C Last 1.  Left, Right, First and Last option in substitutions.
C Last 2.  Multiple dummy: string of function arguments as dummy.
C Last 3.  Production of X/D expressions. Must use name XDexpr.e for output.
C Last 4.  Use of generated X/D expressions.
C Last 5.  Superflags.
C Last 6.  Inverting terms.
C Last 7.  Expression in brackets as function arguments crossing * lines.
C Last 8.  Chaining functions on the basis of indices.
C Last 9.  Reversing order of selected function arguments.
C Last 10. Options Commu command.
C Last 11. Options Order command.
C Last 12. Groups for cyclic command.
C Last 13. Name lists in Cyclic, Symme etc. commands.
C Last 14. Use of rational numbers as function arguments.

*end

C Last 1.  Left, Right, First and Last option in substitutions.

F f1,f2,f3,f4,f5,f10
Z xx=3*f1*aa
IF aa=f10
Id,Addfa,f2
Id,Left,Addfa,f3
Id,Right,Addfa,f4
Id,First,Addfa,f5
ENDIF

*begin
F f1,f2,f3,f4,f5,ff
*fix

Z xx=f1*f2*f3*f4*f5

Id,Ainbe,f2*f4=ff
*begin

Z xx=f1*f2*f3*f4*f5

Id,Left,Ainbe,f2*f4=ff
*begin

Z xx=f1*f2*f3*f4*f5

Id,Right,Ainbe,f2*f4=ff
*begin

Z xx=f1*f2*f3*f4*f5

Id,First,Ainbe,f2*f4=ff
*begin

Z xx=f1*f2*f3*f4*f5

Id,Last,Ainbe,f2*f4=ff

*end

C Last 2.  Multiple dummy: string of function arguments as dummy.

F f1,f2,f3,ff2
V p,q
I mu
A a,b,c,d,e,f,ff,a1,a2,a3
Z xx = f1(a1,b,c,d,e,f,ff,b,c,d,e,f)* f3(a1,b)
 + a1*f1(a1,ff)*p(mu)
Id,f1(a~,b?,ff,b?)*f3(a~,b)=f2(f,b,ff,c)
Id,f1(a~,b?,ff)=ff2(ff,b)
Id,p(mu~)=q(mu)
*begin

F f1,f2,f3,f4,f5,f6,ff2
V p,q
I mu
A a,b,c,d,e,f,ff,a1,a2,a3
Z xx = f1(a)*f2(b)*f3(c)*f4(d)*f5(e)*f6(f) + f1(a)*a1*p(mu)
Id,First,Ainbe,f2(b)*f4(d)=ff2(a,b)
Id,First,a1*p(mu)=ff2(b)
*end

C Last 3.  Production of X/D expressions. Must use name XDexpr.e for output.
C File XDexpr.e is used by the next problem. Therefore:
C Command line: Schip +3 Last.e XDexpr.e

XX
Z AB4(a,b)=(a+b)^4
Z AB5(a,b)=(a+b)^5
*begin
Z AB6(a,b)=(a+b)^6
*begin
DD
Z POW(n,a,b,c)=a+b+c
DO II=2,5
Z x'II'=(a+b+c)^'II'
B a
ENDDO
*begin
XX
Z AB7(a,b)=(a+b)^7

*end

C Last 4.  Use of generated X/D expressions.
C The file XDexpr.e must have been generated by the previous problem.

Read XDexpr.e
A c,d,e
Z xyz=POW(3,c,d,e)

*end

C Last 5.  Superflags.

Z xx=3

Id,Flag,Set,4

C Default is Flag 0.
C
Id,Flag,set

DO II=0,8
IF Flag,on,'II'
Al,Addfa,f'II'on
ENDIF
IF Flag,off,'II'
Al,Addfa,f'II'off
ENDIF
ENDDO

*end

C Last 6.  Inverting terms.

