diff --git a/contfrac.cc b/contfrac.cc
index 7f49c9b..74dfcd5 100644
--- a/contfrac.cc
+++ b/contfrac.cc
@@ -144,13 +144,14 @@ void ContFrac<T>::canonicalize()
 {
 int n=this->length();
 if(n==0) return;
+this->copyonwrite();
 if(n>0 && (*this)[1]<0) //handle negative a_i i>0
 	{
-	for(int i=0; i<=n; ++i) (*this[i]) = -(*this[i]);
+	for(int i=0; i<=n; ++i) (*this)[i] = -(*this)[i];
 	*this = -(*this);
+	n=this->length(); //unary minus changes the length
 	}
-this->copyonwrite();
-if((*this)[n]==1) {(*this)[n]=0; ++(*this)[n-1];} //avoid deepest 1/1
+if(n>0 && (*this)[n]==1) {(*this)[n]=0; ++(*this)[n-1];} //avoid deepest 1/1
 for(int i=1; i<=n; ++i) //truncate if possible
 	{
 	if((*this)[i]==0) //convention for infinity
@@ -393,6 +394,7 @@ if(den<0)
 	den= -den;
 	}
 T g=gcd(num,den); 
+if(g<0) g= -g; //gcd may be negative for negative num
 if(g>1) 
 	{
 	num/=g; 
@@ -405,7 +407,8 @@ Rational<T> & Rational<T>::operator*=(const T  &rhs)
 {
 T r=rhs;
 T g=gcd(r,den);
-if(MYABS(g)>1)
+if(g<0) g= -g; //keep den positive
+if(g>1)
         {
         r/=g;
         den/=g;
@@ -420,12 +423,14 @@ Rational<T> & Rational<T>::operator/=(const T  &rhs)
 {
 T r=rhs;
 T g=gcd(r,num);
-if(MYABS(g)>1)
+if(g<0) g= -g;
+if(g>1)
         {
         r/=g;
         num/=g;
         }
 den*=r;
+if(den<0) {num= -num; den= -den;} //keep den positive
 return *this;
 }
 
diff --git a/contfrac.h b/contfrac.h
index c8ee819..8e0e5ae 100644
--- a/contfrac.h
+++ b/contfrac.h
@@ -124,7 +124,7 @@ public:
 	ContFrac(T p, T q); //should yield a canonical form
 	explicit ContFrac(const Rational<T> &r) : ContFrac(r.num,r.den) {};
 
-	void canonicalize();
+	void canonicalize(); //requires a_1..a_n of the same sign (works on the terms, no overflow for fixed-size T)
 	void convergent(T *p, T*q, const int trunc= -1) const;
 	Rational<T> rational(const int trunc= -1) const {T p,q; convergent(&p,&q,trunc); return Rational<T>(p,q);};
 	double value(const int trunc= -1) const; //we could make also a template usable with an arbitrary-precision type
diff --git a/polynomial.cc b/polynomial.cc
index 00a5d40..ab3ae59 100644
--- a/polynomial.cc
+++ b/polynomial.cc
@@ -177,7 +177,7 @@ Polynomial<T> poly_gcd(const Polynomial<T> &p, const Polynomial<T> &q, const typ
 Polynomial<T> big,small;
 if(p.degree() < q.degree()) {big=q; small=p;} else {big=p; small=q;}
 small.simplify(thr);
-if(small.degree()==0) return small;
+if(small.degree()==0) return MYABS(small[0])<=thr ? big : small; //gcd(p,0)=p, gcd(p,const)=const
 Polynomial<T> help;
 do      {
         help=small;
@@ -185,7 +185,7 @@ do      {
         big=help;
 	small.simplify(thr);
         }
-while((d<0 && small.degree() != 0) || (d>=0 && small.degree()>=d));
+while(!(small.degree()==0 && MYABS(small[0])<=thr) && (d<0 || small.degree()>=d)); //stop at zero remainder or below the expected degree
 return big;
 }
 
diff --git a/polynomial.h b/polynomial.h
index 8b5e24a..17ce948 100644
--- a/polynomial.h
+++ b/polynomial.h
@@ -213,7 +213,7 @@ for(int i=d; i>2; i-=2)
                  sum= sum*x2; //not *= for matrices
                  }
 sum += p[1];
-sum *= x;
+sum= sum*x; //not *= for matrices
 return sum;
 }