diff --git a/deRhamComputation.ipynb b/deRhamComputation.ipynb
index a5f5628..9968cbd 100644
--- a/deRhamComputation.ipynb
+++ b/deRhamComputation.ipynb
@@ -11,12 +11,18 @@
     " $$x^{i-1} dx/y^j,$$\n",
     " where $1 \\le i \\le r-1$, $1 \\le j \\le m-1$, $-mi + rj \\ge \\delta$ and $\\delta := GCD(m, r)$, $r := \\deg f$.\n",
     " \n",
-    " - "
+    " - the above forms along with\n",
+    " $$\\lambda_{ij} = \\left[ \\left( \\frac{\\psi_{ij} \\, dx}{m x^{i+1} y^{m - j}},\n",
+    "  \\frac{-\\phi_{ij} \\, dx}{m x^{i+1} y^{m - j}}, \\frac{y^j}{x^i} \\right) \\right]$$\n",
+    "  (where $s_{ij} = jx f'(x) - mi f(x)$, \n",
+    " $\\psi_{ij}(x) = s_{ij}^{\\ge i+1}$,\n",
+    " $\\phi_{ij}(x) = s_{ij}^{< i+1}$)\n",
+    "form a basis of $H^1_{dR}(C/K)$."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -40,7 +46,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -48,7 +54,7 @@
     "# We treat them as pairs [omega, f], where omega is regular on the affine part\n",
     "# and omega - df is regular on the second atlas.\n",
     "# The coefficient j means that we compute the j-th eigenpart, i.e.\n",
-    "# [y^j * f(x) dx, g(x)/y^j]. Output is [f(x), g(x)]\n",
+    "# [f(x) dx/y^j, y^(m-j)*g(x)]. Output is [f(x), g(x)]\n",
     "\n",
     "def baza_dr(m, f, j, p):\n",
     "    R.<x> = PolynomialRing(GF(p))\n",
@@ -73,7 +79,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 155,
+   "execution_count": 140,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -110,7 +116,7 @@
     "#Any element [f dx, g] is represented as a combination of the basis vectors.\n",
     "\n",
     "def zapis_w_bazie_dr(elt, m, f, j, p):\n",
-    "    #print(elt)\n",
+    "    print(elt, 'czy w dr', czy_w_de_rhamie(elt, m, f, j, p))\n",
     "    R.<x> = PolynomialRing(GF(p))\n",
     "    RR = FractionField(R)\n",
     "    f = R(f)\n",
@@ -143,33 +149,35 @@
     "        return zapis_w_bazie_dr(elt1, m, f, j, p) + vector([a/a1*GF(p)(i == k) for i in range(0, len(baza))])\n",
     "\n",
     "    g = elt[1]\n",
-    "    g1 = R(elt[1].numerator())\n",
-    "    g2 = R(elt[1].denominator())\n",
-    "    d1 = g1.degree()\n",
-    "    d2 = g2.degree()\n",
-    "    a1 = g1.coefficients(sparse = false)[d1]\n",
-    "    a2 = g2.coefficients(sparse = false)[d2]\n",
-    "    a = a1/a2\n",
-    "    d = d2 - d1\n",
+    "    a = wspolczynnik_wiodacy(g)\n",
+    "    d = -stopien_roznica(g)\n",
     "    Rr = r/delta\n",
-    "    M = m/delta\n",
-    "\n",
+    "    Mm = m/delta\n",
+    "    \n",
     "    stopnie2 = stopnie_drugiej_wspolrzednej_bazy_dr(m, f, j, p)\n",
     "    inv_stopnie2 = {v: k for k, v in stopnie2.items()}      \n",
-    "    \n",
-    "    if (d not in inv_stopnie2):\n",
+    "    print('d', d, 'a', a, 'dostepne:', stopnie2, 'czy w stopnie 2', d not in stopnie2)\n",
+    "    if (d not in stopnie2.values()):\n",
     "        print('p3')\n",
     "        if d>= 0:\n",
-    "            elt1 = [elt[0], RR(elt[1]) - a1/a2*1/R(x^d)]\n",
+    "            print('p3a')\n",
+    "            j1 = m-j\n",
+    "            print('?', -j1*Rr+d*Mm)\n",
+    "            elt1 = [elt[0], RR(elt[1]) - a*1/R(x^d)]\n",
     "        else:\n",
-    "            elt1 = [elt[0], RR(elt[1]) - a1/a2*R(x^(-d))]\n",
+    "            print('p3b')\n",
+    "            d1 = -d\n",
+    "            j1 = m-j\n",
+    "            elt1 = [elt[0] - a*(j1*x^(d1) * f.derivative()/m + d1*f*x^(d1 - 1)), RR(elt[1]) - a*R(x^(d1))]\n",
     "        return zapis_w_bazie_dr(elt1, m, f, j, p)\n",
     "    \n",
     "    print('p4')\n",
     "    k = inv_stopnie2[d]\n",
+    "    b = wspolczynnik_wiodacy(baza[k][1])\n",
+    "    print('k', k, 'a', a)\n",
     "    elt1 = [R(0), R(0)]\n",
-    "    elt1[0] = elt[0] - a*baza[k][0]\n",
-    "    elt1[1] = elt[1] - a*baza[k][1]\n",
+    "    elt1[0] = elt[0] - a/b*baza[k][0]\n",
+    "    elt1[1] = elt[1] - a/b*baza[k][1]\n",
     "    return zapis_w_bazie_dr(elt1, m, f, j, p) + vector([a*GF(p)(i == k) for i in range(0, len(baza))])\n",
     "    \n",
     "    \n",
@@ -213,7 +221,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 156,
+   "execution_count": 131,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -261,7 +269,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 157,
+   "execution_count": 132,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -269,8 +277,9 @@
     "    R.<x> = PolynomialRing(GF(p))\n",
     "    RR = FractionField(R)\n",
     "    f = R(f)\n",
-    "    M = floor(j*p/m)\n",
-    "    return [0, f^M * RR(elt[1])^p] #eigenspace = j*p mod m\n",
+    "    j1 = m-j\n",
