diff --git a/.ipynb_checkpoints/Untitled-checkpoint.ipynb b/.ipynb_checkpoints/Untitled-checkpoint.ipynb
new file mode 100644
index 0000000..2fd6442
--- /dev/null
+++ b/.ipynb_checkpoints/Untitled-checkpoint.ipynb
@@ -0,0 +1,6 @@
+{
+ "cells": [],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/Untitled.ipynb b/Untitled.ipynb
new file mode 100644
index 0000000..dca4f4c
--- /dev/null
+++ b/Untitled.ipynb
@@ -0,0 +1,1070 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def extrema(fr):\n",
+    "    t=[]\n",
+    "    for x in fr.free_symbols:\n",
+    "        t+=[fr.diff(x)]\n",
+    "    print(t)\n",
+    "    return solve(t)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from shiroindev import *\n",
+    "from itertools import permutations, combinations\n",
+    "sVars.seed=1\n",
+    "from IPython.display import Latex\n",
+    "sVars.print=lambda x:display(Latex(x))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "numerator: $12a^3-18a^2b+6a^2c+6ab^2-18ac^2+12b^3-18b^2c+6bc^2+12c^3$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "denominator: $4a^2b+2a^2c+2ab^2+9abc+4ac^2+4b^2c+2bc^2$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "status: 0"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "From weighted AM-GM inequality:"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$18a^2b \\le 10a^3+6ab^2+2b^3$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$18ac^2 \\le 2a^3+6a^2c+10c^3$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$18b^2c \\le 10b^3+6bc^2+2c^3$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$ 0 \\le 0 $$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "The sum of all inequalities gives us a proof of the inequality."
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "0"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "formula=cyclize('(a+b)/(2*b+c)')-2\n",
+    "prove(formula*6)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 63,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "a**2 - a*(b + c + d) + b**2 + c**2 + d**2\n",
+      "[-a*(1 - 1/(a*b**2*c)) + 2*b - 2/(a**2*b**3*c**2), -a*(1 - 1/(a*b*c**2)) + 2*c - 2/(a**2*b**2*c**3), 2*a - b - c - 2/(a**3*b**2*c**2)]\n"
+     ]
+    }
+   ],
+   "source": [
+    "point(Sm('(a^2+b^2+c^2+d^2)-a*(b+c+d)'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $a\\to s-s/(a+1)$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $b\\to s-s/(b+1)$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $c\\to s-s/(c+1)$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "numerator: $abcs^2+s^2$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "denominator: $abc+ab+ac+a+bc+b+c+1$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "status: 0"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$ 0 \\le abcs^2+s^2 $$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "The sum of all inequalities gives us a proof of the inequality."
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "0"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "prove(makesubs(Sm('-a(s-b)-b(s-c)-c(s-a)+ s^2'),'[0,s],[0,s],[0,s]'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def nonneg(formula):\n",
+    "    formula=expand(formula)\n",
+    "    for addend in formula.as_ordered_terms():\n",
+    "        coef,facts=addend.as_coeff_mul()\n",
+    "        if coef<0:\n",
+    "            return False\n",
+    "    return True"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\infty$"
+      ],
+      "text/plain": [
+       "oo"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "oo"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def symprove(formula,n):\n",
+    "    formula=S(formula)\n",
+    "    if n==0:\n",
+    "        return\n",
+    "    ls=list(formula.free_symbols)\n",
+    "    for i in range(len(ls)):\n",
+    "        a=ls[i]\n",
+    "        for j in range(i+1,len(ls)):\n",
+    "            b=ls[j]\n",
+    "            if expand(formula-formula.subs({a:b, b:a}, simultaneous=True))==S(0):\n",
+    "                formula=makesubs(formula,[[b,S('oo')]],variables=[a,b])\n",
+    "                sVars.print('$$'+latex(formula)+'$$')\n",
