Fixed tests and version bump

PackageInfo.g

@@ -5,11 +5,11 @@
 SetPackageInfo( rec(
 PackageName := "IMG",
 Subtitle := "Computations with iterated monodromy groups",
-Version := "0.2.2",
-Date := "16/03/2019",
+Version := "0.2.3",
+Date := "19/03/2019",
 ## <#GAPDoc Label="Version">
-## <!ENTITY Version "0.2.2">
-## <!ENTITY Date "16/03/2019">
+## <!ENTITY Version "0.2.3">
+## <!ENTITY Date "19/03/2019">
 ## <#/GAPDoc>
 Persons := [
   rec(

src/img.c

@@ -72,7 +72,8 @@ static Obj COMPLEX_ROOTS (Obj self, Obj coeffs)
   Obj result;
   Int i, numroots, degree = LEN_PLIST(coeffs)-1;
   xcomplex op[degree+1], zero[degree];
-
+  bool real = true;
+
   if (degree < 1)
     return Fail;
 
@@ -81,6 +82,8 @@ static Obj COMPLEX_ROOTS (Obj self, Obj coeffs)
     __imag__(op)[degree-i] = VAL_FLOAT(ELM_PLIST(ELM_PLIST(coeffs,i+1),2));
     if (isnan(__real__(op)[degree-i]) || isnan(__imag__(op)[degree-i]))
       return Fail;
+    if (__imag__(op)[degree-i] != 0.0)
+      real = false;
   }
 
 #ifdef DEBUG_COMPLEX_ROOTS
@@ -106,6 +109,8 @@ static Obj COMPLEX_ROOTS (Obj self, Obj coeffs)
   result = ALLOC_PLIST(numroots);
   for (i = 1; i <= numroots; i++) {
     Obj t = ALLOC_PLIST(2);
+    if (real && fabs(__imag__(zero)[i-1]) < 2*degree*DBL_EPSILON*fabs(__real__(zero)[i-1]))
+      __imag__(zero)[i-1] = 0.0;
     set_elm_plist(t,1, NEW_FLOAT(__real__(zero)[i-1]));
     set_elm_plist(t,2, NEW_FLOAT(__imag__(zero)[i-1]));
     set_elm_plist(result,i, t);

src/p1.c

@@ -776,8 +776,10 @@ static Obj P1PREIMAGES(Obj self, Obj map, Obj objp)
     return Fail;
 
   Obj obj = ALLOC_PLIST(deg);
-  for (i = 0; i < numroots; i++)
+  for (i = 0; i < numroots; i++) {
+    // clean?
     set_elm_plist(obj,i+1, NEW_P1POINT(zero[i]));
+  }
   for (i = numroots; i < deg; i++)
     set_elm_plist(obj,i+1, P1infinity);
   return obj;
@@ -796,8 +798,10 @@ static Obj P1CRITICAL(Obj self, Obj map)
   if (numroots < 0)
     return Fail;
   Obj obj = ALLOC_PLIST(2*deg-2);
-  for (i = 0; i < numroots; i++)
+  for (i = 0; i < numroots; i++) {
+    // clean?
     set_elm_plist(obj,i+1, NEW_P1POINT(zero[i]));
+  }
   for (i = numroots; i < 2*deg-2; i++)
     set_elm_plist(obj,i+1, P1infinity);
   return obj;

tst/chapter-12.tst

@@ -44,6 +44,6 @@ gap>
 gap> 
 gap> STOP_TEST( "chapter-12.tst", 3*10^8 );
 fr:chapter 12
-GAP4stones: 10000
+msecs: 0
 
