diff --git a/DeformacionGenerica.ipynb b/DeformacionGenerica.ipynb
index 9213037..cd9ffba 100644
--- a/DeformacionGenerica.ipynb
+++ b/DeformacionGenerica.ipynb
@@ -354,7 +354,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "SageMath 10.4.rc0",
+   "display_name": "SageMath 10.4.rc1",
    "language": "sage",
    "name": "sagemath-devel"
   },
diff --git a/DeformacionGenerica0.ipynb b/DeformacionGenerica0.ipynb
index 5123f8b..7c82f40 100644
--- a/DeformacionGenerica0.ipynb
+++ b/DeformacionGenerica0.ipynb
@@ -1838,7 +1838,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "SageMath 10.4.rc3",
+   "display_name": "SageMath 10.5.beta3",
    "language": "sage",
    "name": "sagemath-devel"
   },
@@ -1852,7 +1852,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.4"
+   "version": "3.12.5"
   }
  },
  "nbformat": 4,
diff --git a/EjemplosGenerales.ipynb b/EjemplosGenerales.ipynb
index aa38823..eef641a 100644
--- a/EjemplosGenerales.ipynb
+++ b/EjemplosGenerales.ipynb
@@ -673,7 +673,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "SageMath 10.3.rc4",
+   "display_name": "SageMath 10.4.beta6",
    "language": "sage",
    "name": "sagemath-devel"
   },
@@ -687,7 +687,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.1"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,
diff --git a/Mult3.pdf b/Mult3.pdf
index f02383a..b2c0724 100644
Binary files a/Mult3.pdf and b/Mult3.pdf differ
diff --git a/Mult3.tex b/Mult3.tex
index 43b4554..08a324c 100644
--- a/Mult3.tex
+++ b/Mult3.tex
@@ -391,14 +391,17 @@ $$ \prod_{i=1}^n h_i^{2} \prod_{j=1}^m k_j^3 \left (  \prod_{i=1}^n h_i^{3n_i-2}
 
 
 \begin{proposition}
-The singular point is isolated if and only if the disciminant $D_zF$ is reduced.
+The singular point is isolated if and only if the discriminant $D_zF$ is reduced.
 \end{proposition}
 
+\noindent \textcolor{red}{Proof. Ask Enrique.}
 
-\begin{proposition}\label{prop.non-deg}
-The monic Weierstrass polynomial $z^3 -3b_2z + 2b_3$ is non degenerate unless $M_1(c_1+A)$ and $b_3 = M_2(c_2 + B)$ with $M_1^3 = M_2^2$ and \textcolor{red}{$2c_1=3c_2$}
+
+\begin{proposition}\label{prop.non-deg} Let $b_2, b_3 \in \CC[[x, y]]$ with $b_2(0), b_3(0) = 0$. Let us write  $b_2= M_2(c_2+A)$ and $b_3 = M_3(c_3 + B)$ with $M_2, M_3 \in \CC[x,y]$ (monic) monomials, $c_2, c_3 \in \CC^\ast$ and $A, B \in \CC[[x,y]]$ such that $A(0), B(0) = 0$. 
+The monic Weierstrass polynomial $z^3 -3b_2z + 2b_3$ is non degenerate unless  $(c_2M_2)^3 = (c_3M_3)^2$.
 \end{proposition}
 
+\noindent \textcolor{blue}{Proof. The Newton polyhedron of  $z^3 -3b_2z + 2b_3$ can be 2-dimensional, polygonal with two segments or polygonal with a unique segment. In the two first cases, it is non degenerate. The compact faces of the Newton polyhedron of $z^3 -3b_2z + 2b_3$ lie on a segment  if and only if  $(M_2)^3 = (M_3)^2$. The condition of $z^3 -3b_2z + 2b_3$ being non degenerate  is equivalent to $z^3 -3b_2z + 2b_3 \in \CC[z]$ having a double root. Notice a triple root is not possible because the degree 2 monomial is zero. Assume that $z^3 -3b_2z + 2b_3 =(z-a)^2(z-b)$ for some $a, b \in \CC^\ast$. Equivalently, we have $2a+b=0$, and therefor  $c_2=(\frac{b}{2})^2}$ and $c_3=(\frac{-b}{2})^3$.}
 
 \section{Jung´s method for power series of multiplicity three }
 
@@ -585,8 +588,8 @@ N^\Delta_i& 25& {\bf 26}& {\bf 52}& {\bf 78}& {\bf 104}& {\bf 130}& {\bf 156}& {
 \hline
 \hline
 \nu_i&2&3&5&7&9&11&13&6&11\\
-\chi()&-11&1&-1&0&0&0&-2&1&-1\\
-E_i^2& -13& -2& -4& -2& -2& -2& -1&-2&-1\\
+\chi()&-13&1&-1&0&0&0&-2&1&-1\\
+E_i^2& -11& -2& -4& -2& -2& -2& -1&-2&-1\\
 \hline
 \end{array}$$
 
@@ -967,8 +970,8 @@ In this case, the Newton polyhedra of $F$ contains a unique two dimensional comp
 
 
 \item If $M_1^3 = M_2^2$, the point corresponding to the monomial $M_1z$ lies in the unique dimensional compact face of the Newton polyhedron of $F$. The face equation is equal to 
-$$z^3 + c_1z + c_2.$$
-Therefore, $F$ is non degenerate with respect to its Newton polyhedron if and only if $3(c_1)^2 \ne 2(c_2)^3$.
+$$z^3 -3 c_1z + 2 c_2.$$
+Therefore, $F$ is non degenerate with respect to its Newton polyhedron if and only if \textcolor{blue}{$(c_1)^3 \ne (c_2)^2$}.
 
 
 \begin{tikzpicture}
@@ -1137,7 +1140,7 @@ $$J_{\check \tau_0}=\frac{2}{\nu_1(3m_2s + 2\nu_1+m_2)}$$
  We remark that this case it is equivalent to $f=z(z^2 - x^{m_2})$.
 
  
- \subsubsection{Third case $f= z^3 - x^{m_1}z^2 - x^{m_3}$ and $\omega = x^{\nu_1-1}dxdz$ such that $m_3 > m_1$} 
+ \subsubsection{Third case $f= z^3 - x^{m_1}z^2 - x^{m_3}$ and $\omega = x^{\nu_1-1}dxdz$ such that $m_3 >  3 m_1$} 
    Newton polyhedra has five compact faces: the 0-dimensional faces $\tau_0$ corresponding to the monomial $z^3$, $\tau_1$ corresponding to the monomial $x^{m_1}z^2$, and $\tau_2$ corresponding to the monomial $ x^{m_3}$, and the 1-dimensional faces  $\sigma_1$ contained in the hyperplanes
    $$p + m_1r = 3m_1$$
   and $\sigma_2$ contained in the hyperplanes
@@ -1179,9 +1182,9 @@ $$J_{\check \tau_0}=\frac{m_1}{\nu_1(3m_1s + \nu_1+m_1)}$$
  
  
  Similarly we have 
-  $$\zeta_f (t) = $$
- 
- We remark that this case is equivalent to $f=(z-x^{m_1})(z^2 - x^{m_3-m_2})$
+  $$\zeta_f (t) =  \frac{(t^{3m_1}-1)(t^{m_3}-1) }{(t-1)(t^3-1)} $$
+   $$\zeta_f (t) = \frac{(t^{3m_1}-1)(t^{2m_3}-1) }{(t-1)(t^3-1)(t^{m_3}-1)}$$
+ We remark that this case is equivalent to $f=(z-x^{m_1})(z^2 - x^{m_3-m_1})$
  
