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\\frac{101}{82} & 1 & 0 & \\frac{2}{41} & -\\frac{3}{82} & 0 & \\frac{4}{41} & \\frac{3}{82} & 0 & -\\frac{4}{41} & \\frac{1010}{41} \\\\\n", "{\\color{red}{t}}_{2} & -\\frac{579}{164} & 0 & 0 & -\\frac{147}{41} & \\frac{195}{164} & -1 & -\\frac{55}{82} & -\\frac{195}{164} & 1 & \\frac{55}{82} & \\frac{3050}{41} \\\\\n", "{x}_{3} & -\\frac{23}{164} & 0 & 1 & \\frac{29}{41} & -\\frac{5}{164} & 0 & -\\frac{7}{82} & \\frac{5}{164} & 0 & \\frac{7}{82} & \\frac{910}{41} \\\\\n", "\\hline\n", " {W_{ind}} & \\frac{579}{164} & 0 & 0 & \\frac{147}{41} & -\\frac{195}{164} & 1 & \\frac{55}{82} & \\frac{359}{164} & 0 & \\frac{27}{82} & \\frac{3050}{41}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{101}{82} & 1 & 0 & \\frac{2}{41} & -\\frac{3}{82} & 0 & \\frac{4}{41} & \\frac{3}{82} & 0 & -\\frac{4}{41} & \\frac{1010}{41} \\\\\n", "{\\color{red}{t}}_{2} & -\\frac{579}{164} & 0 & 0 & -\\frac{147}{41} & \\frac{195}{164} & -1 & -\\frac{55}{82} & -\\frac{195}{164} & 1 & \\frac{55}{82} & \\frac{3050}{41} \\\\\n", "{x}_{3} & -\\frac{23}{164} & 0 & 1 & \\frac{29}{41} & -\\frac{5}{164} & 0 & -\\frac{7}{82} & \\frac{5}{164} & 0 & \\frac{7}{82} & \\frac{910}{41} \\\\\n", "\\hline\n", " {W_{ind}} & \\frac{579}{164} & 0 & 0 & \\frac{147}{41} & -\\frac{195}{164} & 1 & \\frac{55}{82} & \\frac{359}{164} & 0 & \\frac{27}{82} & \\frac{3050}{41}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 t1 t2 t3| rhs]\n", "[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ x2| 101/82 1 0 2/41 -3/82 0 4/41 3/82 0 -4/41| 1010/41]\n", "[ t2|-579/164 0 0 -147/41 195/164 -1 -55/82 -195/164 1 55/82| 3050/41]\n", "[ x3| -23/164 0 1 29/41 -5/164 0 -7/82 5/164 0 7/82| 910/41]\n", "[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ W| 579/164 0 0 147/41 -195/164 1 55/82 359/164 0 27/82| 3050/41]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 5 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{73}{65} & 1 & 0 & -\\frac{4}{65} & 0 & -\\frac{2}{65} & \\frac{1}{13} & 0 & \\frac{2}{65} & -\\frac{1}{13} & \\frac{350}{13} \\\\\n", "{\\color{green}{s}}_{1} & -\\frac{193}{65} & 0 & 0 & -\\frac{196}{65} & 1 & -\\frac{164}{195} & -\\frac{22}{39} & -1 & \\frac{164}{195} & \\frac{22}{39} & \\frac{2440}{39} \\\\\n", "{x}_{3} & -\\frac{3}{13} & 0 & 1 & \\frac{8}{13} & 0 & -\\frac{1}{39} & -\\frac{4}{39} & 0 & \\frac{1}{39} & \\frac{4}{39} & \\frac{940}{39} \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{73}{65} & 1 & 0 & -\\frac{4}{65} & 0 & -\\frac{2}{65} & \\frac{1}{13} & 0 & \\frac{2}{65} & -\\frac{1}{13} & \\frac{350}{13} \\\\\n", "{\\color{green}{s}}_{1} & -\\frac{193}{65} & 0 & 0 & -\\frac{196}{65} & 1 & -\\frac{164}{195} & -\\frac{22}{39} & -1 & \\frac{164}{195} & \\frac{22}{39} & \\frac{2440}{39} \\\\\n", "{x}_{3} & -\\frac{3}{13} & 0 & 1 & \\frac{8}{13} & 0 & -\\frac{1}{39} & -\\frac{4}{39} & 0 & \\frac{1}{39} & \\frac{4}{39} & \\frac{940}{39} \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 t1 t2 t3| rhs]\n", "[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ x2| 73/65 1 0 -4/65 0 -2/65 1/13 0 2/65 -1/13| 350/13]\n", "[ s1| -193/65 0 0 -196/65 1 -164/195 -22/39 -1 164/195 22/39| 2440/39]\n", "[ x3| -3/13 0 1 8/13 0 -1/39 -4/39 0 1/39 4/39| 940/39]\n", "[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ W| 0 0 0 0 0 0 0 1 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{73}{65} & 1 & 0 & -\\frac{4}{65} & 0 & -\\frac{2}{65} & \\frac{1}{13} & 0 & \\frac{2}{65} & -\\frac{1}{13} & \\frac{350}{13} \\\\\n", "{\\color{green}{s}}_{1} & -\\frac{193}{65} & 0 & 0 & -\\frac{196}{65} & 1 & -\\frac{164}{195} & -\\frac{22}{39} & -1 & \\frac{164}{195} & \\frac{22}{39} & \\frac{2440}{39} \\\\\n", "{x}_{3} & -\\frac{3}{13} & 0 & 1 & \\frac{8}{13} & 0 & -\\frac{1}{39} & -\\frac{4}{39} & 0 & \\frac{1}{39} & \\frac{4}{39} & \\frac{940}{39} \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{73}{65} & 1 & 0 & -\\frac{4}{65} & 0 & -\\frac{2}{65} & \\frac{1}{13} & 0 & \\frac{2}{65} & -\\frac{1}{13} & \\frac{350}{13} \\\\\n", "{\\color{green}{s}}_{1} & -\\frac{193}{65} & 0 & 0 & -\\frac{196}{65} & 1 & -\\frac{164}{195} & -\\frac{22}{39} & -1 & \\frac{164}{195} & \\frac{22}{39} & \\frac{2440}{39} \\\\\n", "{x}_{3} & -\\frac{3}{13} & 0 & 1 & \\frac{8}{13} & 0 & -\\frac{1}{39} & -\\frac{4}{39} & 0 & \\frac{1}{39} & \\frac{4}{39} & \\frac{940}{39} \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 t1 t2 t3| rhs]\n", "[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ x2| 73/65 1 0 -4/65 0 -2/65 1/13 0 2/65 -1/13| 350/13]\n", "[ s1| -193/65 0 0 -196/65 1 -164/195 -22/39 -1 164/195 22/39| 2440/39]\n", "[ x3| -3/13 0 1 8/13 0 -1/39 -4/39 0 1/39 4/39| 940/39]\n", "[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ W| 0 0 0 0 0 0 0 1 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{73}{65} & 1 & 0 & -\\frac{4}{65} & 0 & -\\frac{2}{65} & \\frac{1}{13} & \\frac{350}{13} \\\\\n", "{\\color{green}{s}}_{1} & -\\frac{193}{65} & 0 & 0 & -\\frac{196}{65} & 1 & -\\frac{164}{195} & -\\frac{22}{39} & \\frac{2440}{39} \\\\\n", "{x}_{3} & -\\frac{3}{13} & 0 & 1 & \\frac{8}{13} & 0 & -\\frac{1}{39} & -\\frac{4}{39} & \\frac{940}{39} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{14}{65} & 0 & 0 & \\frac{72}{65} & 0 & \\frac{43}{195} & \\frac{11}{39} & \\frac{7850}{39}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{73}{65} & 1 & 0 & -\\frac{4}{65} & 0 & -\\frac{2}{65} & \\frac{1}{13} & \\frac{350}{13} \\\\\n", "{\\color{green}{s}}_{1} & -\\frac{193}{65} & 0 & 0 & -\\frac{196}{65} & 1 & -\\frac{164}{195} & -\\frac{22}{39} & \\frac{2440}{39} \\\\\n", "{x}_{3} & -\\frac{3}{13} & 0 & 1 & \\frac{8}{13} & 0 & -\\frac{1}{39} & -\\frac{4}{39} & \\frac{940}{39} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{14}{65} & 0 & 0 & \\frac{72}{65} & 0 & \\frac{43}{195} & \\frac{11}{39} & \\frac{7850}{39}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3| rhs]\n", "[--------+--------------------------------------------------------------+--------]\n", "[ x2| 73/65 1 0 -4/65 0 -2/65 1/13| 350/13]\n", "[ s1| -193/65 0 0 -196/65 1 -164/195 -22/39| 2440/39]\n", "[ x3| -3/13 0 1 8/13 0 -1/39 -4/39| 940/39]\n", "[--------+--------------------------------------------------------------+--------]\n", "[ Z| -14/65 0 0 72/65 0 43/195 11/39| 7850/39]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 1 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{65}{73} & 0 & -\\frac{4}{73} & 0 & -\\frac{2}{73} & \\frac{5}{73} & \\frac{1750}{73} \\\\\n", "{\\color{green}{s}}_{1} & 0 & \\frac{193}{73} & 0 & -\\frac{232}{73} & 1 & -\\frac{202}{219} & -\\frac{79}{219} & \\frac{29290}{219} \\\\\n", "{x}_{3} & 0 & \\frac{15}{73} & 1 & \\frac{44}{73} & 0 & -\\frac{7}{219} & -\\frac{19}{219} & \\frac{6490}{219} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & \\frac{14}{73} & 0 & \\frac{80}{73} & 0 & \\frac{47}{219} & \\frac{65}{219} & \\frac{42950}{219}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{65}{73} & 0 & -\\frac{4}{73} & 0 & -\\frac{2}{73} & \\frac{5}{73} & \\frac{1750}{73} \\\\\n", "{\\color{green}{s}}_{1} & 0 & \\frac{193}{73} & 0 & -\\frac{232}{73} & 1 & -\\frac{202}{219} & -\\frac{79}{219} & \\frac{29290}{219} \\\\\n", "{x}_{3} & 0 & \\frac{15}{73} & 