 #E chapter-12.tst . . . . . . . . . . . . . . . . . . . . . . . . . ends here

tst/chapter-9-a.tst

@@ -25,48 +25,49 @@ gap> e := EquivalenceRelationPartition(ExternalAnglesRelation(2,5));
   [ 19/31, 20/31 ], [ 21/31, 22/31 ], [ 5/7, 6/7 ], [ 11/15, 4/5 ],
   [ 23/31, 24/31 ], [ 25/31, 26/31 ], [ 13/15, 14/15 ], [ 27/31, 28/31 ],
   [ 29/31, 30/31 ] ]
-gap> ForAll(e,p->SupportingRays(PolynomialIMGMachine(2,[p[1]]))[2][1][1]*2 in [p[1],p[2],p[1]+1,p[2]+1]);
+gap> ForAll(e,p->SupportingRays(PolynomialSphereMachine(2,[p[1]]))[2][1][1]*2 in [p[1],p[2],p[1]+1,p[2]+1]);
 true
 gap> 
 gap> Info(InfoFR,1,"Testing rabbit and z^2+i twists");
 #I  Testing rabbit and z^2+i twists
-gap> ri := PolynomialIMGMachine(2,[],[1/6]);
-<FR machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Group( [ f\
-1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>
+gap> ri := PolynomialSphereMachine(2,[],[1/6]);
+<sphere machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Group(\
+ [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>
 gap> model := StateSet(ri);
-<free group on the generators [ f1, f2, f3, f4 ]>
+<sphere group on generators [ f1, f2, f3, f4 ], ordering f4*f3*f2*f1>
 gap> twist := GroupHomomorphismByImages(model,model,GeneratorsOfGroup(model),[model.1,model.2^(model.3*model.2),model.3^model.2,model.4]);
-[ f1, f2, f3, f4 ] -> [ f1, f2^-1*f3^-1*f2*f3*f2, f2^-1*f3*f2, f4 ]
+[ f1, f2, f3, f4 ] -> [ f1, f1*f4*f2*f3*f2, f2^-1*f3*f2, f4 ]
 gap> 
-gap> r := PolynomialIMGMachine(2,[1/7],[]);
-<FR machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Group( [ f\
-1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>
+gap> r := PolynomialSphereMachine(2,[1/7],[]);
+<sphere machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Group(\
+ [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>
 gap> model := StateSet(r);
-<free group on the generators [ f1, f2, f3, f4 ]>
+<sphere group on generators [ f1, f2, f3, f4 ], ordering f4*f3*f2*f1>
 gap> twist := GroupHomomorphismByImages(model,model,GeneratorsOfGroup(model),[model.1^(model.2*model.1),model.2^model.1,model.3,model.4]);
-[ f1, f2, f3, f4 ] -> [ f1^-1*f2^-1*f1*f2*f1, f1^-1*f2*f1, f3, f4 ]
+[ f1, f2, f3, f4 ] -> [ f4*f3*f1*f2*f1, f1^-1*f2*f1, f3, f4 ]
 gap> rt := List([0..4],i->r*twist^i);
-[ <FR machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
-  <FR machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
-  <FR machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
-  <FR machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
-  <FR machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]> ]
-gap> m := PolynomialIMGMachine(3,[[3/4,1/12],[1/4,7/12]],[]);
-<FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f3) on Group( [ f\
-1, f2, f3 ] )/[ f3*f2*f1 ]>
+[ <sphere machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 2 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]> ]
+gap> m := PolynomialSphereMachine(3,[[3/4,1/12],[1/4,7/12]],[]);
+<sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f3) on Group(\
+ [ f1, f2, f3 ] )/[ f3*f2*f1 ]>
 gap> 
 gap> Info(InfoFR,1,"Testing a folding");
 #I  Testing a folding
-gap> fold1 := NewIMGMachine("a=<,,b,,,B>(1,2,3)(4,5,6)","b=<,,b*a/b,,,B*A/B>","A=<,,b*a,,,B*A>(3,6)","B=(1,6,5,4,3,2)");
-<FR machine with alphabet [ 1 .. 6 ] on Group( [ a, b, A, B ] )/[ a*B*A*b ]>
+gap> fold1 := NewSphereMachine("a=<,,b,,,B>(1,2,3)(4,5,6)","b=<,,b*a/b,,,B*A/B>","A=<,,(B*A)^-1,,,(b*a)^-1>(3,6)","B=(1,6,5,4,3,2)","A*b*a*B");
+<sphere machine with alphabet [ 1 .. 6 ] on Group( [ a, b, A, B ] ) / [ A*b*a*\
+B ]>
 gap> 
 gap> STOP_TEST( "chapter-9-a.tst", 10^10 );
 fr:chapter 9 (1/2)
-GAP4stones: 4681000
+msecs: 503
 