 
   \subsection{Trinomial forms for strata $E^\circ_{i,j}$}  
@@ -1286,7 +1289,7 @@ $$Z(F_9, \omega_9)_{o_9}=Z(F_{9,31}, \omega_{9,31})_{o_{9,31}}= Z(F_{17}, \omega
  $$f_7=f_{15}=z^3 - x^{78}, \quad f_{7,33}=f_{15,34}=z^3 - x^{52}z + x^{78}y,$$
  and $$\omega_7=\omega_{15}=\omega_{7,33}=\omega_{15,34}= x^{13}yzdxdydz,$$
 From the formulas given in the previous section;  we have 
-$$Z(F_7, \omega_7)_{o_7}=Z(F_{7,33}, \omega_{7,33})_{o_{7,33}}= Z(F_{15}, \omega_{15})_{o_{15}}=Z(F_{15,34}, \omega_{15,34})_{o_{15,34}} = \frac{1}{26(s^2 +3/2 s + 1/2}$$
+$$Z(F_7, \omega_7)_{o_7}=Z(F_{7,33}, \omega_{7,33})_{o_{7,33}}= Z(F_{15}, \omega_{15})_{o_{15}}=Z(F_{15,34}, \omega_{15,34})_{o_{15,34}} = \frac{1}{26(s^2 +3/2 s + 1/2}.$$
 \end{example}
 
   \subsection{Second reduction: Recursive elimination of exceptional  $(-1)$-curve not intersecting the strict transform of the discrimiant}
@@ -1296,6 +1299,9 @@ $$Z(F_7, \omega_7)_{o_7}=Z(F_{7,33}, \omega_{7,33})_{o_{7,33}}= Z(F_{15}, \omega
     \begin{proposition}\label{red2} 
     \end{proposition}
     
+    \begin{example} The Proposition \ref{red2} can be applied twice to eliminate the curves $E_9$ and $E_8$. First, $E_9$ is an exceptional  $(-1)$-curve that does not intersect the strict transform of the discriminant, and $E_8$ is an exceptional with $E_8^2=-2$ After blowing down $E_9$, the exceptional curve $E_8$ becomes a $(-1)$-curve. It does not intersect the strict transform of the discriminant. 
+    \end{example}
+    
     