+    "                symprove(formula,n-1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $x\\to x+y$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$x^{2}$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "symprove('x^2-2*x*y+y^2',4)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(y, x)\n"
+     ]
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $x\\to x+y$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$x^{2} \\left(x + y\\right)^{t} - x y y^{t} + x y z^{t} + x y \\left(x + y\\right)^{t} + x y^{t} z - x z z^{t} - x z \\left(x + y\\right)^{t} + y^{2} z^{t} - 2 y z z^{t} + z^{2} z^{t}$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(y, x)\n",
+      "(y, t)\n",
+      "(x, t)\n",
+      "(y, x, t)\n",
+      "(y, t)\n",
+      "(x, t)\n",
+      "(y, x, t)\n"
+     ]
+    }
+   ],
+   "source": [
+    "provesym(Sm('x^t(x-y)(x-z) + y^t (y-z)(y-x) + z^t (z-x)(z-y)'),4)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $x\\to x+y$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle x^{2} \\left(x + y\\right)^{t} - x y y^{t} + x y z^{t} + x y \\left(x + y\\right)^{t} + x y^{t} z - x z z^{t} - x z \\left(x + y\\right)^{t} + y^{2} z^{t} - 2 y z z^{t} + z^{2} z^{t}$"
+      ],
+      "text/plain": [
+       "x**2*(x + y)**t - x*y*y**t + x*y*z**t + x*y*(x + y)**t + x*y**t*z - x*z*z**t - x*z*(x + y)**t + y**2*z**t - 2*y*z*z**t + z**2*z**t"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "makesubs(Sm('x^t(x-y)(x-z) + y^t (y-z)(y-x) + z^t (z-x)(z-y)'),'[y,oo]',variables='x')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $x\\to x+y$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle x^{2} \\left(x + y\\right)^{t} - x y y^{t} + x y z^{t} + x y \\left(x + y\\right)^{t} + x y^{t} z - x z z^{t} - x z \\left(x + y\\right)^{t} + y^{2} z^{t} - 2 y z z^{t} + z^{2} z^{t}$"
+      ],
+      "text/plain": [
+       "x**2*(x + y)**t - x*y*y**t + x*y*z**t + x*y*(x + y)**t + x*y**t*z - x*z*z**t - x*z*(x + y)**t + y**2*z**t - 2*y*z*z**t + z**2*z**t"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "makesubs(Sm('x^t*(x-y)(x-z) + y^t*(y-z)(y-x) + z^t*(z-x)(z-y)'),'[y,oo]',variables='x')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def provesym(formula,n):\n",
+    "    formula=S(formula)\n",
+    "    if n==0:\n",
+    "        return\n",
+    "    fs=list(formula.free_symbols)\n",
+    "    print \n",
+    "    for i in range(2,len(fs)+1):\n",
+    "        for fs2 in combinations(fs,i):\n",
+    "            for fsp in permutations(fs2[1:]):\n",
+    "                if expand(formula-formula.subs(zip((fs2[0],)+fsp,fsp+(fs2[0],)), simultaneous=True))==S(0):\n",
+    "                    newformula=makesubs(formula,[[fs2[0],oo]]*(len(fsp)),variables=fsp)\n",
+    "                    sVars.print(str(n)+' $$'+latex(newformula)+'$$')\n",
+    "                    provesym(newformula,n-1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $y\\to y+z$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "4 $$x^{2} x^{t} - x x^{t} y - 2 x x^{t} z + x y z^{t} - x y \\left(y + z\\right)^{t} + x^{t} y z + x^{t} z^{2} + y^{2} \\left(y + z\\right)^{t} - y z z^{t} + y z \\left(y + z\\right)^{t}$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $x\\to x+z$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "4 $$x^{2} \\left(x + z\\right)^{t} - x y y^{t} + x y z^{t} - x y \\left(x + z\\right)^{t} + x y^{t} z - x z z^{t} + x z \\left(x + z\\right)^{t} + y^{2} y^{t} - 2 y y^{t} z + y^{t} z^{2}$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $x\\to x+y$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "4 $$x^{2} \\left(x + y\\right)^{t} - x y y^{t} + x y z^{t} + x y \\left(x + y\\right)^{t} + x y^{t} z - x z z^{t} - x z \\left(x + y\\right)^{t} + y^{2} z^{t} - 2 y z z^{t} + z^{2} z^{t}$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $y\\to y+z$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $x\\to x+z$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "4 $$x^{2} \\left(x + z\\right)^{t} + x y z^{t} - x y \\left(x + z\\right)^{t} - x y \\left(y + z\\right)^{t} + y^{2} \\left(y + z\\right)^{t}$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $x\\to