 #E chapter-9-a.tst . . . . . . . . . . . . . . . . . . . . . . . . .ends here

tst/chapter-9-b.tst

@@ -26,59 +26,57 @@ gap> SetFloats(IEEE754FLOAT);
 gap> z := P1z;
 <z>
 gap> a := RootsFloat((z-1)*(3*z^2-2*z^3)+1);
-[ 0.598631+0.565259i, -0.426536, 0.598631-0.565259i, 1.72927-2.22045e-16i ]
+[ 0.598631+0.565259i, -0.426536, 0.598631-0.565259i, 1.72927 ]
 gap> c := RootsFloat((z^3+z)^3+z);
 [ 0., 0.557573+0.540347i, -0.557573+0.540347i, -0.557573-0.540347i,
   0.557573-0.540347i, 0.264425+1.26049i, -0.264425+1.26049i,
   -0.264425-1.26049i, 0.264425-1.26049i ]
-gap> am := List(a,a->IMGMachine((a-1)*(3*z^2-2*z^3)+1));
-[ <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f3*f2*f1*f4 ]>, 
-  <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f2*f3*f1*f4 ]>, 
-  <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f3*f2*f1*f4 ]>, 
-  <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f3*f1*f2*f4 ]> ]
-gap> cm := List(c,c->IMGMachine(z^3+c));
-[ <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f2) on Group( [\
- f1, f2 ] )/[ f1*f2 ]>,
-  <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f3*f1*f2*f4 ]>, 
-  <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f3*f1*f2*f4 ]>, 
-  <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f3*f1*f2*f4 ]>, 
-  <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f3*f1*f2*f4 ]>, 
-  <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f1*f3*f2*f4 ]>, 
-  <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f1*f3*f2*f4 ]>, 
-  <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f1*f3*f2*f4 ]>, 
-  <FR machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Group( [\
- f1, f2, f3, f4 ] )/[ f1*f3*f2*f4 ]> ]
+gap> am := List(a,a->SphereMachine((a-1)*(3*z^2-2*z^3)+1));
+[ <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]> ]
+gap> cm := List(c,c->SphereMachine(z^3+c));
+[ <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f2) on Grou\
+p( [ f1, f2 ] )/[ f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]>,
+  <sphere machine with alphabet [ 1 .. 3 ] and adder FRElement(...,f4) on Grou\
+p( [ f1, f2, f3, f4 ] )/[ f4*f3*f2*f1 ]> ]
 gap> m := ListX(am,cm,Mating);;
-gap> RationalFunction(NewIMGMachine(am[2]));
-<1.9353365831410638_z*z^3+(-6.5315742879608081_z)*z^2+5.2080077920476935_z*z+0\
-.51788488659999687_z>
-gap> RationalFunction(m[9+2]);
-<((0.19853514848979054+0.094747862775783384i_z)*z^3+(0.36448217409192502+1.067\
-1933890697718i_z)*z^2+(0.65828774719150207+0.56768707293267628i_z)*z+(-1.13054\
-18372331943-1.8215142432570175i_z))/((0.42613189662774054+0.10853855675161406i\
-_z)*z^3+(1.1298164009633644+1.950676369983551i_z)*z^2+(1.5115657119504351+0.85\
-698452757134347i_z)*z+1._z)>
+gap> P1MapBySphereMachine(am[2]);
+<z^3+(-2.1398032727526402_z)*z+(-0.36023134081173841_z)>
+gap> P1MapBySphereMachine(m[9+2]);
+<((1.4686858846983573-1.0290716144155767i_z)*z^3+(1.9850056687104112-1.7893204\