   \subsection{Third reduction: $\QQ$-resolution of the discriminant}
  
diff --git a/PruebasDeformaciones.ipynb b/PruebasDeformaciones.ipynb
index 36e108c..8660252 100644
--- a/PruebasDeformaciones.ipynb
+++ b/PruebasDeformaciones.ipynb
@@ -18,8 +18,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
-   "id": "cad50def-ecb8-403f-b50c-ce026fbd216d",
+   "execution_count": null,
+   "id": "fdc11d23-4114-49ef-828a-b7a165169c46",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -28,8 +28,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
-   "id": "5ec9dd77-8118-4439-b8cb-4c475a2a645e",
+   "execution_count": 14,
+   "id": "b67cebe5-4b5a-46be-9055-9ecbdecf96f1",
    "metadata": {},
    "outputs": [
     {
@@ -38,7 +38,7 @@
        "((0, 0, 0, 0, 0, 0, 1), (0, 0, 4, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 3))"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -53,27 +53,53 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 13,
+   "id": "dbf2120c-5214-48e1-a93f-a5079753d5f5",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((0, 0, 0, 0, 1, 0, 0), (0, 0, 0, 1, 1, 0, 0), (0, 0, 0, 0, 1, 0, 2))"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Vfa, Vga, Vda = [vector(QQ, 7) for i in (1, 2, 3)]\n",
+    "Vfa[4] = Vga[3] = Vga[4] = Vda[4] = 1\n",
+    "Vda[6] = 2\n",
+    "Vfa, Vga, Vda"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
    "id": "c5104650-44eb-4c9c-b016-c34994f72f38",
    "metadata": {},
    "outputs": [],
    "source": [
-    "n, Nf, Ng, Nd, Nhs, Nks, euler, nus, pols = trinomiales_general(A, Vf, Vg, (), (), Vd, total=False)"
+    "n, Nf, Ng, Nd, Nhs, Nks, euler, nus, pols = trinomiales_general(A, Vf, Vg, (), (), Vd, total=False)\n",
+    "na, Nfa, Nga, Nda, Nhsa, Nksa, eulera, nusa, polsa = trinomiales_general(A, Vfa, Vga, (), (), Vda, total=False)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 16,
    "id": "8dccac88-2fa3-4365-990a-2571f643b9dc",
    "metadata": {},
    "outputs": [],
    "source": [
-    "zetatop, zetamon, dic = zetas(n, pols, info=True)"
+    "zetatop, zetamon, dic = zetas(n, pols, info=True)\n",
+    "zetatopa, zetamona, dica = zetas(na, polsa, info=True)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 17,
    "id": "097214a4-61e4-4939-bad0-4e5b3c8ac716",
    "metadata": {},
    "outputs": [
@@ -81,16 +107,16 @@
      "data": {
       "text/plain": [
        "((-41/168) * (s + 16/21)^-1 * (s + 19/24)^-1 * (s + 1)^-1 * (s^2 - 283/123*s - 304/123),\n",
-       " {1: 1, 2: 1, 6: 1, 4: 1, 3: 1, 12: 1, 8: 1, 7: 1, 24: 1, 21: 1})"
+       " (-43/175) * (s + 16/21)^-1 * (s + 4/5)^-1 * (s + 1)^-1 * (s^2 - 292/129*s - 320/129))"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "zetatop.factor(), dic"
+    "zetatop.factor(), zetatopa.factor()"
    ]
   },
   {
@@ -129,7 +155,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 8,
    "id": "558ef7c7-39cf-47bf-b224-479f1ff365d4",
    "metadata": {},
    "outputs": [
@@ -429,27 +455,6 @@
     "    print(\"=======================\")"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "id": "8f5e2324-c385-4a99-a4a4-96cc9aa35c12",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(z^3 + x^8*z^2 + x^24*y, (11, 1, 1), 3)"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "pols[6, 'd']"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": 27,
@@ -678,6 +683,377 @@
     "dic, dic2"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 85,
+   "id": "1eda8668-939a-49ff-9741-eecb16b95c29",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1"
+      ]
+     },
+     "execution_count": 85,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "A2 = A1.matrix_from_rows_and_columns([0..5], [0..5])\n",
+    "A2[4, 5] = A2[5, 4] = 1\n",
+    "#A1[4, 6] = A1[6, 4] = A1[5, 6] = A1[6, 5] = 1\n",
+    "#A1[4, 4] = -3\n",
+    "A2[4, 4] = -2\n",
+    "A2[5, 5] = -1\n",
+    "A2.det()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 86,
+   "id": "f79af679-b261-4e6f-9dcb-5775bccb1c8c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((0, 0, 0, 0, 1, 0), (0, 0, 0, 1, 1, 0), (0, 0, 0, 0, 1, 2))"
+      ]
+     },
+     "execution_count": 86,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Vf, Vg, Vd = [vector(QQ, 6) for i in (1, 2, 3)]\n",
+    "Vf[4] = Vg[3] = Vg[4] = Vd[4] = 1\n",
+    "Vd[5] = 2\n",
+    "Vf, Vg, Vd"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 87,
+   "id": "f4f2d497-55d6-42cc-a3c1-6ee815579be8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "n2b, Nf2b, Ng2b, Nd2b, Nhs2b, Nks2b, euler2b, nus2b, pols2b = trinomiales_general(A2, Vf, Vg, (), (), Vd, total=False)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 88,
+   "id": "6d1f647d-c103-4ffc-97da-bdcac4e0625e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(2, 4, 6, 7, 14, 14)\n",
+      "(3, 6, 9, 11, 21, 21)\n",
+      "(6, 12, 18, 21, 42, 44)\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(Nf2b)\n",
+    "print(Ng2b)\n",
+    "print(Nd2b)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 89,
+   "id": "27a012cc-2e37-4545-98a4-7f1ffd7f8566",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "zetatop2b, zetamon2b, dic2b = zetas(n2b, pols2b, info=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 90,
+   "id": "696efeb0-7276-449a-903d-c2e02cdb16f9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((-41/168) * (s + 16/21)^-1 * (s + 19/24)^-1 * (s + 1)^-1 * (s^2 - 283/123*s - 304/123),\n",
+       " (-39/161) * (s + 16/21)^-1 * (s + 18/23)^-1 * (s + 1)^-1 * (s^2 - 274/117*s - 32/13))"
+      ]
+     },
+     "execution_count": 90,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "zetatop.factor(), zetatop2b.factor()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 92,
+   "id": "7d299478-15d6-439a-a0ee-38557a6e303b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "({1: 1, 2: 1, 6: 1, 4: 1, 3: 1, 12: 1, 8: 1, 7: 1, 24: 1, 21: 1},\n",
+       " {1: 1, 7: 1, 21: 1, 23: 1})"
+      ]
+     },
+     "execution_count": 92,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dic, dic2b"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 66,
+   "id": "d236b526-d636-455a-8030-301f39e27f96",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A = Matrix(8, [-2, 1, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 1, -3, 0, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 1, -3, 0, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 1, 1, -1])\n",
+    "A1 = A.matrix_from_rows_and_columns([0..6], [0..6])\n",
+    "A1[4, 5] = A1[5, 4] = 0\n",
+    "A1[4, 6] = A1[6, 4] = A1[5, 6] = A1[6, 5] = 1\n",
+    "A1[4, 4] = -3\n",
+    "A1[5, 5] = -2\n",
+    "A1[6, 6] = -1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 73,
+   "id": "0f6ae8eb-46d6-4d8b-85ff-8b93432f88f5",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((0, 0, 0, 0, 1, 0, 0), (0, 0, 0, 1, 1, 0, 0), (0, 0, 0, 0, 1, 0, 1))"
+      ]
+     },
+     "execution_count": 73,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Vf, Vg, Vd = [vector(QQ, 7) for i in (1, 2, 3)]\n",
+    "Vf[4] = Vg[3] = Vg[4] = Vd[4] = Vd[6] = 1\n",
+    "Vf, Vg, Vd"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 74,
+   "id": "5d18a75f-7a9b-4ada-b28f-f79e9fb69292",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "n2a, Nf2a, Ng2a, Nd2a, Nhs2a, Nks2a, euler2a, nus2a, pols2a = trinomiales_general(A1, Vf, Vg, (), (), Vd, total=False)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 79,
+   "id": "d3af6603-a5ca-45da-8122-5e0973563b88",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(2, 4, 6, 7, 14, 14, 28)\n",
+      "(3, 6, 9, 11, 21, 21, 42)\n",
+      "(6, 12, 18, 21, 42, 43, 86)\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(Nf2a)\n",
+    "print(Ng2a)\n",
+    "print(Nd2a)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 77,
+   "id": "4412f281-4696-4dc1-91ed-0069b58bffa0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "zetatop2a, zetamon2a, dic2a = zetas(n2a, pols2a, info=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 78,
+   "id": "c39bf1b5-1ed0-4d84-8e81-5f4e4bf3fd9b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((-41/168) * (s + 16/21)^-1 * (s + 19/24)^-1 * (s + 1)^-1 * (s^2 - 283/123*s - 304/123),\n",
+       " (-37/154) * (s + 16/21)^-1 * (s + 17/22)^-1 * (s + 1)^-1 * (s^2 - 265/111*s - 272/111))"
+      ]
+     },
+     "execution_count": 78,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "zetatop.factor(), zetatop2a.factor()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 80,
+   "id": "441864d8-5be6-4570-8a30-b9612c0ebcb1",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "({1: 1, 2: 1, 6: 1, 4: 1, 3: 1, 12: 1, 8: 1, 7: 1, 24: 1, 21: 1},\n",
+       " {1: 1, 2: 1, 7: 1, 22: 1, 11: 1, 21: 1})"
+      ]
+     },
+     "execution_count": 80,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dic, dic2a"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "id": "faed71a4-b703-4416-8c86-ce2d989999b0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0, 1))"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Vf, Vg, Vd = [vector(QQ, 8) for i in (1, 2, 3)]\n",
+    "Vf[4] = Vg[3] = Vg[4] = Vd[4] = Vd[7] = 1\n",
+    "Vf, Vg, Vd"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "id": "aa0267bd-3f48-4167-94f4-b6079b77cc46",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "n2, Nf2, Ng2, Nd2, Nhs2, Nks2, euler2, nus2, pols2 = trinomiales_general(A, Vf, Vg, (), (), Vd, total=False)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "id": "f819b1f2-2342-4951-99ee-c62a978d2308",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(6, 12, 18, 21, 42, 42, 42, 84)\n",
+      "(6, 12, 18, 22, 42, 42, 42, 84)\n",
+      "(6, 12, 18, 21, 42, 44, 45, 90)\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(3 * Nf2)\n",
+    "print(2 * Ng2)\n",
+    "print(Nd2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "id": "1a340b4a-c984-46e1-a708-0c962a0912bc",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "zetatop2, zetamon2, dic2 = zetas(n2, pols2, info=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "id": "e737e117-0285-429e-8800-eab63eff90fc",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((-41/168) * (s + 16/21)^-1 * (s + 19/24)^-1 * (s + 1)^-1 * (s^2 - 283/123*s - 304/123),\n",
+       " (-41/168) * (s + 16/21)^-1 * (s + 19/24)^-1 * (s + 1)^-1 * (s^2 - 283/123*s - 304/123))"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "zetatop.factor(), zetatop2.factor()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "id": "535f3607-b56b-4557-b60b-28889a8795c4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "({1: 1, 2: 1, 6: 1, 4: 1, 3: 1, 12: 1, 8: 1, 7: 1, 24: 1, 21: 1},\n",
+       " {1: 1, 2: 1, 6: 1, 4: 1, 3: 1, 12: 1, 8: 1, 7: 1, 24: 1, 21: 1})"
+      ]
+     },
+     "execution_count": 52,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dic, dic2"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 43,
@@ -768,24 +1144,24 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 49,
    "id": "0870be50-c79c-48c9-80b7-24bfd6914737",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "((-41/168) * (s + 16/21)^-1 * (s + 19/24)^-1 * (s + 1)^-1 * (s^2 - 283/123*s - 304/123),\n",
+       "((-5/21) * (s + 16/21)^-1 * (s + 1)^-1 * (s - 16/5),\n",
        " (-5/21) * (s + 16/21)^-1 * (s + 1)^-1 * (s - 16/5))"
       ]
      },
-     "execution_count": 48,
+     "execution_count": 49,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "zetatop.factor(), zetatop3.factor()"
+    "zetatop1.factor(), zetatop3.factor()"
    ]
   },
   {
@@ -861,7 +1237,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "SageMath 10.4.beta9",
+   "display_name": "SageMath 10.4.rc1",
    "language": "sage",
    "name": "sagemath-devel"
   },
diff --git a/UnLado.ipynb b/UnLado.ipynb
index d0cd61d..498c895 100644
--- a/UnLado.ipynb
+++ b/UnLado.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 113,
+   "execution_count": 1,
    "id": "4778e32e-f561-4e4d-b63a-d4d60f91abde",
    "metadata": {},
    "outputs": [],
@@ -12,7 +12,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 115,
+   "execution_count": 2,
    "id": "f042e81b-abf8-4e09-bc67-a19d778033e6",
    "metadata": {},
    "outputs": [],
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 116,
+   "execution_count": 7,
    "id": "0733b364-bbf6-486c-a5d1-e72c7a5d48ca",
    "metadata": {},
    "outputs": [],
@@ -34,7 +34,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 117,
+   "execution_count": 8,
    "id": "b81e1db9-883e-4a03-a38c-1ca296c9d25b",
    "metadata": {},
    "outputs": [],
@@ -45,7 +45,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 118,
+   "execution_count": 9,
    "id": "f97fbf75-4da5-45db-8f66-cdccdd052326",
    "metadata": {},
    "outputs": [],
@@ -60,7 +60,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 119,
+   "execution_count": 10,
    "id": "04072945-1ada-4d66-b44e-95318f073634",
    "metadata": {},
    "outputs": [],
@@ -70,7 +70,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 120,
+   "execution_count": 11,
    "id": "d9834ff4-e09f-4cf9-abd0-9b1eea6ca033",
    "metadata": {},
    "outputs": [
@@ -88,16 +88,32 @@
      },
      "metadata": {},
      "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle \\nu_{2}^{-1} \\cdot \\nu_{1}^{-1} \\cdot (3 \\mathit{ss} a_{2} + a_{2} + 3 \\nu_{2})^{-1} \\cdot (3 \\mathit{ss} a_{1} + a_{1} + 3 \\nu_{1})^{-1} \\cdot (3 \\mathit{ss} a_{1} a_{2} + a_{1} a_{2} + 3 a_{2} \\nu_{1} + 3 a_{1} \\nu_{2})\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle \\nu_{2}^{-1} \\cdot \\nu_{1}^{-1} \\cdot (3 \\mathit{ss} a_{2} + a_{2} + 3 \\nu_{2})^{-1} \\cdot (3 \\mathit{ss} a_{1} + a_{1} + 3 \\nu_{1})^{-1} \\cdot (3 \\mathit{ss} a_{1} a_{2} + a_{1} a_{2} + 3 a_{2} \\nu_{1} + 3 a_{1} \\nu_{2})$"
