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 convenience helpers for multiplying rational numbers by rational functions over rings which don't contain the rational numbers, complementing the existing helpers doing this for addition * Add tests
gap-system · May 18, 2018 · fe11ed7 · fe11ed7
1 parent 832f48e
commit fe11ed7
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diff --git a/hpcgap/lib/ratfun.gi b/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>)
@@ -1031,6 +1051,19 @@ function(r, c)
   return ProdCoefRatfun(c,r);
 end);
 
+InstallMethod( \*, "ratfun * rat", true,
+    [ IsPolynomialFunction, IsRat ],-RankFilter(IsRat),
+function( left, right )
+  return left * (right*FamilyObj(left)!.oneCoefficient);
+end );
+
+InstallMethod( \*, "rat * ratfun ", true,
+    [ IsRat, IsPolynomialFunction], -RankFilter(IsRat),
+function( left, right )
+  return (left*FamilyObj(right)!.oneCoefficient) * right;
+end);
+
+
 #############################################################################
 ##
 #M  <polynomial>     + <coeff>

diff --git a/lib/ratfun.gd b/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>

diff --git a/lib/ratfun.gi b/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>)
@@ -1025,6 +1045,19 @@ function(r, c)
   return ProdCoefRatfun(c,r);
 end);
 
+InstallMethod( \*, "ratfun * rat", true,
+    [ IsPolynomialFunction, IsRat ],-RankFilter(IsRat),
+function( left, right )
+  return left * (right*FamilyObj(left)!.oneCoefficient);
+end );
+
+InstallMethod( \*, "rat * ratfun ", true,
+    [ IsRat, IsPolynomialFunction], -RankFilter(IsRat),
+function( left, right )
+  return (left*FamilyObj(right)!.oneCoefficient) * right;
+end);
+
+
 #############################################################################
 ##
 #M  <polynomial>     + <coeff>

diff --git a/lib/ratfun1.gi b/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);

diff --git a/tst/testinstall/ratfun.tst b/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, 1/2 ];
+[ 0, 1, t, t+1, t^-1, (1)/(t+1), t+u, t/u, t/(u+1), 0, 1/2 ]
+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 IsZero);
+true
+gap> List(data, x -> Zero(t) * x);
+[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
+gap> ForAll(last,IsUnivariatePolynomial and IsZero);
+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, 1/2 ]
+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, 1/2 ]
+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, 1/2 ]
+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, 1/2 ]
+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);;
@@ -71,7 +131,3 @@ t^8*u-u
 
 #
 gap> STOP_TEST( "ratfun.tst", 1);
-
-#############################################################################
-##
-#E
diff --git a/tst/testinstall/ratfun_gf5.tst b/tst/testinstall/ratfun_gf5.tst
@@ -0,0 +1,124 @@
+#############################################################################
+##
+#W  ratfun.tst                  GAP Tests                    Alexander Hulpke
+##
+##
+#Y  (C) 1998 School Math. and Comp. Sci., University of St Andrews, Scotland
+##
+gap> START_TEST("ratfun_gf5.tst");
+
+#
+gap> t:=Indeterminate(GF(5),100);;
+gap> SetName(t,"t");;
+gap> u:=Indeterminate(GF(5),101);;
+gap> SetName(u,"u");;
+
+#
+# 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, 1/2 ];;
+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> ForAll(List(data, x -> x * Zero(t)), IsUnivariatePolynomial and IsZero);
+true
+gap> ForAll(List(data, x -> Zero(t) * x), IsUnivariatePolynomial and IsZero);
+true
+gap> ForAll(List(data, x -> One(t) * x) - data, IsUnivariatePolynomial and IsZero);
+true
+gap> ForAll(List(data, x -> x * One(t)) - data, IsUnivariatePolynomial and IsZero);
+true
+
+# addition
+gap> ForAll(List(data, x -> Zero(t) + x) - data, IsUnivariatePolynomial and IsZero);
+true
+gap> ForAll(List(data, x -> x + Zero(t)) - data, IsUnivariatePolynomial and IsZero);
+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(t^0,1);
+Z(5)^0
+gap> Value(t^0,-1);
+Z(5)^0
+gap> Value(t,-1);
+Z(5)^2
+
+#
+gap> y1:=Indeterminate(Rationals,1);;
+gap> y2:=Indeterminate(Rationals,2);;
+gap> y3:=Indeterminate(Rationals,3);;
+gap> mat:=[[y1,1,0],[y2,y1,1],[y3,y2,y1]];;
+gap> det:=DeterminantMat(mat*y1^0);;
+gap> Value(det,[y1,y2,y3],[1,-5,1]);
+12
+gap> 1/( y1*y2 );
+1/(x_1*x_2)
+
+#
+gap> Factors(t^24-1);
+[ t+Z(5)^0, t+Z(5), t-Z(5)^0, t+Z(5)^3, t^2+Z(5), t^2+Z(5)^3, t^2+t+Z(5)^0, 
+  t^2+t+Z(5), t^2+Z(5)*t-Z(5)^0, t^2+Z(5)*t+Z(5)^3, t^2-t+Z(5)^0, t^2-t+Z(5), 
+  t^2+Z(5)^3*t-Z(5)^0, t^2+Z(5)^3*t+Z(5)^3 ]
+gap> (t^24-1)/(t^16-1);
+(t^16+t^8+Z(5)^0)/(t^8+Z(5)^0)
+gap> (t^24-1)/(t^-16-1);
+(t^32+t^24+t^16)/(-t^8-Z(5)^0)
+
+#
+# multivariate
+#
+gap> (t^24-u^2)/(t^16-u^4);
+(t^24-u^2)/(t^16-u^4)
+gap> f:=u*(t^24-1);; g:=u^2*(t^16-1);;
+gap> f/g;
+(t^24*u-u)/(t^16*u^2-u^2)
+gap> Factors(f);
+[ u, t+Z(5)^0, t+Z(5), t-Z(5)^0, t+Z(5)^3, t^2+Z(5), t^2+Z(5)^3, 
+  t^2+t+Z(5)^0, t^2+t+Z(5), t^2+Z(5)*t-Z(5)^0, t^2+Z(5)*t+Z(5)^3, 
+  t^2-t+Z(5)^0, t^2-t+Z(5), t^2+Z(5)^3*t-Z(5)^0, t^2+Z(5)^3*t+Z(5)^3 ]
+gap> Factors(t^4-u^4);
+[ t+u, t+Z(5)*u, t-u, t+Z(5)^3*u ]
+
+# multivariate gcd
+gap> Gcd(DefaultRing(f),f,g);
+t^8*u-u
+gap> Gcd(f,g);
+t^8*u-u
+
+#
+gap> STOP_TEST( "ratfun_gf5.tst", 1);