Improve Is{Constant,Univariate}RationalFunction, add tests

Change IsConstantRationalFunction and IsUnivariateRationalFunction to
return false for objects which are not even rational functions

Improve UNIVARTEST_RATFUN to deal with some more "trivial" cases before
giving up.

Add tests.

hpcgap/lib/ratfun.gi

@@ -249,6 +249,26 @@ function(o)
   fi;
 end);
 
+InstallOtherMethod(IsConstantRationalFunction,"fallback for non-ratfun",true,
+  [IsObject],0,
+function(o)
+  if IsRationalFunction(o) then
+    TryNextMethod();
+  else
+    return false;
+  fi;
+end);
+
+InstallOtherMethod(IsUnivariateRationalFunction,"fallback for non-ratfun",true,
+  [IsObject],0,
+function(o)
+  if IsRationalFunction(o) then
+    TryNextMethod();
+  else
+    return false;
+  fi;
+end);
+
 #############################################################################
 ##
 #M  ExtRepPolynomialRatFun(<ulaurent>)

lib/ratfun.gd

@@ -1576,7 +1576,7 @@ DeclareGlobalFunction("GcdCoeffs");
 ##  gap> UnivariatenessTestRationalFunction( (-6*y^2+y^3) / (y+1) );
 ##  [ true, 2, false, [ [ -6, 1 ], [ 1, 1 ], 2 ] ]
 ##  gap> UnivariatenessTestRationalFunction( (-6*y^2+y^3) / (x+1));
-##  [ fail, fail, fail, fail ]
+##  [ false, fail, false, fail ]
 ##  gap> UnivariatenessTestRationalFunction( ((y+2)*(x+1)) / ((y-1)*(x+1)) );
 ##  [ fail, fail, fail, fail ]
 ##  ]]></Example>

lib/ratfun.gi

@@ -243,6 +243,26 @@ function(o)
   fi;
 end);
 
+InstallOtherMethod(IsConstantRationalFunction,"fallback for non-ratfun",true,
+  [IsObject],0,
+function(o)
+  if IsRationalFunction(o) then
+    TryNextMethod();
+  else
+    return false;
+  fi;
+end);
+
+InstallOtherMethod(IsUnivariateRationalFunction,"fallback for non-ratfun",true,
+  [IsObject],0,
+function(o)
+  if IsRationalFunction(o) then
+    TryNextMethod();
+  else
+    return false;
+  fi;
+end);
+
 #############################################################################
 ##
 #M  ExtRepPolynomialRatFun(<ulaurent>)

lib/ratfun1.gi

@@ -86,6 +86,17 @@ local coefs, ind, extrep, i, shift,fam;
 
 end;
 
+INDETS_POLY_EXTREP:=function(extrep)
+local indets, i, j;
+  indets:=[];
+  for i in [1,3..Length(extrep)-1] do
+    for j in [1,3..Length(extrep[i])-1] do
+      AddSet(indets, extrep[i][j]);
+    od;
+  od;
+  return indets;
+end;
+
 UNIVARTEST_RATFUN:=function(f)
 local fam,notuniv,cannot,num,den,hasden,indn,col,dcol,val,i,j,nud,pos;
   fam:=FamilyObj(f);
@@ -104,6 +115,14 @@ local fam,notuniv,cannot,num,den,hasden,indn,col,dcol,val,i,j,nud,pos;
     den := ExtRepDenominatorRatFun(f);
   fi;
 
+  # if the symmetric difference of the indeterminates of the numerator and
+  # denominator contains more than one element, can't be univariate
+  i:=INDETS_POLY_EXTREP(num);
+  j:=INDETS_POLY_EXTREP(den);
+  if Size(Union(i,j)) > Size(Intersection(i,j))+1 then
+    return notuniv;
+  fi;
+
   if Length(den[1])> 0 then
     # try a GCD cancellation
     i:=TryGcdCancelExtRepPolynomials(fam,num,den);

tst/testinstall/ratfun.tst

@@ -14,24 +14,84 @@ gap> u:=Indeterminate(Rationals,101);;
 gap> SetName(u,"u");;
 