+      ],
+      "text/plain": [
+       "nu2^-1 * nu1^-1 * (3*ss*a2 + a2 + 3*nu2)^-1 * (3*ss*a1 + a1 + 3*nu1)^-1 * (3*ss*a1*a2 + a1*a2 + 3*a2*nu1 + 3*a1*nu2)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
     }
    ],
    "source": [
     "vertical = cono3(e1, e2, e3, V1, nu) - cono3(Q1, Q2, e3, V1, nu)\n",
-    "show(vertical.subs(sb).factor())"
+    "show(vertical.subs(sb).factor())\n",
+    "show(vertical.factor())"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 121,
+   "execution_count": 13,
    "id": "fe5aa4f3-db61-4a38-a1d1-dd100d819937",
    "metadata": {},
    "outputs": [
@@ -115,12 +131,28 @@
      },
      "metadata": {},
      "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle \\left(9\\right) \\cdot (3 \\mathit{ss} a_{2} + a_{2} + 3 \\nu_{2})^{-1} \\cdot (3 \\mathit{ss} a_{1} + a_{1} + 3 \\nu_{1})^{-1}\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle \\left(9\\right) \\cdot (3 \\mathit{ss} a_{2} + a_{2} + 3 \\nu_{2})^{-1} \\cdot (3 \\mathit{ss} a_{1} + a_{1} + 3 \\nu_{1})^{-1}$"
+      ],
+      "text/plain": [
+       "(9) * (3*ss*a2 + a2 + 3*nu2)^-1 * (3*ss*a1 + a1 + 3*nu1)^-1"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
     }
    ],
    "source": [
     "horizontal = cono3(Q1, Q2, e3, V0, nu)\n",
     "horizontal = (horizontal.numerator() / 9) / (horizontal.denominator() / 9)\n",
-    "show(horizontal.subs(sb).factor())"
+    "show(horizontal.subs(sb).factor())\n",
+    "show(horizontal.factor())"
    ]
   },
   {
@@ -151,7 +183,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 123,
+   "execution_count": 14,
    "id": "29605b7d-37f7-4f22-80bd-1694134cd9b7",
    "metadata": {},
    "outputs": [
@@ -161,7 +193,7 @@
        "[9/(alpha1*alpha2), 3*a2/(alpha1*alpha2), (-3*a1)/(alpha1*alpha2)]"
       ]
      },
-     "execution_count": 123,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -172,7 +204,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 124,
+   "execution_count": 15,
    "id": "83121ff8-547c-424b-b3ce-860a80f0541e",
    "metadata": {},
    "outputs": [],
@@ -182,7 +214,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 125,
+   "execution_count": 16,
    "id": "b3963226-7397-4cb5-bdff-5382f74df8df",
    "metadata": {},
    "outputs": [
@@ -192,7 +224,7 @@
        "(3*a1/alpha1, 3*a1/alpha1, 3*a2/alpha2, 3*a2/alpha2, (a1 + 3*nu1)/alpha1)"
       ]
      },
-     "execution_count": 125,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -203,7 +235,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 126,
+   "execution_count": 17,
    "id": "36201bc7-a7e2-4c9e-a8e9-5865cb9686f9",
    "metadata": {},
    "outputs": [],
@@ -214,7 +246,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 127,
+   "execution_count": 18,
    "id": "d77f48f5-2236-4cb6-a211-14f3623539c0",
    "metadata": {},
    "outputs": [
@@ -241,7 +273,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 128,
+   "execution_count": 19,
    "id": "c18631c1-f18a-48a2-8e9a-727d347ef89a",
    "metadata": {},
    "outputs": [
@@ -259,12 +291,102 @@
      },
      "metadata": {},
      "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle \\left(-1\\right) \\cdot \\nu_{2}^{-1} \\cdot \\nu_{1}^{-1} \\cdot (\\mathit{ss} + 1)^{-1} \\cdot (3 \\mathit{ss} a_{2} + a_{2} + 3 \\nu_{2})^{-1} \\cdot (3 \\mathit{ss} a_{1} + a_{1} + 3 \\nu_{1})^{-1} \\cdot (3 \\mathit{ss} \\nu_{1} \\nu_{2} \\mathit{cd}^{2} - 3 \\mathit{ss}^{2} a_{1} a_{2} - 4 \\mathit{ss} a_{1} a_{2} - 3 \\mathit{ss} a_{2} \\nu_{1} - 3 \\mathit{ss} a_{1} \\nu_{2} - 9 \\mathit{ss} \\nu_{1} \\nu_{2} - a_{1} a_{2} - 3 a_{2} \\nu_{1} - 3 a_{1} \\nu_{2} - 9 \\nu_{1} \\nu_{2})\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle \\left(-1\\right) \\cdot \\nu_{2}^{-1} \\cdot \\nu_{1}^{-1} \\cdot (\\mathit{ss} + 1)^{-1} \\cdot (3 \\mathit{ss} a_{2} + a_{2} + 3 \\nu_{2})^{-1} \\cdot (3 \\mathit{ss} a_{1} + a_{1} + 3 \\nu_{1})^{-1} \\cdot (3 \\mathit{ss} \\nu_{1} \\nu_{2} \\mathit{cd}^{2} - 3 \\mathit{ss}^{2} a_{1} a_{2} - 4 \\mathit{ss} a_{1} a_{2} - 3 \\mathit{ss} a_{2} \\nu_{1} - 3 \\mathit{ss} a_{1} \\nu_{2} - 9 \\mathit{ss} \\nu_{1} \\nu_{2} - a_{1} a_{2} - 3 a_{2} \\nu_{1} - 3 a_{1} \\nu_{2} - 9 \\nu_{1} \\nu_{2})$"
+      ],
+      "text/plain": [
+       "(-1) * nu2^-1 * nu1^-1 * (ss + 1)^-1 * (3*ss*a2 + a2 + 3*nu2)^-1 * (3*ss*a1 + a1 + 3*nu1)^-1 * (3*ss*nu1*nu2*cd^2 - 3*ss^2*a1*a2 - 4*ss*a1*a2 - 3*ss*a2*nu1 - 3*ss*a1*nu2 - 9*ss*nu1*nu2 - a1*a2 - 3*a2*nu1 - 3*a1*nu2 - 9*nu1*nu2)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
     }
    ],
    "source": [
     "prueba = horizontal - arista + vertical\n",
     "# prueba.numerator().variables() + prueba.denominator().variables()\n",
-    "show(prueba.subs(sb).factor())"
+    "show(prueba.subs(sb).factor())\n",
+    "show(prueba.factor())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "5c36c8a4-f5f0-43d8-bbfc-35e889012f6e",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle 3 \\mathit{ss} \\nu_{1} \\nu_{2} \\mathit{cd}^{2} - 3 \\mathit{ss}^{2} a_{1} a_{2} - 4 \\mathit{ss} a_{1} a_{2} - 3 \\mathit{ss} a_{2} \\nu_{1} - 3 \\mathit{ss} a_{1} \\nu_{2} - 9 \\mathit{ss} \\nu_{1} \\nu_{2} - a_{1} a_{2} - 3 a_{2} \\nu_{1} - 3 a_{1} \\nu_{2} - 9 \\nu_{1} \\nu_{2}\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle 3 \\mathit{ss} \\nu_{1} \\nu_{2} \\mathit{cd}^{2} - 3 \\mathit{ss}^{2} a_{1} a_{2} - 4 \\mathit{ss} a_{1} a_{2} - 3 \\mathit{ss} a_{2} \\nu_{1} - 3 \\mathit{ss} a_{1} \\nu_{2} - 9 \\mathit{ss} \\nu_{1} \\nu_{2} - a_{1} a_{2} - 3 a_{2} \\nu_{1} - 3 a_{1} \\nu_{2} - 9 \\nu_{1} \\nu_{2}$"
+      ],
+      "text/plain": [
+       "3*ss*nu1*nu2*cd^2 - 3*ss^2*a1*a2 - 4*ss*a1*a2 - 3*ss*a2*nu1 - 3*ss*a1*nu2 - 9*ss*nu1*nu2 - a1*a2 - 3*a2*nu1 - 3*a1*nu2 - 9*nu1*nu2"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "uuu= (ss + 1) * ((3 * ss + 1) * a1 * a2 + 3 * (nu1 * a2 + nu2 * a1 + 3 * nu1 * nu2)) - 3 * nu1 * nu2 * cd^2 *ss\n",
+    "show(-uuu)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "52254bac-4ce0-473f-a6c8-9853e4180df9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "-3 \\mathit{ss} \\nu_{1} \\nu_{2} \\mathit{cd}^{2} + 3 \\mathit{ss}^{2} a_{1} a_{2} + 4 \\mathit{ss} a_{1} a_{2} + 3 \\mathit{ss} a_{2} \\nu_{1} + 3 \\mathit{ss} a_{1} \\nu_{2} + 9 \\mathit{ss} \\nu_{1} \\nu_{2} + a_{1} a_{2} + 3 a_{2} \\nu_{1} + 3 a_{1} \\nu_{2} + 9 \\nu_{1} \\nu_{2}"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "latex(uuu)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "b4f731bf-7872-4e7f-a8dc-f1a7666fcd31",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle \\left(-1\\right) \\cdot \\nu_{1}^{-1} \\cdot (\\mathit{ss} + 1)^{-1} \\cdot (3 \\mathit{ss} a_{1} + a_{1} + 3 \\nu_{1})^{-1} \\cdot (\\mathit{ss} \\nu_{1} \\mathit{cd}^{2} - \\mathit{ss} a_{1} - 3 \\mathit{ss} \\nu_{1} - a_{1} - 3 \\nu_{1})\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle \\left(-1\\right) \\cdot \\nu_{1}^{-1} \\cdot (\\mathit{ss} + 1)^{-1} \\cdot (3 \\mathit{ss} a_{1} + a_{1} + 3 \\nu_{1})^{-1} \\cdot (\\mathit{ss} \\nu_{1} \\mathit{cd}^{2} - \\mathit{ss} a_{1} - 3 \\mathit{ss} \\nu_{1} - a_{1} - 3 \\nu_{1})$"