x+y$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "3 $$x^{2} \\left(x + y + z\\right)^{t} + x y z^{t} - x y \\left(y + z\\right)^{t} + x y \\left(x + y + z\\right)^{t} + y^{2} z^{t}$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $x\\to x+z$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $y\\to y+z$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "4 $$x^{2} \\left(x + z\\right)^{t} + x y z^{t} - x y \\left(x + z\\right)^{t} - x y \\left(y + z\\right)^{t} + y^{2} \\left(y + z\\right)^{t}$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $x\\to x+y$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "3 $$x^{2} \\left(x + y + z\\right)^{t} + x y z^{t} - x y \\left(y + z\\right)^{t} + x y \\left(x + y + z\\right)^{t} + y^{2} z^{t}$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "provesym(Sm('x^t(x-y)(x-z) + y^t (y-z)(y-x) + z^t (z-x)(z-y)'),4)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Sm('x^t(x-y)(x-z) + y^t (y-z)(y-x) + z^t (z-x)(z-y)')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle 3 x + y + 2 z$"
+      ],
+      "text/plain": [
+       "3*x + y + 2*z"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "S('x+2*y+3*z').subs(zip(S('[x,y,z]'),S('[y,z,x]')),simultaneous=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[x, y, z]"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "S('[x,y,z]')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle - t x y^{2} + t x z^{2} - x^{2} \\left(x + y\\right)^{t} + x^{2} \\left(x + z\\right)^{t} + x y y^{t} - x y \\left(x + y\\right)^{t} - x y \\left(x + z\\right)^{t} - x z z^{t} + x z \\left(x + y\\right)^{t} + x z \\left(x + z\\right)^{t} + y^{2} y^{t} - y^{2} z^{t} - 2 y y^{t} z + 2 y z z^{t} + y^{t} z^{2} - z^{2} z^{t}$"
+      ],
+      "text/plain": [
+       "-t*x*y**2 + t*x*z**2 - x**2*(x + y)**t + x**2*(x + z)**t + x*y*y**t - x*y*(x + y)**t - x*y*(x + z)**t - x*z*z**t + x*z*(x + y)**t + x*z*(x + z)**t + y**2*y**t - y**2*z**t - 2*y*y**t*z + 2*y*z*z**t + y**t*z**2 - z**2*z**t"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "formula=Sm('x^2(x+y)^t-xyy^t+xyz^t+xy(x+y)^t+xy^tz-xzzt-xz(x+y)^t+y^2z^t-2yzz^t+z^2z^t')\n",
+    "expand(formula.subs(S('[y,z],[z,y]'),simultaneous=True)-formula)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 71,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "a**2 - a*(b + c + 1/(a*b*c)) + b**2 + c**2 + 1/(a**2*b**2*c**2)\n",
+      "[-a*(1 - 1/(a*b**2*c)) + 2*b - 2/(a**2*b**3*c**2), -a*(1 - 1/(a*b*c**2)) + 2*c - 2/(a**2*b**2*c**3), 2*a - b - c - 2/(a**3*b**2*c**2)]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[]"
+      ]
+     },
+     "execution_count": 71,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def point(formula):\n",
+    "    fs=list(formula.free_symbols)\n",
+    "    il=1\n",
+    "    for s in fs[1:]:\n",
+    "        il*=s\n",
+    "    fr=formula.subs(fs[0],1/il)\n",
+    "    print(fr)\n",
+    "    return(extrema(fr))\n",
+    "point(Sm('(a^2+b^2+c^2+d^2)-a*(b+c+d)'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 69,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $a\\to 343a/216$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $b\\to 6b/7$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $c\\to 6c/7$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "Substitute $d\\to 6d/7$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "numerator: $5764801a^2-3111696ab-3111696ac-3111696ad+1679616b^2+1679616c^2+1679616d^2$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "denominator: $2286144$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "status: 0"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "From weighted AM-GM inequality:"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$3111696ab \\le 1555848a^2+1555848b^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$3111696ac \\le 1555848a^2+1555848c^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$3111696ad \\le 1555848a^2+1555848d^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$ 0 \\le 1097257a^2+123768b^2+123768c^2+123768d^2 $$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "The sum of all inequalities gives us a proof of the inequality."