+    "    M = floor(j1*p/m)\n",
+    "    return [0, f^M * RR(elt[1])^p] #eigenspace = j1*p mod m\n",
     "\n",
     "def macierz_frob_dr(p, m, f, j):\n",
     "    baza = baza_dr(m, f, j, p)\n",
@@ -279,21 +288,97 @@
     "        frob = frobenius_dr(p, m, f, baza[k], j)\n",
     "        v = zapis_w_bazie_dr(frob, m, f, j, p)\n",
     "        A[k, :] = matrix(v)\n",
-    "    return A.transpose()"
+    "    return A.transpose()\n",
+    "\n",
+    "def wspolczynnik_wiodacy(f):\n",
+    "    R.<x> = PolynomialRing(GF(p))\n",
+    "    RR = FractionField(R)\n",
+    "    f = RR(f)\n",
+    "    f1 = f.numerator()\n",
+    "    f2 = f.denominator()\n",
+    "    d1 = f1.degree()\n",
+    "    d2 = f2.degree()\n",
+    "    a1 = f1.coefficients(sparse = false)[d1]\n",
+    "    a2 = f2.coefficients(sparse = false)[d2]\n",
+    "    return(a1/a2)\n",
+    "\n",
+    "def stopien_roznica(f):\n",
+    "    R.<x> = PolynomialRing(GF(p))\n",
+    "    RR = FractionField(R)\n",
+    "    f = RR(f)\n",
+    "    f1 = f.numerator()\n",
+    "    f2 = f.denominator()\n",
+    "    d1 = f1.degree()\n",
+    "    d2 = f2.degree()\n",
+    "    return(d1 - d2)\n",
+    "\n",
+    "def czy_w_de_rhamie(elt, m, f, j, p):\n",
+    "    j1 = m - j\n",
+    "    R.<x> = PolynomialRing(GF(p))\n",
+    "    RR = FractionField(R)\n",
+    "    f = R(f)\n",
+    "    elt = [RR(elt[0]), RR(elt[1])]\n",
+    "    auxiliary = elt[0] - j1/m*elt[1]*f.derivative() - f*elt[1].derivative()\n",
+    "    deg = stopien_roznica(auxiliary)\n",
+    "    \n",
+    "    r = f.degree()\n",
+    "    delta = GCD(r, m)\n",
+    "    Rr = r/delta\n",
+    "    Mm = m/delta\n",
+    "    return(j*Rr - deg*Mm >= 0)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 158,
-   "metadata": {},
+   "execution_count": 134,
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{0: [1, 0], 1: [x, 2/x]}\n",
+      "[0, 0] czy w dr True\n",
+      "p1\n",
+      "[0, (2*x^6 + 4*x^4 + 2*x^3 + 2*x^2 + 2*x + 3)/x^5] czy w dr True\n",
+      "d -1 a 2 dostepne: {1: 1} czy w stopnie 2 True\n",
+      "p3\n",
+      "[2*x + 4, (4*x^4 + 2*x^3 + 2*x^2 + 2*x + 3)/x^5] czy w dr True\n",
+      "d 1 a 4 dostepne: {1: 1} czy w stopnie 2 False\n",
+      "p4\n",
+      "k 1 a 4\n",
+      "[4, (2*x^3 + 2*x^2 + 2*x + 3)/x^5] czy w dr True\n",
+      "d 2 a 2 dostepne: {1: 1} czy w stopnie 2 True\n",
+      "p3\n",
+      "? 1\n",
+      "[4, (2*x^2 + 2*x + 3)/x^5] czy w dr True\n",
+      "d 3 a 2 dostepne: {1: 1} czy w stopnie 2 True\n",
+      "p3\n",
+      "? 3\n",
+      "[4, (2*x + 3)/x^5] czy w dr True\n",
+      "d 4 a 2 dostepne: {1: 1} czy w stopnie 2 True\n",
+      "p3\n",
+      "? 5\n",
+      "[4, 3/x^5] czy w dr True\n",
+      "d 5 a 3 dostepne: {1: 1} czy w stopnie 2 True\n",
+      "p3\n",
+      "? 7\n",
+      "[4, 0] czy w dr True\n",
+      "p2\n",
+      "[0, 0] czy w dr True\n",
+      "p1\n"
+     ]
+    },
     {
      "data": {
       "text/plain": [
-       "{0: [1, 0], 1: [x, 2/x]}"
+       "[0 4]\n",
+       "[0 4]"
       ]
      },
-     "execution_count": 158,
+     "execution_count": 134,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -303,13 +388,13 @@
     "j = 1\n",
     "p = 5\n",
     "f = x^3 + x+3\n",
-    "baza_dr(m, f, j, p)\n",
-    "#macierz_frob_dr(p, m, f, j)"
+    "print(baza_dr(m, f, j, p))\n",
+    "macierz_frob_dr(p, m, f, j)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 159,
+   "execution_count": 135,
    "metadata": {},
    "outputs": [
     {
@@ -318,7 +403,7 @@
        "[0, (2*x^6 + 4*x^4 + 2*x^3 + 2*x^2 + 2*x + 3)/x^5]"
       ]
      },
-     "execution_count": 159,
+     "execution_count": 135,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -329,993 +414,51 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 160,
+   "execution_count": 136,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
+      "[0, (2*x^6 + 4*x^4 + 2*x^3 + 2*x^2 + 2*x + 3)/x^5] czy w dr True\n",
+      "d -1 a 2 dostepne: {1: 1} czy w stopnie 2 True\n",
       "p3\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n",
-      "p4\n"
+      "[2*x + 4, (4*x^4 + 2*x^3 + 2*x^2 + 2*x + 3)/x^5] czy w dr True\n",
+      "d 1 a 4 dostepne: {1: 1} czy w stopnie 2 False\n",
+      "p4\n",
+      "k 1 a 4\n",
+      "[4, (2*x^3 + 2*x^2 + 2*x + 3)/x^5] czy w dr True\n",
+      "d 2 a 2 dostepne: {1: 1} czy w stopnie 2 True\n",
+      "p3\n",
+      "? 1\n",
+      "[4, (2*x^2 + 2*x + 3)/x^5] czy w dr True\n",
+      "d 3 a 2 dostepne: {1: 1} czy w stopnie 2 True\n",
+      "p3\n",
+      "? 3\n",
+      "[4, (2*x + 3)/x^5] czy w dr True\n",
+      "d 4 a 2 dostepne: {1: 1} czy w stopnie 2 True\n",