1 & \\frac{44}{73} & 0 & -\\frac{7}{219} & -\\frac{19}{219} & \\frac{6490}{219} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & \\frac{14}{73} & 0 & \\frac{80}{73} & 0 & \\frac{47}{219} & \\frac{65}{219} & \\frac{42950}{219}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3| rhs]\n", "[---------+---------------------------------------------------------------------+---------]\n", "[ x1| 1 65/73 0 -4/73 0 -2/73 5/73| 1750/73]\n", "[ s1| 0 193/73 0 -232/73 1 -202/219 -79/219|29290/219]\n", "[ x3| 0 15/73 1 44/73 0 -7/219 -19/219| 6490/219]\n", "[---------+---------------------------------------------------------------------+---------]\n", "[ Z| 0 14/73 0 80/73 0 47/219 65/219|42950/219]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{65}{73} & 0 & -\\frac{4}{73} & 0 & -\\frac{2}{73} & \\frac{5}{73} & \\frac{1750}{73} \\\\\n", "{\\color{green}{s}}_{1} & 0 & \\frac{193}{73} & 0 & -\\frac{232}{73} & 1 & -\\frac{202}{219} & -\\frac{79}{219} & \\frac{29290}{219} \\\\\n", "{x}_{3} & 0 & \\frac{15}{73} & 1 & \\frac{44}{73} & 0 & -\\frac{7}{219} & -\\frac{19}{219} & \\frac{6490}{219} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & \\frac{14}{73} & 0 & \\frac{80}{73} & 0 & \\frac{47}{219} & \\frac{65}{219} & \\frac{42950}{219}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{65}{73} & 0 & -\\frac{4}{73} & 0 & -\\frac{2}{73} & \\frac{5}{73} & \\frac{1750}{73} \\\\\n", "{\\color{green}{s}}_{1} & 0 & \\frac{193}{73} & 0 & -\\frac{232}{73} & 1 & -\\frac{202}{219} & -\\frac{79}{219} & \\frac{29290}{219} \\\\\n", "{x}_{3} & 0 & \\frac{15}{73} & 1 & \\frac{44}{73} & 0 & -\\frac{7}{219} & -\\frac{19}{219} & \\frac{6490}{219} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & \\frac{14}{73} & 0 & \\frac{80}{73} & 0 & \\frac{47}{219} & \\frac{65}{219} & \\frac{42950}{219}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3| rhs]\n", "[---------+---------------------------------------------------------------------+---------]\n", "[ x1| 1 65/73 0 -4/73 0 -2/73 5/73| 1750/73]\n", "[ s1| 0 193/73 0 -232/73 1 -202/219 -79/219|29290/219]\n", "[ x3| 0 15/73 1 44/73 0 -7/219 -19/219| 6490/219]\n", "[---------+---------------------------------------------------------------------+---------]\n", "[ Z| 0 14/73 0 80/73 0 47/219 65/219|42950/219]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='min' #max o min\n", "n=4 # número de variables x's\n", "m=3 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[2,3,5,4] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[15,14,16,12],\n", "[19,20,15,8],\n", "[-7,-5,6,4]\n", "])\n", "\n", "b=matrix(QQ,m,1,[700,900,10]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[-1,-1,-1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "\n", "#######################################################\n", "\n", "\n", "\n", "\n", "\n", "\n", "#load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "load('https://sage.unex.es/501708/simplex2023Auto_MC.sage')" ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "#v=matrix(QQ,1,nv,[0,-193/73,0,-(232/73)*(163/56),0,-202*163/(219*56),-(79/219)*(163/56)] ); R=-163/219;\n", "#añadeRes(v,R) # hecho sin mejoras" ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$ " ], "text/latex": 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"[-----------+-----------------------------------------------------------------------------------------------------------------------+-----------]\n", "[ Z| 0 0 0 38/73 0 5/219 23/219 0 287/146 0| 43118/219]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(2)" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ NO NO