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "0"
+      ]
+     },
+     "execution_count": 69,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "prove(Sm('(a^2+b^2+c^2+d^2)-a*(b+c+d)'),'343/216,6/7,6/7,6/7')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 68,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "23/375"
+      ]
+     },
+     "execution_count": 68,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "216/125-5/3"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "SageMath 9.0",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/__pycache__/shiroindev.cpython-37.pyc b/__pycache__/shiroindev.cpython-37.pyc
index ac4b1c5..e8efac0 100644
Binary files a/__pycache__/shiroindev.cpython-37.pyc and b/__pycache__/shiroindev.cpython-37.pyc differ
diff --git a/examples.ipynb b/examples.ipynb
index 4df967b..ecc0aa6 100644
--- a/examples.ipynb
+++ b/examples.ipynb
@@ -1,5 +1,12 @@
 {
  "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this notebook there are presented examples of usage of shiroin, a python library for proving inequalities of multivariate polynomials."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 1,
@@ -16,7 +23,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The first line obviously loads this package. The second one sets a seed for proving functions. If you don't write it, you can get slightly different proof each time you run a function. The next two lines\n",
+    "The first line obviously loads this package. The second one sets a seed for proving functions. If you don't write it, you can get a slightly different proof each time you run a function. The next two lines provide a nicer display of proofs, i.e. formulas will be shown instead of LaTeX code of these formulas. Note that this works on Jupyter, but not on the git page.\n",
     "\n",
     "Now let's make some proofs. We will use problems from https://www.imomath.com/index.php?options=593&lmm=0."
    ]
@@ -89,16 +96,6 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "data": {
-      "text/latex": [],
-      "text/plain": [
-       "<IPython.core.display.Latex object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/latex": [
@@ -208,7 +205,31 @@
     {
      "data": {
       "text/latex": [
-       "$$2ab \\le a^2+b^2$$$$2ac \\le a^2+c^2$$$$2bc \\le b^2+c^2$$"
+       "$$2ab \\le a^2+b^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$2ac \\le a^2+c^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$2bc \\le b^2+c^2$$"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
@@ -312,16 +333,6 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "data": {
-      "text/latex": [],
-      "text/plain": [
-       "<IPython.core.display.Latex object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/latex": [
@@ -436,7 +447,31 @@
     {
      "data": {
       "text/latex": [
-       "$$2ab \\le a^2+b^2$$$$2ac \\le a^2+c^2$$$$2ad \\le a^2+d^2$$"
+       "$$2ab \\le a^2+b^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$2ac \\le a^2+c^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$2ad \\le a^2+d^2$$"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
@@ -559,7 +594,31 @@
     {
      "data": {
       "text/latex": [
-       "$$28ab \\le 14a^2+14b^2$$$$28ac \\le 14a^2+14c^2$$$$28ad \\le 14a^2+14d^2$$"
+       "$$28ab \\le 14a^2+14b^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$28ac \\le 14a^2+14c^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$28ad \\le 14a^2+14d^2$$"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
@@ -661,16 +720,6 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "data": {
-      "text/latex": [],
-      "text/plain": [