+      "p3\n",
+      "? 5\n",
+      "[4, 3/x^5] czy w dr True\n",
+      "d 5 a 3 dostepne: {1: 1} czy w stopnie 2 True\n",
+      "p3\n",
+      "? 7\n",
+      "[4, 0] czy w dr True\n",
+      "p2\n",
+      "[0, 0] czy w dr True\n",
+      "p1\n"
      ]
     },
     {
-     "ename": "RecursionError",
-     "evalue": "maximum recursion depth exceeded while calling a Python object",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mRecursionError\u001b[0m                            Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-160-b5994066838e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m<ipython-input-155-baa93df16142>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     85\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     86\u001b[0m             \u001b[0melt1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma1\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0ma2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     88\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     89\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'p4'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m<ipython-input-155-baa93df16142>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     92\u001b[0m     \u001b[0melt1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     93\u001b[0m     \u001b[0melt1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 94\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mvector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mGF\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     95\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     96\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "... last 1 frames repeated, from the frame below ...\n",
-      "\u001b[0;32m<ipython-input-155-baa93df16142>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     92\u001b[0m     \u001b[0melt1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     93\u001b[0m     \u001b[0melt1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 94\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mvector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mGF\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     95\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     96\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mRecursionError\u001b[0m: maximum recursion depth exceeded while calling a Python object"
-     ]
+     "data": {
+      "text/plain": [
+       "(4, 4)"
+      ]
+     },
+     "execution_count": 136,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
@@ -1324,7 +467,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 106,
+   "execution_count": 137,
    "metadata": {},
    "outputs": [
     {
@@ -1333,7 +476,7 @@
        "4*x^4 + 4*x^3 + 4*x^2 + 4*x + 4"
       ]
      },
-     "execution_count": 106,
+     "execution_count": 137,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1345,48 +488,158 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 138,
    "metadata": {},
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{0: [0, 4/x], 1: [1, 4/x^2]}\n",
+      "{0: 1, 1: 2}\n"
+     ]
+    },
     {
      "data": {
       "text/plain": [
-       "{0: [x^2, 0], 1: [x, 0], 2: [1, 0]}"
+       "True"
       ]
      },
-     "execution_count": 60,
+     "execution_count": 138,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "m = 5\n",
+    "m = 4\n",
     "j = 1\n",
     "p = 5\n",
-    "f = x^4 + x+2\n",
-    "baza_dr(m, f, j, p)"
+    "f = x^3 + x+2\n",
+    "print(baza_dr(m, f, j, p))\n",
+    "print(stopnie_drugiej_wspolrzednej_bazy_dr(m, f, j, p))\n",
+    "t = stopnie_drugiej_wspolrzednej_bazy_dr(m, f, j, p)\n",
+    "1 in t.values()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 141,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0, (4*x^9 + 2*x^7 + 4*x^6 + 2*x^5 + 3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr True\n",
+      "d -4 a 4 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
+      "p3\n",
+      "p3b\n",
+      "[x^4 + 3*x^3, (2*x^7 + 4*x^6 + 2*x^5 + 3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr True\n",
+      "d -2 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
+      "p3\n",
+      "p3b\n",
+      "[3*x^3 + 2*x^2 + 2*x, (4*x^6 + 2*x^5 + 3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr True\n",
+      "d -1 a 4 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
+      "p3\n",
+      "p3b\n",
+      "[2*x^2 + 2, (2*x^5 + 3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr True\n",
+      "d 0 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 False\n",