+      ],
+      "text/plain": [
+       "(-1) * nu1^-1 * (ss + 1)^-1 * (3*ss*a1 + a1 + 3*nu1)^-1 * (ss*nu1*cd^2 - ss*a1 - 3*ss*nu1 - a1 - 3*nu1)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "show(prueba(a2=0, nu2=1).factor())"
    ]
   },
   {
@@ -944,9 +1066,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "SageMath 10.3.rc3",
+   "display_name": "SageMath 10.4.beta6",
    "language": "sage",
-   "name": "sagemath-310"
+   "name": "sagemath-devel"
   },
   "language_info": {
    "codemirror_mode": {
@@ -958,7 +1080,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.1"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,
diff --git a/deformaciones1.ipynb b/deformaciones1.ipynb
index 0b24641..e623dc5 100644
--- a/deformaciones1.ipynb
+++ b/deformaciones1.ipynb
@@ -723,7 +723,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "SageMath 10.4.beta3",
+   "display_name": "SageMath 10.4.rc1",
    "language": "sage",
    "name": "sagemath-devel"
   },
@@ -737,7 +737,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.2"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,
diff --git a/deformaciones2.ipynb b/deformaciones2.ipynb
index 2d44437..51d12ab 100644
--- a/deformaciones2.ipynb
+++ b/deformaciones2.ipynb
@@ -488,7 +488,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.2"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,
diff --git a/monomios.ipynb b/monomios.ipynb
index ebb4331..db6c3e2 100644
--- a/monomios.ipynb
+++ b/monomios.ipynb
@@ -468,7 +468,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "SageMath 10.4.beta3",
+   "display_name": "SageMath 10.4.beta6",
    "language": "sage",
    "name": "sagemath-devel"
   },
@@ -482,7 +482,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.2"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,
diff --git a/suspension.ipynb b/suspension.ipynb
index b136796..11d2345 100644
--- a/suspension.ipynb
+++ b/suspension.ipynb
@@ -987,7 +987,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "SageMath 10.4.beta3",
+   "display_name": "SageMath 10.4.beta4",
    "language": "sage",
    "name": "sagemath-devel"
   },
diff --git a/zetas_triples_trenzas.py b/zetas_triples_trenzas.py
new file mode 100644
index 0000000..3724e38
--- /dev/null
+++ b/zetas_triples_trenzas.py
@@ -0,0 +1,458 @@
+def trinomiales_general(A, Vf, Vg, Vhs, Vd, total=True):
+    r"""
+    Return data necessary to compute the zeta functions of
+    a triple singularity defined by
+
+        .. math::
+            z^3 -3 \prod_{i=1}^h h_i^{n_i} f z^2
+            + \prod_{i=1}^h h_i g,
+
+    where :math:`f, g, h_i` are polynomials in two variables,
+    and :math:`n_i \geq 1`.
+
+    We consider an embedded resolution of :math:`fg(f^3 - g^2)` with
+    a stratification of the exceptional divisor:
+
+    - :math:`\check{E}_i`: the smooth part of the total divisor
+
+    - :math:`E_i\cap E_j`: the double points of the divisor
+
+    - :math:`E_i\cap \{f=0\}`: the intersections with the strict
+      transform of :math:`f`
+
+    - :math:`E_i\cap \{g=0\}`: the intersections with the strict
+      transform of :math:`g`
+
+    - :math:`E_i\cap \{f^3=g^2\}`: the intersections with the strict
+      transform of :math:`f^3-g^2`
+
+    It is also possible to forget the strict transforms of :math:`f, g`
+    and even to consider only resolutions of :math:`f^3 - g^2`.
+
+    INPUT:
+
+    - ``A`` -- the incidence matrix of a resolution
+
+    - ``Vf`` -- the vector with the intersection numbers of the strict
+      transform of :math:`f` with the divisors of the resolution
+
+    - ``Vg`` -- the vector with the intersection numbers of the strict
+      transform of :math:`g` with the divisors of the resolution
+
+    - ``Vhs`` -- a list of tuple whose elements are tuples `(h_i, n_i)`
+
+
+    - ``Vd`` -- the vector with the intersection numbers of the strict
+      transform of :math:`f^3 - g^2` with the divisors of the resolution
+
+    - ``total`` -- boolean (default: ``True``), whether we consider also
+      the strata corresponding to the strict transforms of :math:`f, g`.
+
+    OUTPUT:
+
+    Polynomials :math:`z^3 + M_1 z + M_0` or :math:`z^3 + M_2 z^2 + M_0` are
+    assigned to each strata. The monomials are of the form :math:`x^k` for the
+    smooth parts of the divisors and :math:`x^k y^l` for the double points.
+    Each variable is associated to a divisor or to a strict transform
+
+    - ``n`` -- the number of irreducible components of the exceptional divisor
+
+    - ``Nf`` -- the vector in :math:`\mathbb{Z}^n` of the multiplicities for
+      the total transform of :math:`f`
+
+    - ``Ng`` -- the vector in :math:`\mathbb{Z}^n` of the multiplicities for
+      the total transform of :math:`g`
+
+    - ``Nhs`` -- a list of tuple whose elements are tuples, the first element
+      is the vector in :math:`\mathbb{Z}^n` of the multiplicities for
+      the total transform of :math:`h_i` and the second is :math:`n_i`
+
+    - ``Nd`` -- the vector in :math:`\mathbb{Z}^n` of the multiplicities for
+      the total transform of :math:`f^3 - g^2`
+
+    - ``euler`` -- the vector in :math:`\mathbb{Z}^n` of the Euler
+      characteristic of the smooth part of the strata. If ``total=True`` this
+      smooth part does not contain the intersections with total transform
+      of :math:`f, g`
+
+    - ``nus`` -- the vector in :math:`\mathbb{Z}^n` of the canonical
+      multiplicities
+
+    - ``pols`` -- a dictionary with keys ``(i, )``, ``(i, j)``, ``(i, 'f')``
+      (if ``total=True``), ``(i, 'g')`` (if ``total=True``), and ``(i, 'd')``
+      assigning the polynomial of the stratum (non-degenerated with respect
+      to its Newton polytope), the weights ``(nui, nuj, 1)`` coding
+      the form
+      :math:`x^{\nu_i-1}y^{\nu_j-1}\operatorname{d}\! x \operatorname{d}\! y \operatorname{d}\! z`
+
+    EXAMPLES::
+
+        sage: R.<x, y, z> = QQ[]
+        sage: f, g = (x, y)
+        sage: A = Matrix(QQ, 3, [-3, 0, 1, 0, -2, 1, 1, 1, -1])
+        sage: Vf = vector(QQ, [1, 0, 0])
+        sage: Vg = vector(QQ, [0, 1, 0])
+        sage: Vd = vector(QQ, [0, 0, 1])
+        sage: trinomiales_general(A, Vf, Vg, (), Vd)