-       "<IPython.core.display.Latex object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/latex": [
@@ -710,7 +759,7 @@
     {
      "data": {
       "text/latex": [
-       "prove(makesubs(S(\"-x**3*y + 2*x**2*y**2 - x**2 - x*y**3 + 2*x*y - y**2\"),[('y', 'inf')])"
+       "prove(makesubs(S(\"-x**3*y + 2*x**2*y**2 - x**2 - x*y**3 + 2*x*y - y**2\"),[('y', 'oo')])"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
@@ -824,7 +873,43 @@
     {
      "data": {
       "text/latex": [
-       "$$12x^2y^2 \\le 6x^3y+6xy^3$$$$3x^2y \\le 2x^3+y^3$$$$3xy^2 \\le x^3+2y^3$$$$6xy \\le 3x^2+3y^2$$"
+       "$$12x^2y^2 \\le 6x^3y+6xy^3$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$3x^2y \\le 2x^3+y^3$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$3xy^2 \\le x^3+2y^3$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$6xy \\le 3x^2+3y^2$$"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
@@ -984,7 +1069,31 @@
     {
      "data": {
       "text/latex": [
-       "$$2x^3y \\le x^4y^2+x^2$$$$4x^2y \\le x^3y^2+2x^2+xy^2$$$$2xy \\le x^2+y^2$$"
+       "$$2x^3y \\le x^4y^2+x^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$4x^2y \\le x^3y^2+2x^2+xy^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$2xy \\le x^2+y^2$$"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
@@ -1101,7 +1210,31 @@
     {
      "data": {
       "text/latex": [
-       "$$2ab \\le a^2+b^2$$$$2ac \\le a^2+c^2$$$$2bc \\le b^2+c^2$$"
+       "$$2ab \\le a^2+b^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$2ac \\le a^2+c^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$2bc \\le b^2+c^2$$"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
@@ -1201,16 +1334,6 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "data": {
-      "text/latex": [],
-      "text/plain": [
-       "<IPython.core.display.Latex object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/latex": [
@@ -1310,16 +1433,6 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "data": {
-      "text/latex": [],
-      "text/plain": [
-       "<IPython.core.display.Latex object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/latex": [
@@ -1356,7 +1469,7 @@
     }
    ],
    "source": [
-    "prove(makesubs('(x-1)^4','(1,inf)'))"
+    "prove(makesubs('(x-1)^4','(1,oo)'))"
    ]
   },
   {
@@ -1414,16 +1527,6 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "data": {
-      "text/latex": [],
-      "text/plain": [
-       "<IPython.core.display.Latex object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/latex": [
@@ -1460,7 +1563,7 @@
     }
    ],
    "source": [
-    "prove(makesubs('(x-1)^4','(-inf,1)'))"
+    "prove(makesubs('(x-1)^4','(-oo,1)'))"
    ]
   },
   {
@@ -1540,16 +1643,6 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "data": {
-      "text/latex": [],
-      "text/plain": [
-       "<IPython.core.display.Latex object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/latex": [
@@ -1673,16 +1766,6 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "data": {
-      "text/latex": [],
-      "text/plain": [
-       "<IPython.core.display.Latex object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/latex": [
@@ -1719,7 +1802,7 @@
     }
    ],
    "source": [
-    "prove(makesubs(formula,'[c,inf],[d,inf]'))"
+    "prove(makesubs(formula,'[c,oo],[d,oo]'))"
    ]
   },
   {
@@ -1847,7 +1930,7 @@
     }
    ],
    "source": [
-    "prove(makesubs(formula,'[c,inf],[d,inf]')*2)"
+    "prove(makesubs(formula,'[c,oo],[d,oo]')*2)"
    ]
   },
   {
@@ -1937,7 +2020,19 @@
     {
      "data": {
       "text/latex": [
-       "$$2a^2b^2c^3d \\le a^3bc^2d^2+ab^3c^4$$$$2a^2c^3d \\le a^3c^2d^2+ac^4$$"