+      "p3\n",
+      "p3a\n",
+      "? -9\n",
+      "[2*x^2 + 2, (3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr False\n",
+      "d 1 a 3 dostepne: {0: 1, 1: 2} czy w stopnie 2 False\n",
+      "p4\n",
+      "k 0 a 3\n",
+      "[2*x^2 + 2, (2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr False\n",
+      "d 2 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
+      "p4\n",
+      "k 1 a 2\n",
+      "[2*x^2 + 4, (4*x^2 + 3*x + 2)/x^5] czy w dr False\n",
+      "d 3 a 4 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
+      "p3\n",
+      "p3a\n",
+      "? 3\n",
+      "[2*x^2 + 4, (3*x + 2)/x^5] czy w dr False\n",
+      "d 4 a 3 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
+      "p3\n",
+      "p3a\n",
+      "? 7\n",
+      "[2*x^2 + 4, 2/x^5] czy w dr False\n",
+      "d 5 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
+      "p3\n",
+      "p3a\n",
+      "? 11\n",
+      "[2*x^2 + 4, 0] czy w dr False\n",
+      "p2\n"
+     ]
+    },
+    {
+     "ename": "KeyError",
+     "evalue": "2",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-141-86a3d5ca17ee>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmacierz_frob_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-132-3ef6f7d47fcd>\u001b[0m in \u001b[0;36mmacierz_frob_dr\u001b[0;34m(p, m, f, j)\u001b[0m\n\u001b[1;32m     12\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m         \u001b[0mfrob\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfrobenius_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbaza\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m         \u001b[0mv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfrob\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m         \u001b[0mA\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     16\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtranspose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-140-9ce96c4e8631>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     85\u001b[0m             \u001b[0mj1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     86\u001b[0m             \u001b[0melt1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mderivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mm\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0md1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     88\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     89\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'p4'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-140-9ce96c4e8631>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     85\u001b[0m             \u001b[0mj1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     86\u001b[0m             \u001b[0melt1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mderivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mm\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0md1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     88\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     89\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'p4'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-140-9ce96c4e8631>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     85\u001b[0m             \u001b[0mj1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     86\u001b[0m             \u001b[0melt1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mderivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mm\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0md1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     88\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     89\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'p4'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-140-9ce96c4e8631>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     85\u001b[0m             \u001b[0mj1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     86\u001b[0m             \u001b[0melt1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mderivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mm\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0md1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     88\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     89\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'p4'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-140-9ce96c4e8631>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     94\u001b[0m     \u001b[0melt1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     95\u001b[0m     \u001b[0melt1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 