A a,b,c,d,e
F f1,f2,f2_,f3,f4
I i1,i2
V p,q
Z xx = 3*a^3*pDq^-3*i1^7*f1(b,c)
 +  1/7*b^3*pDq^-3*i1^7*f2(d,e)
 +  1/13*c^3*pDq^-3*i1^7*f2_(a,b)
Id,Invert

*end

C Last 7.  Expression in brackets as function arguments crossing * lines.

Z xx = f1((8.-2E-27),(-3.),(128),(-128))
P output
*yep
*begin

C Here the expression as function argument contains a dummy.

A a,b,c,d,e,f
Z xx = f1(a,b,c)*f1(d,e,f)
Id,f1(a~,b~,c~)=ff(a,(9*a))
P output
*yep
Id,ff(a~,b~)=b
*begin

F f,g,h,xpow
A x,y,n,n1,n2
Z xx = f(x,3,y,2) + f(x,y,2) + f(x,y,3)
Id,f(x,n~,y,n1~) = g(n+n1-3)*f(x,n-3,y,n1+3)
Id,f(x,0,y,n~)=f(x,y,n)
Id,g(n1~)*f(x,y,n2~) = xpow(n1+n2)*f(x,y,n2-2*n1)
Id,f(x~,y~,2)=0
Id,f(x~,y~,3)=h(x,y)
*begin

Common yy
F f1,f2,f3,f4
A a1,a2,a3,a4
I i1,i2,i3,i4
Z yy = f4(a,b)
Z xx = f3(4,5,(1/3))
Id,f3(a~,b~,c~)=f2(-(2),-(2*aa1),(a+2*b-c))+aa1
Al,f4(a~,b~)=f2(a,(1.23),b,c)+aa1
P output
*yep
Keep xx
*next

Z yz=xx
Id,f2(a~,b~,c~)=a*f3

*begin
Z yz=yy
Id,f2(a,a1~,b,c)=a1*f3(a,b)

*end

C Last 8.  Chaining functions on the basis of indices.

I a,b,c,d,a1,b1,c1
A x1,x2,x3
F Tr,St,ff
Z xx=ff(x1)*f1(a,b,A)*f1(b,c,C,D)*ff(x2)*f1(d,a,E)*ff(x3)
 *f2(c1,b1)*f2(b1,a1)*ff(x4)
Id,Left,Chain,"S,Tr,St,a,b,c,d,a1,b1,c1
*begin

I s1,s2,s3,s4
F Tr,St
Z xx =f1(s1,s2,A)
 *f1(s3,s4,C)
 *f1(s2,s3,B)
Z yy =f1(s1,s2,A)
 *f1(s3,s1,C)
 *f1(s2,s3,B)
Id,Chain,"S,Tr,St,s1,s2,s3,s4
*end

C Last 9.  Reversing order of selected function arguments.
C The order of the arguments ** not ** mentioned is reversed.

F f1
A a,b,c,d,e,f
Z xx=f1(a,b,c,d,e)*f2(a,b,c,d,e)*f1(a,b,c,d,e)
Id,Revert,f1,2,3,4,f2,1,4

*end

C Last 10. Options Commu command.

F f0,f3,f1,f2,f4
Z xx=f0(a)*f1(a,b,c)*f2(a1,a2)*f3*f4(b1,b2)
Id,Commu,f1,f3
C xx = + f0(a)*f2(a1,a2)*f4(b1,b2)*f3*f1(a,b,c) + 0.
*begin

F f0,f3,f1,f2,f4
Z xx=f0(a)*f1(a,b,c)*f2(a1,a2)*f3*f4(b1,b2)
Id,First,Commu,f1,f3
C xx = + f0(a)*f3*f1(a,b,c)*f2(a1,a2)*f4(b1,b2) + 0.
*begin

F f0,f3,f1,f2,f4
Z xx=f0(a)*f1(a,b,c)*f2(a1,a2)*f3*f4(b1,b2)
Id,Last,Commu,f1,f3
C xx = + f0(a)*f2(a1,a2)*f3*f1(a,b,c)*f4(b1,b2) + 0.
*begin