+       "$$2a^2b^2c^3d \\le a^3bc^2d^2+ab^3c^4$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$2a^2c^3d \\le a^3c^2d^2+ac^4$$"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
@@ -2082,16 +2177,6 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "data": {
-      "text/latex": [],
-      "text/plain": [
-       "<IPython.core.display.Latex object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/latex": [
@@ -2165,16 +2250,6 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "data": {
-      "text/latex": [],
-      "text/plain": [
-       "<IPython.core.display.Latex object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/latex": [
@@ -2379,16 +2454,6 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "data": {
-      "text/latex": [],
-      "text/plain": [
-       "<IPython.core.display.Latex object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/latex": [
@@ -2574,7 +2639,19 @@
     {
      "data": {
       "text/latex": [
-       "$$2ab \\le a^2+b^2$$$$2bc \\le b^2+c^2$$"
+       "$$2ab \\le a^2+b^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$2bc \\le b^2+c^2$$"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
@@ -2683,7 +2760,31 @@
     {
      "data": {
       "text/latex": [
-       "$$2abc^3 \\le a^2bc^3+bc^3$$$$2ab \\le a^2+b^2$$$$2bc \\le b^2+c^2$$"
+       "$$2abc^3 \\le a^2bc^3+bc^3$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$2ab \\le a^2+b^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$2bc \\le b^2+c^2$$"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
@@ -2804,7 +2905,19 @@
     {
      "data": {
       "text/latex": [
-       "$$4abc \\le a^2c^2+2ab^2+c^2$$$$2bc \\le b^2+c^2$$"
+       "$$4abc \\le a^2c^2+2ab^2+c^2$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$2bc \\le b^2+c^2$$"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
@@ -2886,16 +2999,6 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "data": {
-      "text/latex": [],
-      "text/plain": [
-       "<IPython.core.display.Latex object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
     {
      "data": {
       "text/latex": [
@@ -3091,7 +3194,31 @@
     {
      "data": {
       "text/latex": [
-       "$$21f(1, 2, 3) \\le 11f(-1, 4, 3)+8f(3, -1, 4)+2f(4, 3, -1)$$$$21f(2, 3, 1) \\le 8f(-1, 4, 3)+2f(3, -1, 4)+11f(4, 3, -1)$$$$21f(3, 1, 2) \\le 2f(-1, 4, 3)+11f(3, -1, 4)+8f(4, 3, -1)$$"
+       "$$21f(1, 2, 3) \\le 11f(-1, 4, 3)+8f(3, -1, 4)+2f(4, 3, -1)$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$21f(2, 3, 1) \\le 8f(-1, 4, 3)+2f(3, -1, 4)+11f(4, 3, -1)$$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$$21f(3, 1, 2) \\le 2f(-1, 4, 3)+11f(3, -1, 4)+8f(4, 3, -1)$$"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
diff --git a/shiroindev.py b/shiroindev.py
index 1c21cea..873b512 100644
--- a/shiroindev.py
+++ b/shiroindev.py
@@ -26,7 +26,7 @@ for phrase in translationList:
 	sVars.translation[phrase]=phrase
 from scipy.optimize import linprog
 import random
-from sympy import S,cancel,fraction,Pow,expand,solve,latex
+from sympy import S,cancel,fraction,Pow,expand,solve,latex,oo
 import re
 def _remzero(coef,fun): 
 #coef, fun represents an expression.
@@ -76,7 +76,7 @@ def Sm(formula):
 #Adds multiplication signs and sympifies a formula.
 #For example, Sm('(2x+y)(7+5xz)') -> S('(2*x+y)*(7+5*x*z)')
 	if type(formula)==str:
-		formula.replace(' ','')
+		formula=formula.replace(' ','')
 		for i in range(2):
 			formula=re.sub(r'([0-9a-zA-Z)])([(a-zA-Z])',r'\1*\2',formula)
 	formula=S(formula)
@@ -156,7 +156,7 @@ def _list2proof(lcoef,lfun,rcoef,rfun,variables,itermax,linprogiter,_writ2=_writ
 		#them from the original one.
 		#If LHS is empty, then break. 