96\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mvector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mGF\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     97\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     98\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-140-9ce96c4e8631>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     94\u001b[0m     \u001b[0melt1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     95\u001b[0m     \u001b[0melt1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 96\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mvector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mGF\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     97\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     98\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-140-9ce96c4e8631>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     85\u001b[0m             \u001b[0mj1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     86\u001b[0m             \u001b[0melt1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mderivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mm\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0md1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     88\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     89\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'p4'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-140-9ce96c4e8631>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     85\u001b[0m             \u001b[0mj1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     86\u001b[0m             \u001b[0melt1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mderivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mm\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0md1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     88\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     89\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'p4'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-140-9ce96c4e8631>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     85\u001b[0m             \u001b[0mj1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     86\u001b[0m             \u001b[0melt1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mderivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mm\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0md1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     88\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     89\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'p4'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-140-9ce96c4e8631>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m     56\u001b[0m         \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdegree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     57\u001b[0m         \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoefficients\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msparse\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 58\u001b[0;31m         \u001b[0mk\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minv_stopnie_holo\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m#ktory element bazy jest stopnia d? ten o indeksie k\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     59\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     60\u001b[0m         \u001b[0ma1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbaza\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoefficients\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msparse\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mKeyError\u001b[0m: 2"
+     ]
+    }
+   ],
+   "source": [
+    "macierz_frob_dr(p, m, f, 1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 96,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "[0 0 0]\n",
-       "[0 0 0]\n",
-       "[0 0 0]"
+       "2"
       ]
      },
-     "execution_count": 61,
+     "execution_count": 96,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "macierz_frob_dr(p, m, f, j)"
+    "wspolczynnik_wiodacy(2/x)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "TypeError",
+     "evalue": "degree() takes exactly one argument (0 given)",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-97-2687f469fb6b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdegree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;31mTypeError\u001b[0m: degree() takes exactly one argument (0 given)"
+     ]
+    }
+   ],
+   "source": [
+    "(2/x).degree()"
    ]
   },
   {