NO -23.365 NO -0.19834 -113.14 NO -0.072539 NO]" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(6)" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & -\\frac{3693}{1351} & 0 & -\\frac{3877}{4053} & -\\frac{6665}{8106} & 0 & 0 & \\frac{65}{193} & \\frac{11785}{579} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{1013}{91} & 1 & -\\frac{335}{91} & -\\frac{547}{182} & 0 & 0 & 1 & 123 \\\\\n", "{x}_{3} & 0 & 0 & 1 & -\\frac{271}{17563} & 0 & -\\frac{12982}{52689} & -\\frac{30803}{105378} & 0 & 0 & \\frac{15}{193} & \\frac{16675}{579} \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{52837}{17563} & 0 & \\frac{54983}{52689} & \\frac{105415}{105378} & 0 & 0 & -\\frac{73}{193} & \\frac{2353}{579} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & \\frac{271}{17563} & 0 & \\frac{669737}{4215120} & \\frac{231029}{4215120} & 1 & 0 & -\\frac{15}{193} & \\frac{116}{579} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & \\frac{592}{720083} & 0 & \\frac{9176}{2160249} & \\frac{74}{2160249} & 0 & 1 & -\\frac{292}{7913} & \\frac{148}{23739} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{1302}{2509} & 0 & \\frac{109}{7527} & \\frac{790}{7527} & 0 & 0 & \\frac{14}{193} & \\frac{114004}{579}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & -\\frac{3693}{1351} & 0 & -\\frac{3877}{4053} & -\\frac{6665}{8106} & 0 & 0 & \\frac{65}{193} & \\frac{11785}{579} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{1013}{91} & 1 & -\\frac{335}{91} & -\\frac{547}{182} & 0 & 0 & 1 & 123 \\\\\n", "{x}_{3} & 0 & 0 & 1 & -\\frac{271}{17563} & 0 & -\\frac{12982}{52689} & -\\frac{30803}{105378} & 0 & 0 & \\frac{15}{193} & \\frac{16675}{579} \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{52837}{17563} & 0 & \\frac{54983}{52689} & \\frac{105415}{105378} & 0 & 0 & -\\frac{73}{193} & \\frac{2353}{579} 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0 52837/17563 0 54983/52689 105415/105378 0 0 -73/193| 2353/579]\n", "[ s4| 0 0 0 271/17563 0 669737/4215120 231029/4215120 1 0 -15/193| 116/579]\n", "[ s5| 0 0 0 592/720083 0 9176/2160249 74/2160249 0 1 -292/7913| 148/23739]\n", "[--------------+-----------------------------------------------------------------------------------------------------------------------------------------------------+--------------]\n", "[ Z| 0 0 0 1302/2509 0 109/7527 790/7527 0 0 14/193| 114004/579]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(6,9)" ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "[205/579, 0, 463/579, 37/579, 116/579, 148/23739]" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pardec()" ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & -\\frac{3693}{1351} & 0 & -\\frac{3877}{4053} & -\\frac{6665}{8106} & 0 & 0 & \\frac{65}{193} & 0 & \\frac{11785}{579} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{1013}{91} & 1 & -\\frac{335}{91} & -\\frac{547}{182} & 0 & 0 & 1 & 0 & 123 \\\\\n", "{x}_{3} & 0 & 0 & 1 & -\\frac{271}{17563} & 0 & -\\frac{12982}{52689} & -\\frac{30803}{105378} & 0 & 0 & \\frac{15}{193} & 0 & \\frac{16675}{579} \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{52837}{17563} & 0 & \\frac{54983}{52689} & \\frac{105415}{105378} & 0 & 0 & -\\frac{73}{193} & 0 & \\frac{2353}{579} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & \\frac{271}{17563} & 0 & \\frac{669737}{4215120} & \\frac{231029}{4215120} & 1 & 0 & -\\frac{15}{193} & 0 & \\frac{116}{579} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & \\frac{592}{720083} & 0 & \\frac{9176}{2160249} & \\frac{74}{2160249} & 0 & 1 & -\\frac{292}{7913} & 0 & \\frac{148}{23739} \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & -\\frac{148}{17563} & 0 & -\\frac{2294}{52689} & -\\frac{37}{105378} & 0 & 0 & -\\frac{2701}{104606} & 1 & -\\frac{37}{579} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{1302}{2509} & 0 & \\frac{109}{7527} & \\frac{790}{7527} & 0 & 0 & \\frac{14}{193} & 0 & \\frac{114004}{579}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & -\\frac{3693}{1351} & 0 & -\\frac{3877}{4053} & -\\frac{6665}{8106} & 0 & 0 & \\frac{65}{193} & 0 & \\frac{11785}{579} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{1013}{91} & 1 & -\\frac{335}{91} & -\\frac{547}{182} & 0 & 0 & 1 & 0 & 123 \\\\\n", "{x}_{3} & 0 & 0 & 1 & -\\frac{271}{17563} & 0 & -\\frac{12982}{52689} & -\\frac{30803}{105378} & 0 & 0 & \\frac{15}{193} & 0 & \\frac{16675}{579} \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{52837}{17563} & 0 & \\frac{54983}{52689} & \\frac{105415}{105378} & 0 & 0 & -\\frac{73}{193} & 0 & \\frac{2353}{579} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & \\frac{271}{17563} & 0 & \\frac{669737}{4215120} & \\frac{231029}{4215120} & 1 & 0 & -\\frac{15}{193} & 0 & \\frac{116}{579} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & \\frac{592}{720083} & 0 & \\frac{9176}{2160249} & \\frac{74}{2160249} & 0 & 1 & -\\frac{292}{7913} & 0 & \\frac{148}{23739} \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & -\\frac{148}{17563} & 0 & -\\frac{2294}{52689} & -\\frac{37}{105378} & 0 & 0 & -\\frac{2701}{104606} & 1 & -\\frac{37}{579} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{1302}{2509} & 0 & \\frac{109}{7527} & \\frac{790}{7527} & 0 & 0 & \\frac{14}{193} & 0 & \\frac{114004}{579}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[--------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------]\n", "[ x1| 1 0 0 -3693/1351 0 -3877/4053 -6665/8106 0 0 65/193 0| 11785/579]\n", "[ s1| 0 0 0 -1013/91 1 -335/91 -547/182 0 0 1 0| 123]\n", "[ x3| 0 0 1 -271/17563 0 -12982/52689 -30803/105378 0 0 15/193 0| 16675/579]\n", "[ x2| 0 1 0 52837/17563 0 54983/52689 105415/105378 0 0 -73/193 0| 2353/579]\n", "[ s4| 0 0 0 271/17563 0 669737/4215120 231029/4215120 1 0 -15/193 0| 116/579]\n", "[ s5| 0 0 0 592/720083 0 9176/2160249 74/2160249 0 1 -292/7913 0| 148/23739]\n", "[ s7| 0 0 0 -148/17563 0 -2294/52689 -37/105378 0 0 -2701/104606 1| -37/579]\n", "[--------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------]\n", "[ Z| 0 0 0 1302/2509 0 109/7527 790/7527 0 0 14/193 0| 114004/579]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(4)" ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ NO NO NO -61.581 NO -0.33261 -298.92 NO NO -2.8093 NO]" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(7)" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & -\\frac{79}{31} & 0 & 0 & -\\frac{101}{124} & 0 & 0 & \\frac{30381}{33604} & -\\frac{50401}{2294} & \\frac{1349}{62} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{323}{31} & 1 & 0 & -\\frac{369}{124} & 0 & 0 & \\frac{106969}{33604} & -\\frac{193965}{2294} & \\frac{7961}{62} \\\\\n", "{x}_{3} & 0 & 0 & 1 & \\frac{1}{31} & 0 & 0 & -\\frac{9}{31} & 0 & 0 & \\frac{3761}{16802} & -\\frac{6491}{1147} & \\frac{904}{31} \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{87}{31} & 0 & 0 & \\frac{123}{124} & 0 & 0 & -\\frac{33507}{33604} & \\frac{54983}{2294} & \\frac{157}{62} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & -\\frac{19}{1240} & 0 & 0 & \\frac{531}{9920} & 1 & 0 & -\\frac{462257}{2688320} & \\frac{18101}{4960} & -\\frac{163}{4960} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -\\frac{438}{11111} & \\frac{4}{41} & 0 