 	localseed=sVars.seed
-	bufer=''
+	bufer=[]
 	itern=0
 	if len(lcoef)==0: #if LHS is empty
 		sVars.print(sVars.translation['status:']+' 0')
@@ -210,13 +210,13 @@ def _list2proof(lcoef,lfun,rcoef,rfun,variables,itermax,linprogiter,_writ2=_writ
 				#step back 
 				lcoef,lfun=oldlcoef,oldlfun
 				rcoef,rfun=oldrcoef,oldrfun
-				bufer=''
+				bufer=[]
 				continue
 		if status==0:#if found a solution with real coefficients
-			if bufer:
-				sVars.print(bufer)
+			for ineq in bufer:
+				sVars.print(ineq)
 			foundreal=1
-			bufer=''
+			bufer=[]
 			oldlfun,oldrfun=lfun,rfun
 			oldlcoef,oldrcoef=lcoef[:],rcoef[:]
 			for i in range(m):
@@ -231,20 +231,22 @@ def _list2proof(lcoef,lfun,rcoef,rfun,variables,itermax,linprogiter,_writ2=_writ
 					isok=_check(lcoef[i],lfun[i],res.x[i*n:i*n+n],rfun)
 					if not isok:
 						continue
-					bufer+='$$'+_writ2(lcoef[i],lfun[i],variables)+' \\le '
+					bufer+=['']
+					bufer[-1]+='$$'+_writ2(lcoef[i],lfun[i],variables)+' \\le '
 					lcoef[i]=0
 					for j in range(n):
 						rcoef[j]-=int(round(res.x[i*n+j]))
 					for j,k in zip(res.x[i*n:i*n+n],rfun):
 						if j<0.0001:
 							continue
-						if(c):bufer+='+'
+						if(c):bufer[-1]+='+'
 						else:c=1
-						bufer+=_writ2(int(round(j)),k,variables)
-					bufer+='$$'
+						bufer[-1]+=_writ2(int(round(j)),k,variables)
+					bufer[-1]+='$$'
 			lcoef,lfun=_remzero(lcoef,lfun)
 			rcoef,rfun=_remzero(rcoef,rfun)
-	sVars.print(bufer)
+	for ineq in bufer:
+		sVars.print(ineq)
 	lhs='+'.join([_writ2(c,f,variables) for c,f in zip(lcoef,lfun)])
 	if lhs=='':
 		lhs='0'
@@ -295,7 +297,7 @@ def prove(formula,values=None,variables=None,niter=200,linprogiter=10000):
 		"You can assume without loss of generality that "]+
 		' >= '.join([str(x) for x in fs])+'. '+sVars.translation['Try'])
 		sVars.print('prove(makesubs(S("'+str(num)+'"),'+
-		str([(str(x),'inf') for x in variables[1:]])+')')
+		str([(str(x),'oo') for x in variables[1:]])+')')
 	return st
 def powerprove(formula,values=None,variables=None,niter=200,linprogiter=10000):
 #This is a bruteforce and ineffective function for proving inequalities.
@@ -339,17 +341,17 @@ def makesubs(formula,intervals,values=None,variables=None,numden=False):
 		equations=[]
 	for var,interval in zip(variables,intervals):
 		end1,end2=interval
-		if end1 in {S('-inf'),S('inf')}:
+		if end1 in {S('-oo'),S('oo')}:
 			end1,end2=end2,end1
-		if {end1,end2}=={S('-inf'),S('inf')}:
+		if {end1,end2}=={S('-oo'),S('oo')}:
 			formula=formula.subs(var,var-1/var)
 			equations=[equation.subs(var,var-1/var) for equation in equations]
 			sVars.print(sVars.translation['Substitute']+' $'+str(var)+'\\to '+var-1/var+'$')
-		elif end2==S('inf'):
+		elif end2==S('oo'):
 			formula=formula.subs(var,end1+var)
 			equations=[equation.subs(var,end1+var) for equation in equations]
 			sVars.print(sVars.translation['Substitute']+' $'+str(var)+'\\to '+sstr(end1+var)+'$')
-		elif end2==S('-inf'):
+		elif end2==S('-oo'):
 			formula=formula.subs(var,end1-var)
 			equations=[equation.subs(var,end1-var) for equation in equations]
 			sVars.print(sVars.translation['Substitute']+" $"+str(var)+'\\to '+sstr(end1-var)+'$')
@@ -359,7 +361,7 @@ def makesubs(formula,intervals,values=None,variables=None,numden=False):
 			equations=[equation.subs(var,end2+(end1-end2)/var) for equation in equations]
 	num,den=fractioncancel(formula)
 	for var,interval in zip(variables,intervals):
-		if {interval[0],interval[1]} & {S('inf'),S('-inf')}==set():
+		if {interval[0],interval[1]} & {S('oo'),S('-oo')}==set():
 			num=num.subs(var,var+1)
 			den=den.subs(var,var+1)
 			equations=[equation.subs(var,var+1) for equation in equations]