 #
-gap> p0:=0*t^0;;
-gap> p1:=p0+0*t^0;;
-gap> p2:=p0+1*t^0;;
-gap> q0:=0;;
-gap> q1:=q0+0*t^0;;
-gap> q2:=q0+1*t^0;;
-gap> List([p1,p2,q1,q2],x->IsPolynomial(x));
-[ true, true, true, true ]
-gap> List([p1,p2,q1,q2],x->IsRat(x));
-[ false, false, false, false ]
-gap> Value(p1,1);
+# test basic properties
+#
+gap> data := [ 0*t, t^0, t, t+1, 1/t, 1/(t+1), t+u, t/u, t/(u+1), 0, 1 ];
+[ 0, 1, t, t+1, t^-1, (1)/(t+1), t+u, t/u, t/(u+1), 0, 1 ]
+gap> List(data, IsRat);
+[ false, false, false, false, false, false, false, false, false, true, true ]
+gap> List(data, IsRationalFunction);
+[ true, true, true, true, true, true, true, true, true, false, false ]
+gap> List(data, IsConstantRationalFunction);
+[ true, true, false, false, false, false, false, false, false, false, false ]
+gap> List(data, IsPolynomial);
+[ true, true, true, true, false, false, true, false, false, false, false ]
+gap> List(data, IsUnivariatePolynomial);
+[ true, true, true, true, false, false, false, false, false, false, false ]
+gap> List(data, IsUnivariateRationalFunction);
+[ true, true, true, true, true, true, false, false, false, false, false ]
+gap> List(data, IsLaurentPolynomial);
+[ true, true, true, true, true, false, false, false, false, false, false ]
+
+#
+# arithmetics
+#
+
+# multiplication
+gap> List(data, x -> x * Zero(t));
+[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
+gap> ForAll(last,IsUnivariatePolynomial and IsConstantRationalFunction);
+true
+gap> List(data, x -> Zero(t) * x);
+[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
+gap> ForAll(last,IsUnivariatePolynomial and IsConstantRationalFunction);
+true
+gap> List(data, x -> One(t) * x);
+[ 0, 1, t, t+1, t^-1, (1)/(t+1), t+u, t/u, t/(u+1), 0, 1 ]
+gap> last = data*t^0;
+true
+gap> List(data, x -> x * One(t));
+[ 0, 1, t, t+1, t^-1, (1)/(t+1), t+u, t/u, t/(u+1), 0, 1 ]
+gap> last = data*t^0;
+true
+
+# addition
+gap> List(data, x -> x + Zero(t));
+[ 0, 1, t, t+1, t^-1, (1)/(t+1), t+u, t/u, t/(u+1), 0, 1 ]
+gap> last = data*t^0;
+true
+gap> List(data, x -> Zero(t) + x);
+[ 0, 1, t, t+1, t^-1, (1)/(t+1), t+u, t/u, t/(u+1), 0, 1 ]
+gap> last = data*t^0;
+true
+
+# commutative
+gap> SetX(data, data, {x,y} -> x*y = y*x);
+[ true ]
+gap> SetX(data, data, {x,y} -> x+y = y+x);
+[ true ]
+
+# associative
+gap> SetX(data, data, data, {x,y,z} -> (x*y)*z = x*(y*z));
+[ true ]
+gap> SetX(data, data, data, {x,y,z} -> (x+y)+z = x+(y+z));
+[ true ]
+
+# distributive
+gap> SetX(data, data, data, {x,y,z} -> (x+y)*z = x*z+y*z);
+[ true ]
+
+#
+gap> Value(0*t,1);
 0
-gap> Value(p2,1);
+gap> Value(t^0,1);
 1
-gap> Value(q1,1);
-0
-gap> Value(q2,-1);
+gap> Value(t^0,-1);
 1
+gap> Value(t,-1);
+-1
+
+#
 gap> y1:=Indeterminate(Rationals,1);;
 gap> y2:=Indeterminate(Rationals,2);;
 gap> y3:=Indeterminate(Rationals,3);;