+        (3, (1, 1, 2), (1, 2, 3), (2, 3, 6), (0, 0, -1), (2, 3, 5),
+         {(0, 'f'): (x + x*y*z + z^3, (2, 1, 1), 1),
+          (0, 2): (z^3 + x*y^3 + x*y^2*z, (2, 5, 1), 1),
+          (1, 'g'): (x*z + x^2*y + z^3, (3, 1, 1), 1),
+          (1, 2): (z^3 + x*y^2*z + x^2*y^3, (3, 5, 1), 1),
+          (2, 'd'): (x*z^2 + z^3 + x^3*y, (5, 1, 1), 1),
+          0: (x + x*z + z^3, (2, 1, 1), 0),
+          1: (x^2 + x*z + z^3, (3, 1, 1), 0),
+          2: (x^3 + x^2*z + z^3, (5, 1, 1), -1)})
+        sage: trinomiales(A, Vf, Vg, Vd, (), total=False)
+        (3, (1, 1, 2), (1, 2, 3), (2, 3, 6), (1, 1, -1), (2, 3, 5),
+         {(0, 2): (z^3 + x*y^3 + x*y^2*z, (2, 5, 1), 1),
+          (1, 2): (z^3 + x*y^2*z + x^2*y^3, (3, 5, 1), 1),
+          (2, 'd'): (x*z^2 + z^3 + x^3*y, (5, 1, 1), 1),
+          0: (x + x*z + z^3, (2, 1, 1), 1),
+          1: (x^2 + x*z + z^3, (3, 1, 1), 1),
+          2: (x^3 + x^2*z + z^3, (5, 1, 1), -1)})
+    """
+    R = PolynomialRing(QQ, 'x, y, z', order='negdeglex')
+    x, y, z = R.gens()
+    n = A.nrows()
+    A1 = -A ** -1
+    Nf, Ng, Nd = [A1 * N0 for N0 in (Vf, Vg, Vd)]
+    Nhs = [(A1 * N0, h) for N0, h in Vhs]
+    ch = len(Nhs)
+    NNf = Nf + sum(j * V0 for V0, j in Nhs)
+    NNg = Ng + sum(V0 for V0, j in Nhs)
+    NNd = Nd + 2 * sum(V0 for V0, j in Nhs)
+    diag = vector(A.diagonal())
+    unos = vector(n * [1])
+    if total:
+        VV = Vf + Vg
+    else:
+        VV = Vf.parent()(0)
+    resta = VV + Vd + sum(V0 for V0, m in Vhs)
+    euler = (-A + 2 * identity_matrix(n)) * unos + diag - resta
+    nus = A1 * (diag + 2 * unos) + unos
+    expos = {}
+    for j in range(n):
+        a, b = (NNf[j], NNg[j])
+        eq = 3 * a == 2 * NNg[j]
+        nnd = min(3 * a, 2 * b) == NNd[j]
+        if nnd:
+            expos[j] = ((a, b), (a / 2, b), nus[j], eq, nnd)
+        else:
+            expos[j] = ((a, b), (a / 2, NNd[j] - b), nus[j], eq, nnd)
+    cadenas = ('d', )
+    cadenash = tuple(('h', h) for h in range(ch))
+    if total:
+        expos['f'] = ((1, 0), (0, 0), 1, False, True)
+        expos['g'] = ((0, 1), (0, 0), 1, False, True)
+        cadenas = ('f', 'g') + cadenas
+    expos['d'] = ((0, 0), (0, 1), 1, True, False)
+    for h, V0 in enumerate(Vhs):
+        expos['h', h] = ((V0[1], 1), (0, 0), 1, False, True)
+    pols = {}
+    for j in range(n):
+        if expos[j][-1]:
+            a, b = expos[j][0]
+            pols[j] = (z ** 3 + x ** a * z + x ** b, (expos[j][2], 1, 1),
+                       euler[j])
+        else:
+            a, b = expos[j][1]
+            pols[j] = (z ** 3 + x ** a * z ** 2 + x ** b,
+                       (expos[j][2], 1, 1), euler[j])
+    interdiv = [(i, j) for i, j in Combinations(n, 2) if A[i, j] != 0]
+    interstrict = [(i, j) for i in range(n) for j in cadenas
+                   if eval('V' + j)[i] != 0]
+    interh = [(i, j) for i in range(n) for j in cadenash if Vhs[j[1]][0][i] != 0]
+    for i, j in interdiv + interstrict + interh:
+        if isinstance(j, str):
+            ep = eval('V' + j)[i]
+        else:
+            ep = 1
+        eqi, nndi = expos[i][-2:]
+        eqj, nndj = expos[j][-2:]
+        nd = eqi and eqj and not (nndi and nndj)
+        if not nd:
+            ai, bi = expos[i][0]
+            aj, bj = expos[j][0]
+            pols[i, j] = (z ** 3 + x ** ai * y ** aj * z + x ** bi * y ** bj,
+                          (expos[i][2], expos[j][2], 1), ep)
+        else:
+            ai, bi = expos[i][1]
+            aj, bj = expos[j][1]
+            pols[i, j] = (z ** 3 + x ** ai * y ** aj * z ** 2 +
+                          x ** bi * y ** bj, (expos[i][2], expos[j][2], 1), ep)
+    return n, Nf, Ng, Nd, Nhs, euler, nus, pols
+
+def exp_trenza_dis(tau):
+    B = tau.parent()
+    m = tau.exponent_sum()
+    a, b = m.quo_rem(6)
+    no = False
+    while not no:
+      no = bool(tau.conjugating_braid(B.delta()**(2 * a) * B.gen(0)**b))
+      if not no:
+        a, b = a - 1, b + 6
+    return (2 * a, None, 3 * a + b)
+
+def exp_trenza(tau):
+    B = tau.parent()
+    m = tau.exponent_sum()
+    if m.gcd(6) == 1:
+      return exp_trenza_dis(tau)
+    elif m.gcd(6) == 3:
+      polo = bool(tau.conjugating_braid(B.delta()**(m / 3)))
+      if polo:
+        return (None, m / 3, None)
+      else:
+        return exp_trenza_dis(tau)
+    elif m.gcd(6) == 2:
+      cero = bool(tau.conjugating_braid(B([1, 2])**(m / 2)))
+      if cero:
+        return (None, None, m / 2)
+      else:
+        return exp_trenza_dis(tau)
+    else:
+      ct = bool(tau.conjugating_braid(B.delta()**(m / 3)))
+      if ct:
+        return (m / 6, m / 3, m / 2)
+      else:
+        return exp_trenza_dis(tau)
+
+
+
+
+def trinomiales_trenza(A, trenzas, Vhs, Vd):
+    r"""
+    Return data necessary to compute the zeta functions of
+    a triple singularity defined by
+
+        .. math::
+            z^3 -3 \prod_{i=1}^h h_i^{n_i} f z^2
+            + \prod_{i=1}^h h_i g,
+
+    where :math:`f, g, h_i` are polynomials in two variables,
+    and :math:`n_i \geq 1`.
+
+    We consider an embedded resolution of :math:`fg(f^3 - g^2)` with
+    a stratification of the exceptional divisor:
+
+    - :math:`\check{E}_i`: the smooth part of the total divisor
+
+    - :math:`E_i\cap E_j`: the double points of the divisor
+
+    - :math:`E_i\cap \{f=0\}`: the intersections with the strict
+      transform of :math:`f`
+
+    - :math:`E_i\cap \{g=0\}`: the intersections with the strict
+      transform of :math:`g`
+
+    - :math:`E_i\cap \{f^3=g^2\}`: the intersections with the strict
+      transform of :math:`f^3-g^2`
+
+    It is also possible to forget the strict transforms of :math:`f, g`
+    and even to consider only resolutions of :math:`f^3 - g^2`.
+
+    INPUT:
+
+    - ``A`` -- the incidence matrix of a resolution
+
+    - ``Vf`` -- the vector with the intersection numbers of the strict
+      transform of :math:`f` with the divisors of the resolution
+
+    - ``Vg`` -- the vector with the intersection numbers of the strict
+      transform of :math:`g` with the divisors of the resolution
+
+    - ``Vhs`` -- a list of tuple whose elements are tuples `(h_i, n_i)`
+
+
+    - ``Vd`` -- the vector with the intersection numbers of the strict
+      transform of :math:`f^3 - g^2` with the divisors of the resolution
+
+    - ``total`` -- boolean (default: ``True``), whether we consider also
+      the strata corresponding to the strict transforms of :math:`f, g`.
+
+    OUTPUT:
+
+    Polynomials :math:`z^3 + M_1 z + M_0` or :math:`z^3 + M_2 z^2 + M_0` are
+    assigned to each strata. The monomials are of the form :math:`x^k` for the
+    smooth parts of the divisors and :math:`x^k y^l` for the double points.
+    Each variable is associated to a divisor or to a strict transform
