diff --git a/Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/AlgebraicKernel_d_1.tex b/Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/AlgebraicKernel_d_1.tex
index 3d0695bbe33..690214ec727 100644
--- a/Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/AlgebraicKernel_d_1.tex
+++ b/Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/AlgebraicKernel_d_1.tex
@@ -24,10 +24,12 @@ Must provide:\\
 \ccc{template <class InputIterator>}\\
 \ccc{Polynomial_1 operator()(InputIterator first, InputIterator last)}\\
 that constructs a polynomial from a range of coefficients of type
-\ccc{Coefficient}, given in the increasing order of monomial degrees.\\
+\ccc{Coefficient}, given in the increasing order of monomial degrees,\\
+and\\
+\ccc{template <class InputIterator1, InputIterator2>}\\
+\ccc{Polynomial_1 operator()(InputIterator1 first_coeff, InputIterator1 last_coeff, InputIt2 deg)}\\
+that takes as input a range of coefficients of type \ccc{Coefficient}, and an iterator on corresponding degrees of type \ccc{unsigned int}.
 }
-\footnote{to be added: constructor for sparse polynomials input range of
-\ccc{std::pair<Coefficient, unsigned int>} (int = degree)}
 
 \ccNestedType{Solve_1}{A model of the concept
 \ccc{AlgebraicKernel_d_1::Solve_1}.} 
diff --git a/Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/AlgebraicKernel_d_2.tex b/Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/AlgebraicKernel_d_2.tex
index 0fb1055140e..43df55db9ff 100644
--- a/Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/AlgebraicKernel_d_2.tex
+++ b/Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/AlgebraicKernel_d_2.tex
@@ -23,9 +23,9 @@ bivariate polynomials on an \ccc{IntegralDomain} coefficient type.}
 of two bivariate polynomials of type \ccc{Polynomial_2}.}
 
 \ccNestedType{Construct_polynomial_2}{
-Must provide 
-\ccc{template <class InputIterator> 
-Polynomial_2 operator()(InputIterator first, InputIterator last)}
+Must provide:\\
+\ccc{template <class InputIterator>}\\ 
+\ccc{Polynomial_2 operator()(InputIterator first, InputIterator last)}\\
 that constructs a polynomial from a range of coefficients of type
 \ccc{Coefficient}, given in the lexicographic order of monomial degrees.
 }
diff --git a/Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/SolveC_2.tex b/Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/SolveC_2.tex
index cb94df717aa..f80d46eeab1 100644
--- a/Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/SolveC_2.tex
+++ b/Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/SolveC_2.tex
@@ -6,7 +6,6 @@
 
 A model \ccVar\ of this type must provide:
 
-\footnote{TBD, I am getting tired... anything to think about before 
-adapting the \ccc{_1} case? }
+\footnote{TBD, I am getting tired... what about the case of 1-dimensional components? a choice must be made}
 
 \end{ccRefConcept}