+8860004i_z)*z^2+(-1.8069445331386629-0.83371844877356505i_z)*z+(-1.66797918021\
+99766+0.67701449505226674i_z))/((1.3981038147796185-1.4150160285253968i_z)*z^3\
++(1.8103784467122102-2.3473103431921412i_z)*z^2+(-2.1376242871497211-0.5505179\
+5026414962i_z)*z+1._z)>
 gap> 
 gap> Info(InfoFR,1,"An obstructed mating");
 #I  An obstructed mating
-gap> RationalFunction(m[9+8]);
-rec( machine := <FR machine with alphabet [ 1 .. 3 ] on Group(
-    [ f1, f2, f3, g1, g2, g3 ] )/[ f2*f3*f1*g1*g3*g2 ]>,
-  matrix := [ [ 1/2, 1 ], [ 1/2, 0 ] ], obstruction := [ f1*g1, f2^-1*g2^-1 ], 
-  spider := <marked sphere on <triangulation with 9 vertices, 42 edges and 14 \
-faces> marked by [ f1, f2, f3, g1, g2, g3 ] -> [ f1^-1*f4^-1, f3^-1*f2*f3, f3^\
--1*f5, f4*f1*f5^-1*f4^-1, f2^-1*f3, f4 ]> )
+gap> P1MapBySphereMachine(m[9+6]);
+rec(
+  machine := <sphere machine with alphabet [ 1, 2, 3 ] on Group( [ f1, f2, f3, g1, g2, g3 ] ) / [ f\
+3*f2*f1*g3*g2*g1 ]>, matrix := [ [ 1/2, 1 ], [ 1/2, 0 ] ],
+  multicurve := [ f1*f3*f2*f1*f3*f2*f1*f3*f2*f1*g1*g3*g2*g1*g3*g2*g1*g3*g2*g1^G,
+      f1^-1*f2^-1*f1*f3*f2*f1*f3*f2*f1*f3*f2*f1*g2^-1*g3*g2*g1*g3*g2*g1*g3*g2*g1^G ] )
 gap> 
 gap> Info(InfoFR,1,"Testing Triangulations");
 #I  Testing Triangulations
@@ -91,54 +89,54 @@ gap> DelaunayTriangulation(cube);
 gap> DelaunayTriangulation(cube{[1,5]});
 <triangulation with 6 vertices, 24 edges and 8 faces>
 gap> p := List([[0.,0.,1.],[0.,0.,-1.],SphereP1(P1Point(1.e-4)),SphereP1(P1Point(0.,1.e4))],P1Sphere);
-[ <0+0i>, <P1infinity>, <0.0001+0i>, <-0+10000i> ]
+[ <0+0i>, <P1infinity>, <0.0001+0i>, <0+10000i> ]
 gap> DelaunayTriangulation(p,100.);
 <triangulation with 32 vertices, 180 edges and 60 faces>
 gap> 
 gap> Info(InfoFR,1,"Testing RationalFunction");
 #I  Testing RationalFunction
-gap> f := RationalFunction(PolynomialIMGMachine(2,[],[7/16]):param_unicritical);
-<z^2+(-1.7712570233568821+0.066161509080687936i_z)>
+gap> f := P1MapBySphereMachine(PolynomialSphereMachine(2,[],[7/16]):param_unicritical);
+<z^2+(-1.771257023356245+0.066161509079844388i_z)>
 gap> 
 gap> Info(InfoFR,1,"Testing Pilgrim's obstructed blowup of the torus");
 #I  Testing Pilgrim's obstructed blowup of the torus
 gap> F := SphereGroup(4,[0,0,0,0],FreeGroup("a","b","c","d"));
-<fp group of size infinity on the generators [ a, b, c, d ]>
-gap> AssignGeneratorVariables(F); o := One(F);;
-#I  Assigned the global variables [ a, b, c, d ]
+<sphere group on generators [ a, b, c, d ], ordering d*c*b*a>
+gap> a := F.1;; b := F.2;; c := F.3;; d := F.4;; o := One(F);;
 gap> M := FRMachine(F,[[c^-1,o,o,o,c],[o,o,o,d,d^-1],[a,o,o,a^-1,o],[b,o,d,a,c]],
 >                   [(1,5)(2,4,3),(1,2)(4,5),(1,4)(2,3,5),()]);
-<FR machine with alphabet [ 1 .. 5 ] on Group( [ a, b, c, d ] )>
+<sphere machine with alphabet [ 1 .. 5 ] on Group( [ a, b, c, d ] ) / [ d*c*b*\
+a ]>
 gap> P1MapBySphereMachine(M);
 rec(
-  machine := <FR machine with alphabet [ 1 .. 5 ] on Group( [ a, b, c, d ] )/[\
