Add feasibility checking for the scheme related to tight 4-designs

Author: jaanos

index.ipynb

@@ -116,8 +116,9 @@
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mInfeasibleError\u001b[0m                           Traceback (most recent call last)",
       "\u001b[0;32m<ipython-input-5-58e3e45d7a79>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfam2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcheck_feasible\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/home/janos/repos/git/sage-drg/drg/drg.pyc\u001b[0m in \u001b[0;36mcheck_feasible\u001b[0;34m(self, checked, skip, derived)\u001b[0m\n\u001b[1;32m    705\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcheck\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mchecks\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    706\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mname\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mskip\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 707\u001b[0;31m                 \u001b[0mcheck\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    708\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mderived\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    709\u001b[0m             \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/home/janos/repos/git/sage-drg/drg/drg.pyc\u001b[0m in \u001b[0;36mcheck_family\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    666\u001b[0m                           vars)\n\u001b[1;32m    667\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0many\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcheckConditions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcond\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msol\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0msol\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msols\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 668\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mInfeasibleError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrefs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mref\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    669\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    670\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mcheck_feasible\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecked\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mskip\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mderived\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/home/janos/repos/git/sage-drg/drg/assoc_scheme.pyc\u001b[0m in \u001b[0;36mcheck_feasible\u001b[0;34m(self, checked, skip, derived, levels, queue, part)\u001b[0m\n\u001b[1;32m    823\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcheck\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mlvl\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    824\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mname\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mskip\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 825\u001b[0;31m                     \u001b[0mcheck\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    826\u001b[0m                     \u001b[0;32mif\u001b[0m \u001b[0mi\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    827\u001b[0m                         \u001b[0mskip\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/home/janos/repos/git/sage-drg/drg/assoc_scheme.pyc\u001b[0m in \u001b[0;36mcheck_family\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m   1361\u001b[0m         \u001b[0mnonexistence\u001b[0m \u001b[0mhas\u001b[0m \u001b[0mbeen\u001b[0m \u001b[0mshown\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0ma\u001b[0m \u001b[0mpart\u001b[0m \u001b[0mof\u001b[0m \u001b[0man\u001b[0m \u001b[0minfinite\u001b[0m \u001b[0mfamily\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1362\u001b[0m         \"\"\"\n\u001b[0;32m-> 1363\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_check_family\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   1364\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1365\u001b[0m     \u001b[0;34m@\u001b[0m\u001b[0mcheck\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/home/janos/repos/git/sage-drg/drg/assoc_scheme.pyc\u001b[0m in \u001b[0;36m_check_family\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m   1626\u001b[0m             if any(checkConditions(cond, sol) for sol in sols\n\u001b[1;32m   1627\u001b[0m                    if is_integral(sol)):\n\u001b[0;32m-> 1628\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mInfeasibleError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrefs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mref\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1629\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1630\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_check_multiplicity\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mInfeasibleError\u001b[0m: nonexistence by JurišićVidali12"
      ]
     }

jupyter/Demo.ipynb

@@ -912,7 +912,7 @@
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mInfeasibleError\u001b[0m                           Traceback (most recent call last)",
       "\u001b[0;32m<ipython-input-21-cbb835cbd7bf>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mdrg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDRGParameters\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m266\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m220\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m210\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcheck_feasible\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/home/janos/repos/git/sage-drg/jupyter/drg/drg.pyc\u001b[0m in \u001b[0;36mcheck_feasible\u001b[0;34m(self, checked, skip, derived)\u001b[0m\n\u001b[1;32m    720\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcomplement\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcheck_feasible\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchecked\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    721\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mInfeasibleError\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mex\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 722\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mInfeasibleError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpart\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"complement\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    723\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mia\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpart\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdistance_graphs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\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    724\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/home/janos/repos/git/sage-drg/jupyter/drg/assoc_scheme.pyc\u001b[0m in \u001b[0;36mcheck_feasible\u001b[0;34m(self, checked, skip, derived, levels, queue, part)\u001b[0m\n\u001b[1;32m    846\u001b[0m                                        levels=levels, queue=queue, part=pt)\n\u001b[1;32m    847\u001b[0m                 \u001b[0;32mexcept\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mInfeasibleError\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mex\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 848\u001b[0;31m                     \u001b[0;32mraise\u001b[0m \u001b[0mInfeasibleError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpart\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mpt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    849\u001b[0m                 \u001b[0mi\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    850\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mInfeasibleError\u001b[0m: complement: nonexistence by GavrilyukMakhnev05"
      ]
     }

jupyter/QPoly-d4-tight4design.ipynb

@@ -247,13 +247,29 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We now compute the triple intersection numbers with respect to three vertices $u, v, w$ mutually in relation $1$. Note that we have $p^1_{11} = (r^2 - 3r + 6)(r^2 - 1)/24 > 0$ for all $r \\ge 5$, so such triples must exist. The parameter $\\alpha$ will denote the number of vertices in relations $1, 2, 3$ to $u, v, w$, respectively."
+    "Let us check that the first member of the family satisfies the known feasibility conditions. We skip the family nonexistence check since the Krein array of the entire family is already included."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 5,
    "metadata": {},
+   "outputs": [],
+   "source": [
+    "p.subs(r == 5).check_feasible(skip=[\"family\"])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We now compute the triple intersection numbers with respect to three vertices $u, v, w$ mutually in relation $1$. Note that we have $p^1_{11} = (r^2 - 3r + 6)(r^2 - 1)/24 > 0$ for all $r \\ge 5$, so such triples must exist. The parameter $\\alpha$ will denote the number of vertices in relations $1, 2, 3$ to $u, v, w$, respectively."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -264,7 +280,7 @@
        "1/48*(r^5 + 2*r^3 - 48*alpha*r - 18*r^2 - 3*r + 18)/r"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -283,7 +299,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
@@ -295,7 +311,7 @@
        "t^4 + 2*t^3 + 2*t^2 - alpha + t"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -313,7 +329,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -325,7 +341,7 @@
        "-alpha + 410/3"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }