    	+ MA0*DT(-MA10,-MA21,MA20)
		,
		 -1-	(
			MA0*DT(-MA10,-MA20)+MA1*DT(MA10,-MA21)
	         	+MA2*DT(MA20,MA21)
	         	-MA0*DK(MA0,MA1)*DT(-MA20)
	         	-MA1*DK(MA1,MA2)*DT(MA10)
	         	-MA2*DK(MA2,MA0)*DT(MA21)
	         	+MA0*DT(-MA10,-MA21,MA20)) )

L 6	Id,MXFS2(CX1~,CX2~,CX3~) = MXFS(CX1*DT(CX2)-DT(CX3))
	*end
 
test = + MXFS(0) + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:26:28.  Memory: start 0001B84C, length 476348.


C Tests 10. Spin 3/2.

	I Mu,Mup,i1,i2,al,be
	A m
	V p
	F Dia=u
	Z xx=Dia(Mu,i1,1)
L 1	Id,Dia(Mu~,i1~,n~)=Ug(i1,be,m,p)*Ubg(i2,al,m,p)

	   -{ D(be,al)*Gi(i1,2) - 1/3*i*G(i1,2,be)*p(al)/m
	     + 1/3*i*G(i1,2,al)*p(be)/m
	     - 1/3*G(i1,2,be,al) + 2/3*Gi(i1,2)*p(be)*p(al)/m^2 }
		* { - i*G(2,i2,p) + m*Gi(2,i2) }

> P output
	*yep
 
xx = 
 + G(i1,2,al)*G(2,i2,p)*p(be)
  * ( - 1/3*m^-1 )
 
 + G(i1,2,al)*Gi(2,i2)*p(be)
  * ( - 1/3*i )
 
 + G(i1,2,be,al)*G(2,i2,p)
  * ( - 1/3*i )
 
 + G(i1,2,be,al)*Gi(2,i2)
  * ( 1/3*m )
 
 + G(i1,2,be)*G(2,i2,p)*p(al)
  * ( 1/3*m^-1 )
 
 + G(i1,2,be)*Gi(2,i2)*p(al)
  * ( 1/3*i )
 
 + Gi(i1,2)*G(2,i2,p)*p(al)*p(be)
  * ( 2/3*i*m^-2 )
 
 + Gi(i1,2)*G(2,i2,p)*D(al,be)
  * ( i )
 
 + Gi(i1,2)*Gi(2,i2)*p(al)*p(be)
  * ( - 2/3*m^-1 )
 
 + Gi(i1,2)*Gi(2,i2)*D(al,be)
  * ( - m )
 
 + Ug(i1,be,m,p)*Ubg(i2,al,m,p) + 0.
 
> P output
L 1	Id,Spin,i1,i2,1,2
	*yep
 
xx = 
 + G(i1,i2,al,p)*p(be)
  * ( 1/3*m^-1 )
 
 + G(i1,i2,al)*p(be)
  * ( 1/3*i )
 
 + G(i1,i2,be,al,p)
  * ( 1/3*i )
 
 + G(i1,i2,be,al)
  * ( - 1/3*m )
 
 + G(i1,i2,be,p)*p(al)
  * ( - 1/3*m^-1 )
 
 + G(i1,i2,be)*p(al)
  * ( - 1/3*i )
 
 + G(i1,i2,p)*p(al)*p(be)
  * ( - 2/3*i*m^-2 )
 
 + G(i1,i2,p)*D(al,be)
  * ( - i )
 
 + G(i1,2,al)*G(2,i2,p)*p(be)
  * ( - 1/3*m^-1 )
 
 + G(i1,2,al)*Gi(2,i2)*p(be)
  * ( - 1/3*i )
 
 + G(i1,2,be,al)*G(2,i2,p)
  * ( - 1/3*i )
 
 + G(i1,2,be,al)*Gi(2,i2)
  * ( 1/3*m )
 
 + G(i1,2,be)*G(2,i2,p)*p(al)
  * ( 1/3*m^-1 )
 
 + G(i1,2,be)*Gi(2,i2)*p(al)
  * ( 1/3*i )
 
 + Gi(i1,i2)*p(al)*p(be)
  * ( 2/3*m^-1 )
 
 + Gi(i1,i2)*D(al,be)
  * ( m )
 
 + Gi(i1,2)*G(2,i2,p)*p(al)*p(be)
  * ( 2/3*i*m^-2 )
 
 + Gi(i1,2)*G(2,i2,p)*D(al,be)
  * ( i )
 
 + Gi(i1,2)*Gi(2,i2)*p(al)*p(be)
  * ( - 2/3*m^-1 )
 
 + Gi(i1,2)*Gi(2,i2)*D(al,be)
  * ( - m ) + 0.
 
L 1	Id,Gammas
	*end
 
xx = 0. + 0.
 

End run. Time 1 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:26:31.  Memory: start 0001B84C, length 476348.


C Tests 11. Test of Count command with "F option.

	F Fx,Fy
	A a1,a2,a3
	V p,q
	Z aa = p(mu)*Fx(a1,a2,a3,p,q,p)
L 1	Id,Count,Fy,"F,Fx,a1,10 :"F,Fx,p,1 :"F,Fx,q,7

C Result must be:
  aa = + Fy(10,3,7)*Fx(a1,a2,a3,p,q,p)*p(mu) + 0.

	*end
 
aa = + Fy(10,3,7)*Fx(a1,a2,a3,p,q,p)*p(mu) + 0.
 

End run. Time 0 sec.
Schoonschip, 68000 version of June 27, 1991. Public version.
Date: Thu Aug  8 1991 21:26:34.  Memory: start 0001B84C, length 476348.


C Tests 12. Traces with mixed 4 and N-dim quantities.

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

	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

C The "A applies to index 1.
  Answer expected:
 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 )
	*end
 
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 0 sec.