+
+    - ``n`` -- the number of irreducible components of the exceptional divisor
+
+    - ``Nf`` -- the vector in :math:`\mathbb{Z}^n` of the multiplicities for
+      the total transform of :math:`f`
+
+    - ``Ng`` -- the vector in :math:`\mathbb{Z}^n` of the multiplicities for
+      the total transform of :math:`g`
+
+    - ``Nhs`` -- a list of tuple whose elements are tuples, the first element
+      is the vector in :math:`\mathbb{Z}^n` of the multiplicities for
+      the total transform of :math:`h_i` and the second is :math:`n_i`
+
+    - ``Nd`` -- the vector in :math:`\mathbb{Z}^n` of the multiplicities for
+      the total transform of :math:`f^3 - g^2`
+
+    - ``euler`` -- the vector in :math:`\mathbb{Z}^n` of the Euler
+      characteristic of the smooth part of the strata. If ``total=True`` this
+      smooth part does not contain the intersections with total transform
+      of :math:`f, g`
+
+    - ``nus`` -- the vector in :math:`\mathbb{Z}^n` of the canonical
+      multiplicities
+
+    - ``pols`` -- a dictionary with keys ``(i, )``, ``(i, j)``, ``(i, 'f')``
+      (if ``total=True``), ``(i, 'g')`` (if ``total=True``), and ``(i, 'd')``
+      assigning the polynomial of the stratum (non-degenerated with respect
+      to its Newton polytope), the weights ``(nui, nuj, 1)`` coding
+      the form
+      :math:`x^{\nu_i-1}y^{\nu_j-1}\operatorname{d}\! x \operatorname{d}\! y \operatorname{d}\! z`
+
+    EXAMPLES::
+
+        sage: R.<x, y, z> = QQ[]
+        sage: f, g = (x, y)
+        sage: A = Matrix(QQ, 3, [-3, 0, 1, 0, -2, 1, 1, 1, -1])
+        sage: Vf = vector(QQ, [1, 0, 0])
+        sage: Vg = vector(QQ, [0, 1, 0])
+        sage: Vd = vector(QQ, [0, 0, 1])
+        sage: trinomiales_general(A, Vf, Vg, (), Vd)
+        (3, (1, 1, 2), (1, 2, 3), (2, 3, 6), (0, 0, -1), (2, 3, 5),
+         {(0, 'f'): (x + x*y*z + z^3, (2, 1, 1), 1),
+          (0, 2): (z^3 + x*y^3 + x*y^2*z, (2, 5, 1), 1),
+          (1, 'g'): (x*z + x^2*y + z^3, (3, 1, 1), 1),
+          (1, 2): (z^3 + x*y^2*z + x^2*y^3, (3, 5, 1), 1),
+          (2, 'd'): (x*z^2 + z^3 + x^3*y, (5, 1, 1), 1),
+          0: (x + x*z + z^3, (2, 1, 1), 0),
+          1: (x^2 + x*z + z^3, (3, 1, 1), 0),
+          2: (x^3 + x^2*z + z^3, (5, 1, 1), -1)})
+        sage: trinomiales(A, Vf, Vg, Vd, (), total=False)
+        (3, (1, 1, 2), (1, 2, 3), (2, 3, 6), (1, 1, -1), (2, 3, 5),
+         {(0, 2): (z^3 + x*y^3 + x*y^2*z, (2, 5, 1), 1),
+          (1, 2): (z^3 + x*y^2*z + x^2*y^3, (3, 5, 1), 1),
+          (2, 'd'): (x*z^2 + z^3 + x^3*y, (5, 1, 1), 1),
+          0: (x + x*z + z^3, (2, 1, 1), 1),
+          1: (x^2 + x*z + z^3, (3, 1, 1), 1),
+          2: (x^3 + x^2*z + z^3, (5, 1, 1), -1)})
+    """
+    R = PolynomialRing(QQ, 'x, y, z', order='negdeglex')
+    x, y, z = R.gens()
+    n = A.nrows()
+    A1 = -A ** -1
+    Nd = A1 * Vd
+    Nhs = [(A1 * N0, h) for N0, h in Vhs]
+    ch = len(Nhs)
+    NNd = Nd + 2 * sum(V0 for V0, j in Nhs)
+    diag = vector(A.diagonal())
+    unos = vector(n * [1])
+    resta = Vd + sum(V0 for V0, m in Vhs)
+    euler = (-A + 2 * identity_matrix(n)) * unos + diag - resta
+    nus = A1 * (diag + 2 * unos) + unos
+    expos = {j: exp_trenza(trenzas[j]) for j in range(n)}
+    cadenas = ('d', )
+    cadenash = tuple(('h', h) for h in range(ch))
+    expos['d'] = (0, 0, 1)
+    for h, V0 in enumerate(Vhs):
+        expos['h', h] = (0, V0[1], 1)
+    pols = {}
+    for j in range(n):
+        p = z**3
+        for k, e in enumerate(expos[j]):
+            if e:
+                p += x**e * z**(2 - k)
+        pols[j] = (p, (nus[j], 1, 1), euler[j])
+    interdiv = [(i, j) for i, j in Combinations(n, 2) if A[i, j] != 0]
+    interstrict = [(i, j) for i in range(n) for j in cadenas
+                   if eval('V' + j)[i] != 0]
+    interh = [(i, j) for i in range(n) for j in cadenash if Vhs[j[1]][0][i] != 0]
+    for i, j in interdiv + interstrict + interh:
+        if isinstance(j, str):
+            ep = eval('V' + j)[i]
+            nu = (nus[i], 1, 1)
+        else:
+            ep = 1
+            nu = (nus[i], nus[j], 1)
+        p = z**3
+        for k, (e1, e2) in enumerate(zip(expos[i], expos[j])):
+            if e1 and e2:
+                p += x**e1 * y**e2 * z**(2 - k)
+        pols[i, j] = (p, nu, ep)
+    return n, Nd, Nhs, euler, nus, pols
+
+def estrato(pol, pesos, euler, info=False):
+    r"""
+    Return the topological and Igusa zeta functions associated to a stratum
+
+    INPUT:
+
+    - ``pol`` -- a trinomial non degenerated with respect to its Newton
+      polyhedron
+
+    - ``pesos`` -- the canonical weights :math:`\nu:i`
+
+    - `euler`` -- the Euler characteristic of the stratum
+
+    - ``info`` -- boolean (default: False), if ``True`` a dictionary giving
+      the powers of cyclotomic polynomials for the monodromy zeta function
+      is given
+
+    EXAMPLES::
+
+        sage: R.<x, y, z> = QQ[]
+        sage: F = z**3 + x**4 * y**6 * z + x**7 * y**9
+        sage: estrato(F, (1, 1, 1), 1, info=True)
+        ((1/3*s**2 + 1/2*s + 2/9)/(s^3 + 35/18*s^2 + 7/6*s + 2/9), -t^3 + 1,
+         {1: 1, 3: 1})
+    """
+    Z1 = ZetaFunctions(pol)
+    zetatop = euler * Z1.topological_zeta(local=True, weights=pesos)
+    zetamon = Z1.monodromy_zeta() ** euler
+    if info:
+        dic = {}
+        for p, j in zetamon.factor():
+            c = p.is_cyclotomic(certificate=True)
+            dic[c] = j
+        return zetatop, zetamon, dic
+    return zetatop, zetamon
+
+
+def zetas(n, pols, info=False):
+    r"""
+    Return the topological and Igusa zeta functions from the data of
+    a stratification
+
+    INPUT:
+
+    - ``n`` -- the number of exceptional divisors
+
+    - ``pols`` -- a dictionary from ``trinomiales``
+
+    - ``info`` -- boolean (default: False), if ``True`` a dictionary giving
+      the powers of cyclotomic polynomials for the monodromy zeta function
+      is given
+
+    EXAMPLES::
+
+        sage: A = Matrix(QQ, 3, [-3, 0, 1, 0, -2, 1, 1, 1, -1])
+        sage: Vf = vector(QQ, [1, 0, 0])
+        sage: Vg = vector(QQ, [0, 1, 0])
+        sage: Vd = vector(QQ, [0, 0, 1])
+        sage: n, Nf, Ng, Nd, euler, nus, pols = trinomiales(A, Vf, Vg, Vd)
+        sage: zetas(n, pols, info=True)
+        (1/(s + 1), -t + 1, {1: 1})
+    """
+    zetatop = 0
+    T = PolynomialRing(QQ, 't')
+    t = T.gen(0)
+    zetamon = 1 / (1 - t ** 3) ** n
+    for k in pols:
+        zt, zm = estrato(*pols[k])
+        zetatop += zt
+        zetamon *= zm
+    if info:
+        dic = {}
+        for p, j in zetamon.factor():
+            c = p.is_cyclotomic(certificate=True)
+            dic[c] = j
+        return zetatop, zetamon, dic
+    return zetatop, zetamon