F f0,f3,f1,f2,f4
Z xx=f0(a)*f1(a,b,c)*f2(a1,a2)*f3*f4(b1,b2)
Id,Left,Commu,f1,f3
C xx = + f3*f1(a,b,c)*f0(a)*f2(a1,a2)*f4(b1,b2) + 0.
*begin

F f0,f3,f1,f2,f4
Z xx=f0(a)*f1(a,b,c)*f2(a1,a2)*f3*f4(b1,b2)
Id,Right,Commu,f1,f3
C xx = + f0(a)*f2(a1,a2)*f4(b1,b2)*f3*f1(a,b,c) + 0.
*begin

F f0,f3,f1,f2,f4
Z xx=f0(a)*f1(a,b,c)*f2(a1,a2)*f3*f4(b1,b2)
Id,Commu,"B,f1,f3
C xx = + f3*f1(a,b,c)*f0(a)*f2(a1,a2)*f4(b1,b2) + 0.
*begin

F f0,f3,f1,f2,f4
Z xx=f0(a)*f1(a,b,c)*f2(a1,a2)*f3*f4(b1,b2)
Id,Commu,"N,f1,f3
C xx = + f0(a)*f2(a1,a2)*f4(b1,b2)*f1(a,b,c)*f3 + 0.
*begin

F f0,f3,f1,f2,f4
Z xx=f0(a)*f1(a,b,c)*f2(a1,a2)*f3*f4(b1,b2)
Id,Commu,"N,"B,f1,f3
C xx = + f1(a,b,c)*f3*f0(a)*f2(a1,a2)*f4(b1,b2) + 0.
*end

C Last 11. Options Order command.

I s1,s2,s3,s4
*fix

Z xx =f1(s1,s2,A)
 *f1(s3,s4,C)
 *f1(s2,s3,B)
Id,Order,"C,f1
*begin

Z xx =
 f1(s1,s2,A)
 *f1(s3,s4,C)
 *f1(s2,s3,B)
 *f2(s1,s2,A)
 *f2(s3,s4,C)
 *f2(s2,s3,B)
Id,Order,"C,"L,f1
*begin

Z xx =
 f1(s1,s2,A)
 *f1(s3,s4,C)
 *f1(s2,s3,B)
 *f2(s1,s2,A)
 *f2(s3,s4,C)
 *f2(s2,s3,B)
Id,Order,20,"C,"L,f1,f2
*begin

Z xx =
 f1(s1,s2,A)
 *f1(s3,s4,C)
 *f1(s2,s3,B)
 *f2(s1,s2,A)
 *f2(s3,s4,C)
 *f2(s2,s3,B)
Id,Order,20,"C,f1,f2
*end

C Last 12. Groups for cyclic command.

A m1,m2,m3
I i1,i2,i3
F f,f1
Z xx= f(m2,i2,m1,i1,m3,i3)
Id,Cyclic,f,1,2,3,4,5,6
*begin
A m1,m2,m3
I i1,i2,i3
F f,f1
Z xx= f(m2,i2,m1,i1,m3,i3)
Id,Cyclic,f:1,2:3,4:5,6
*begin
A m1,m2,m3
I i1,i2,i3
Z xx=f(m3,i3,m1,i1,m2,i2)
Id,Symme,f:1,2:3,4:5,6:
*end

C Last 13. Name lists in Cyclic, Symme etc. commands.

A m1,m2,m3
F f,f1
Z xx= f(m2,2,-m1,1,m3,3)
Id,Cyclic,"L,-m1,m2,f1,"L,f,1,2,3,4,5,6
*begin

A m1,m2,m3
Z xx=f(m3,3,m1,1,m2,2)
Id,Symme,f:1,2:3,4:5,6:
*end

C Last 14. Use of rational numbers as function arguments.

A a,c,d,e
Z xx=f1(a,-17,85,b,(21),(-3.14))*f3(9,2)
Id,f3(d~,e~)=f2(b,65,13,b,c,(3*d+e/3),(-511))
*yep
Id,Rnum,f1,2,6,f2
*end