Shidoku solving with no constraint.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the beginning, we need to determine the base ring, the number of variables, the variables, and the term order to find the Gröbner bases. In the below, we give these to create the polynomial ring."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "P.<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16> = PolynomialRing (FiniteField(37), order =\"lex\")#(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We choose a base ring as $Finite Field(37)$ because 37 is a prime number and the ring allows us to compute the ideal set correctly. We use the lexicographical term order for the monomial ordering and we have 16 variables. Now, we can import the polynomials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "ls = [x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16]; f = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; "
   ]
  },
  {
   "attachments": {
    "shidoku3.jpg": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![shidoku3.jpg](attachment:shidoku3.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a row. $x1 + x2 + x3 + x4 = 10$ and $x1x2x3x4  = 24$. We can write these equations for each row, column and $2\\times2$ block. Also, each cell of the Shidoku board can be thought of as a variable that can take only values 1,2,3 and 4. $(x1-1)(x1-2)(x1-3)(x1-4) = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(0,16):\n",
    "    f[i] = (ls[i]-1)*(ls[i]-2)*(ls[i]-3)*(ls[i] - 4);\n",
    "\n",
    "k = 0;d = 0;\n",
    "for j in range(16,24):\n",
    "    if j<20:\n",
    "        f[j] = ls[k] + ls[k+1] + ls[k+2] +ls[k+3]-10\n",
    "        k = k + 4; \n",
    "    if j>=20:\n",
    "        f[j] = ls[d]*ls[d+1]*ls[d+2]*ls[d+3]-24\n",
    "        d = d + 4;\n",
    "\n",
    "q=0;p=0;\n",
    "for a in range(24,32):\n",
    "    if a<28:\n",
    "        f[a] = ls[q] + ls[q+4] + ls[q+8] +ls[q+12]-10;\n",
    "        q = q + 1; \n",
    "    if a>=28:\n",
    "        f[a] = ls[p]*ls[p+4]*ls[p+8]*ls[p+12]-24;\n",
    "        p = p + 1; \n",
    "l=0;\n",
    "for w in range(32,36):\n",
    "    if w<34:\n",
    "        f[w] = ls[l] + ls[l+1] + ls[l+4] +ls[l+5]-10;\n",
    "        l = l + 2; \n",
    "    if w>=34:\n",
    "        f[w] = ls[l+4] + ls[l+5] + ls[l+8] +ls[l+9]-10;\n",
    "        l = l + 2;\n",
    "z=0;\n",
    "for t in range(36,40):\n",
    "    if t<38:\n",
    "        f[t] = ls[z]*ls[z+1]*ls[z+4]*ls[z+5]-24;\n",
    "        z = z + 2; \n",
    "    if t>=38:\n",
    "        f[t] = ls[z+4]*ls[z+5]*ls[z+8]*ls[z+9]-24;\n",
    "        z = z + 2;\n",
    "        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We import the polynomials in $f$. Now, we can generate an ideal with the set of $f$. The ideal $I$ is generated by $f$ on the polynomial ring $R[x_1,x_2,\\ldots,x_{16}]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ideal (x1^4 - 10*x1^3 - 2*x1^2 - 13*x1 - 13, x2^4 - 10*x2^3 - 2*x2^2 - 13*x2 - 13, x3^4 - 10*x3^3 - 2*x3^2 - 13*x3 - 13, x4^4 - 10*x4^3 - 2*x4^2 - 13*x4 - 13, x5^4 - 10*x5^3 - 2*x5^2 - 13*x5 - 13, x6^4 - 10*x6^3 - 2*x6^2 - 13*x6 - 13, x7^4 - 10*x7^3 - 2*x7^2 - 13*x7 - 13, x8^4 - 10*x8^3 - 2*x8^2 - 13*x8 - 13, x9^4 - 10*x9^3 - 2*x9^2 - 13*x9 - 13, x10^4 - 10*x10^3 - 2*x10^2 - 13*x10 - 13, x11^4 - 10*x11^3 - 2*x11^2 - 13*x11 - 13, x12^4 - 10*x12^3 - 2*x12^2 - 13*x12 - 13, x13^4 - 10*x13^3 - 2*x13^2 - 13*x13 - 13, x14^4 - 10*x14^3 - 2*x14^2 - 13*x14 - 13, x15^4 - 10*x15^3 - 2*x15^2 - 13*x15 - 13, x16^4 - 10*x16^3 - 2*x16^2 - 13*x16 - 13, x1 + x2 + x3 + x4 - 10, x5 + x6 + x7 + x8 - 10, x9 + x10 + x11 + x12 - 10, x13 + x14 + x15 + x16 - 10, x1*x2*x3*x4 + 13, x5*x6*x7*x8 + 13, x9*x10*x11*x12 + 13, x13*x14*x15*x16 + 13, x1 + x5 + x9 + x13 - 10, x2 + x6 + x10 + x14 - 10, x3 + x7 + x11 + x15 - 10, x4 + x8 + x12 + x16 - 10, x1*x5*x9*x13 + 13, x2*x6*x10*x14 + 13, x3*x7*x11*x15 + 13, x4*x8*x12*x16 + 13, x1 + x2 + x5 + x6 - 10, x3 + x4 + x7 + x8 - 10, x9 + x10 + x13 + x14 - 10, x11 + x12 + x15 + x16 - 10, x1*x2*x5*x6 + 13, x3*x4*x7*x8 + 13, x9*x10*x13*x14 + 13, x11*x12*x15*x16 + 13) of Multivariate Polynomial Ring in x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16 over Finite Field of size 37"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I = P.ideal([f[0],f[1],f[2],f[3],f[4],f[5],f[6],f[7],f[8],f[9],f[10],f[11],f[12],f[13],f[14],f[15],f[16],f[17],f[18],f[19],f[20],f[21],f[22],f[23],f[24],f[25],f[26],f[27],f[28],f[29],f[30],f[31],f[32],f[33],f[34],f[35],f[36],f[37],f[38],f[39]]); I"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we ready to compute the Gröbner bases. The below code finds the minimal ideal because there are no constraints right now. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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3*x7*x12*x15 + 10*x7*x12*x16^2 - 3*x7*x12*x16 - 15*x7*x12 + 13*x7*x14*x15^2*x16^2 - 9*x7*x14*x15^2*x16 + 10*x7*x14*x15^2 - 9*x7*x14*x15*x16^2 + 3*x7*x14*x15*x16 - 3*x7*x14*x15 + 10*x7*x14*x16^2 - 3*x7*x14*x16 - 15*x7*x14 + 14*x7*x15^2*x16^2 - 17*x7*x15^2*x16 + 17*x7*x15^2 - 17*x7*x15*x16^2 - 6*x7*x15*x16 + 7*x7*x15 + 17*x7*x16^2 + 7*x7*x16 + 13*x7 - 17*x8*x10*x12*x15^2*x16^2 + 11*x8*x10*x12*x15^2*x16 - 14*x8*x10*x12*x15^2 - 17*x8*x10*x12*x15*x16^3 + 9*x8*x10*x12*x15*x16^2 + 15*x8*x10*x12*x15*x16 + 2*x8*x10*x12*x15 - 13*x8*x10*x12*x16^3 - 18*x8*x10*x12*x16^2 + 14*x8*x10*x12*x16 - 14*x8*x10*x12 - 13*x8*x10*x15^2*x16^2 + 9*x8*x10*x15^2*x16 - 10*x8*x10*x15^2 - 13*x8*x10*x15*x16^3 + 5*x8*x10*x15*x16^2 - 6*x8*x10*x15*x16 + 6*x8*x10*x15 - 14*x8*x10*x16^3 - 8*x8*x10*x16^2 - 8*x8*x10*x16 - 8*x8*x10 - 17*x8*x12*x14*x15*x16^3 - 2*x8*x12*x14*x15*x16^2 - 5*x8*x12*x14*x15*x16 - 10*x8*x12*x14*x15 - 13*x8*x12*x14*x16^3 - 5*x8*x12*x14*x16^2 + 7*x8*x12*x14*x16 - 17*x8*x12*x14 - 13*x8*x12*x15^2*x16^2 + 9*x8*x12*x15^2*x16 - 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10, x14^2 + x14*x15 + x14*x16 - 10*x14 + x15^2 + x15*x16 - 10*x15 + x16^2 - 10*x16 - 2, x15^3 + x15^2*x16 - 10*x15^2 + x15*x16^2 - 10*x15*x16 - 2*x15 + x16^3 - 10*x16^2 - 2*x16 - 13, x16^4 - 10*x16^3 - 2*x16^2 - 13*x16 - 13]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K = I.groebner_basis(); K "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we get the minimal ideal that contains the Gröbner basis. Also, we reduce 40 polynomials to 17 polynomials. "
   ]
  }
 ],
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