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\centerline{\bf Errata et Addenda to the Second Printing of the Book}
\smallskip
\centerline{\bf A Course in Computational Algebraic Number Theory}
\smallskip
\centerline{by \bf Henri Cohen}
\smallskip
\centerline{(19940607 version)}
\medskip
{\obeylines
Graduate Texts in Mathematics 138, Springer-Verlag, 1993, XXI + 534 pages.
ISBN 3-540-55640-0 Springer-Verlag Berlin Heidelberg New York
ISBN 0-387-55640-0 Springer-Verlag New York Berlin Heidelberg
\bigskip
p. 4\quad line -2, instead of ``$a*b$'' read ``$a\cdot b$''
p. 55\quad line 20, instead of ``$p_m(X)=...$'' read ``$p_m(X)\gets...$''
p. 60\quad line 3, instead of ``$X'_i$'' read ``$M'_i$, $X'_i$'' and instead of ``$X$)'' read ``$M$, $X$)''
p. 79\quad line 1, instead of ``for all'' read ``for all non-zero''
p. 82\quad line 4, instead of ``exists'' read ``exist''
p. 88\quad line 11, instead of ``Gram-Schmidt'' read ``Gram''
p. 88\quad line 13, instead of ``so that statements ... removed'' read ``and the updating of the vectors $\bb_i$ done in Sub-algorithms RED and SWAP must be done directly on the Gram matrix''
p. 89\quad line 13, instead of ``to be LLL'' read ``from being LLL''
p. 93\quad line 3 of Algorithm REDI, after ``$H_k\gets H_k-qH_l$,'' insert `` $\bb_k\gets \bb_k-q\bb_l$,''
p. 93\quad line 1 of Algorithm SWAPI, after ``$H_k$ and $H_{k-1}$,'' insert `` exchange $\bb_k$ and $\bb_{k-1}$,''
p. 93\quad line 4 of Algorithm SWAPI, instead of ``$t+\lambda\lambda_{i,k}/B$'' read ``$(Bt+\lambda\lambda_{i,k})/d_k$''
p. 94\quad line 2 of step 2, instead of ``$\mu_{k,j}=0$'' read ``$\mu_{k,j}\gets0$''
p. 120\quad line 13, instead of ``$\ell(A)^{2m-2}$'' read ``$\ell(A)^{m-1+\deg(A')}$''
p. 120\quad line -8, instead of ``$a^{2m-1}$'' read ``$a^{m+\deg(A')}$''
p. 120\quad line -7, instead of ``proposition.'' read ``proposition. Note that we have $\deg(A')=m-1$ except when the characteristic of $R$ is non-zero and divides $m$.''
p. 131\quad line 3 of Step 1, add ``$\pmod{A(X)}$'' at the end of the formula
p. 135\quad line -15, instead of ``any factor of $A$'' read ``up to sign, any factor of $A$''
p. 137\quad line -12, instead of ``find'' read ``finds''
p. 154\quad line 7, instead of ``More generally, for'' read ``For''
p. 155\quad line 17, instead of ``a polynomial'' read ``an irreducible polynomial''
p. 197\quad line -11, instead of ``$Z_K$'' read ``$\Z_K$''
p. 211\quad line 8, instead of ``Although more ... preferred.'' read ``Although Algorithm 4.9.10 is more pleasing to the mind, Algorithm 4.9.9 is considerably faster and should therefore be preferred in practice.''
%p. 259\quad line -1, replace ``one-to-one.\fp'' by ``one-to-one.
%Finally, from the results of Section 5.7 it follows that $\rho$ acts transitively on the set of reduced forms equivalent to $f$.\fp''
p. 283\quad line -11, instead of ``and it is easy to check that this distance $\Delta_C$ belongs to one of the hyperplanes $\sum_ix_i=2ik\pi$ for $k\in\Z$'' read ``and it is clear that the real part of $\Delta_C$ lies in the hyperplane $\sum_ix_i=0$''
p. 348\quad line 3, instead of ``an ideal'' read ``a vector $v$ as above and an ideal''
p. 348\quad line 3, instead of `` this'' read ``, this''
p. 349\quad line 7, instead of ``a $(r_1+$'' read ``an $(r_1+$''
p. 349\quad line 15, instead of ``$\goth p_i^{e_i}$'' read ``$\goth p_i$''
p. 349\quad line 22, instead of ``the zero vector'' read ``$v$ equal to the zero vector''
p. 349\quad line -5, instead of ``step 5'' read ``step 4''
p. 350\quad line 18, instead of ``step 10'' read ``step 9''
p. 350\quad line 20, instead of ``$MC$'' read ``$M_C$''
p. 376\quad lines 4, 6, 7, 8, 9, 10, 16, 18, instead of ``$))/2)$'' read ``$)/2)$''
p. 376\quad lines 16 and 17, instead of the given formula for $j((1+i\sqrt{15})/2)$ read
}
\smallskip
$$\alignat3 j((1+i\sqrt{15}))/2)&=\dfrac{-191025-85995\sqrt5}{2}\cr
&=\dfrac{1-\sqrt5}{2}\left(\dfrac{75+27\sqrt5}{2}\right)^3=
1728-3\left(\dfrac{273+105\sqrt5}{2}\right)^2\cr
\endalignat$$
\smallskip
{\obeylines

}
\end