- d*c*b*a ]>, matrix := [ [ 1 ] ], obstruction := [ a^-1*c^-1 ],
-  spider := <marked sphere on <triangulation with 7 vertices, 30 edges and 10 \
-faces> marked by [ a, b, c, d ] -> [ f1^-1*f2^-1, f3^-1*f1, f3, f2 ]> )
+  machine := <sphere machine with alphabet [ 1, 2, 3, 4, 5 ] on Group( [ a, b,\
+ c, d ] ) / [ d*c*b*a ]>, matrix := [ [ 1 ] ], multicurve := [ a*c^G ] )
 gap> 
 gap> Info(InfoFR,1,"Testing mating of airplane with z^2+i");
 #I  Testing mating of airplane with z^2+i
-gap> m := Mating(PolynomialIMGMachine(2,[3/7],[]),PolynomialIMGMachine(2,[],[1/6]));
-<FR machine with alphabet [ 1 .. 2 ] on Group( [ f1, f2, f3, g1, g2, g3 ] )/[ \
-f3*f2*f1*g3*g2*g1 ]>
+gap> m := Mating(PolynomialSphereMachine(2,[3/7],[]),PolynomialSphereMachine(2,[],[1/6]));
+<sphere machine with alphabet [ 1 .. 2 ] on Group( [ f1, f2, f3, g1, g2, g3 ] \
+) / [ f3*f2*f1*g3*g2*g1 ]>
 gap> Unbind(f1); Unbind(f2); Unbind(f3); Unbind(g1); Unbind(g2); Unbind(g3); 
 gap> AssignGeneratorVariables(StateSet(m));
 #I  Assigned the global variables [ f1, f2, f3, g1, g2, g3 ]
 gap> i := FreeGroup("f1","f2","f3","g1","x");
 <free group on the generators [ f1, f2, f3, g1, x ]>
+gap> i := SphereGroup([1,4,3,2,5],[0,0,0,0,0],i);
+<sphere group on generators [ f1, f2, f3, g1, x ], ordering f1*g1*f3*f2*x>
 gap> tm := ChangeFRMachineBasis(m,[f1^-1*g2,One(StateSet(m))]);;
 gap> inj := GroupHomomorphismByImages(i,StateSet(m),GeneratorsOfGroup(i),[f1^g2,f2,f3,g1,f1*g3/f1*g2]);
 [ f1, f2, f3, g1, x ] -> [ g2^-1*f1*g2, f2, f3, g1, f1*g3*f1^-1*g2 ]
 gap> m2 := SubFRMachine(tm,inj);
-<FR machine with alphabet [ 1 .. 2 ] on Group( [ f1, f2, f3, g1, x ] )/[ f3*f2\
-*x*f1*g1 ]>
-gap> RationalFunction(m2);
-<((2.1173218773245877+0.092523780325534474i_z)*z^2+(3.6019898773482266+1.59353\
-23696078603i_z)*z+(2.3547834193556909+1.5278264334816143i_z))/((-4.64791571561\
-72919-5.8835287029321073i_z)*z+1._z)>
+<sphere machine with alphabet [ 1 .. 2 ] on Group( [ f1, f2, f3, g1, x ] ) / [\
+ f1*g1*f3*f2*x ]>
+gap> P1MapBySphereMachine(m2);
+<((-1.1898473846113464+0.24902829777699695i_z)*z^2+(1.9648756079548171+1.99403\
+77105934426i_z)*z+(-0.65573526775326108-2.4418235808459454i_z))/((3.4179914358\
+760768+2.610275400738987i_z)*z+1._z)>
 gap> 
 gap> STOP_TEST( "chapter-9-b.tst", 10^10 );
 fr:chapter 9 (2/2)
-GAP4stones: 2498000
+msecs: 13604
 
 #E chapter-9-b.tst . . . . . . . . . . . . . . . . . . . . . . . . .ends here

tst/testall.g

@@ -1,6 +1,6 @@
 LoadPackage("img");
 SetInfoLevel(InfoIMG,1);
 dirs := DirectoriesPackageLibrary("img","tst");
-ReadTest(Filename(dirs,"chapter-12.tst"));
-ReadTest(Filename(dirs,"chapter-9-a.tst"));
-ReadTest(Filename(dirs,"chapter-9-b.tst"));
+Test(Filename(dirs,"chapter-12.tst"), rec(compareFunction := "uptowhitespace"));
+Test(Filename(dirs,"chapter-9-a.tst"), rec(compareFunction := "uptowhitespace"));
+Test(Filename(dirs,"chapter-9-b.tst"), rec(compareFunction := "uptowhitespace"));