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & \\frac{6}{31} & 0 & 1 & \\frac{1}{124} & 0 & 0 & \\frac{19929}{33604} & -\\frac{52689}{2294} & \\frac{91}{62} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{16}{31} & 0 & 0 & \\frac{13}{124} & 0 & 0 & \\frac{2149}{33604} & \\frac{763}{2294} & \\frac{12209}{62}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & -\\frac{79}{31} & 0 & 0 & -\\frac{101}{124} & 0 & 0 & \\frac{30381}{33604} & -\\frac{50401}{2294} & \\frac{1349}{62} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{323}{31} & 1 & 0 & -\\frac{369}{124} & 0 & 0 & \\frac{106969}{33604} & -\\frac{193965}{2294} & \\frac{7961}{62} \\\\\n", "{x}_{3} & 0 & 0 & 1 & \\frac{1}{31} & 0 & 0 & -\\frac{9}{31} & 0 & 0 & \\frac{3761}{16802} & -\\frac{6491}{1147} & \\frac{904}{31} \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{87}{31} & 0 & 0 & \\frac{123}{124} & 0 & 0 & -\\frac{33507}{33604} & \\frac{54983}{2294} & \\frac{157}{62} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & -\\frac{19}{1240} & 0 & 0 & \\frac{531}{9920} & 1 & 0 & -\\frac{462257}{2688320} & \\frac{18101}{4960} & -\\frac{163}{4960} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -\\frac{438}{11111} & \\frac{4}{41} & 0 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & \\frac{6}{31} & 0 & 1 & \\frac{1}{124} & 0 & 0 & \\frac{19929}{33604} & -\\frac{52689}{2294} & \\frac{91}{62} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{16}{31} & 0 & 0 & \\frac{13}{124} & 0 & 0 & \\frac{2149}{33604} & \\frac{763}{2294} & \\frac{12209}{62}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[---------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------]\n", "[ x1| 1 0 0 -79/31 0 0 -101/124 0 0 30381/33604 -50401/2294| 1349/62]\n", "[ s1| 0 0 0 -323/31 1 0 -369/124 0 0 106969/33604 -193965/2294| 7961/62]\n", "[ x3| 0 0 1 1/31 0 0 -9/31 0 0 3761/16802 -6491/1147| 904/31]\n", "[ x2| 0 1 0 87/31 0 0 123/124 0 0 -33507/33604 54983/2294| 157/62]\n", "[ s4| 0 0 0 -19/1240 0 0 531/9920 1 0 -462257/2688320 18101/4960| -163/4960]\n", "[ s5| 0 0 0 0 0 0 0 0 1 -438/11111 4/41| 0]\n", "[ s2| 0 0 0 6/31 0 1 1/124 0 0 19929/33604 -52689/2294| 91/62]\n", "[---------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------]\n", "[ Z| 0 0 0 16/31 0 0 13/124 0 0 2149/33604 763/2294| 12209/62]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(7,6)" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ NO NO NO -33.684 NO NO NO NO NO -0.37191 NO]" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(5)" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & -\\frac{1215251}{462257} & 0 & 0 & -\\frac{492833}{924514} & \\frac{2430480}{462257} & 0 & 0 & -\\frac{47595730}{17103509} & \\frac{9977945}{462257} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{4947543}{462257} & 1 & 0 & -\\frac{1835037}{924514} & \\frac{8557520}{462257} & 0 & 0 & -\\frac{290654546}{17103509} & \\frac{59074065}{462257} \\\\\n", "{x}_{3} & 0 & 0 & 1 & \\frac{5691}{462257} & 0 & 0 & -\\frac{203985}{924514} & \\frac{601760}{462257} & 0 & 0 & -\\frac{15536430}{17103509} & \\frac{13460235}{462257} \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{1338375}{462257} & 0 & 0 & \\frac{630087}{924514} & -\\frac{2680560}{462257} & 0 & 0 & \\frac{47990306}{17103509} & \\frac{1258645}{462257} \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & \\frac{41192}{462257} & 0 & 0 & -\\frac{143901}{462257} & -\\frac{2688320}{462257} & 0 & 1 & -\\frac{9810742}{462257} & \\frac{88346}{462257} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & \\frac{66576}{18952537} & 0 & 0 & -\\frac{232578}{18952537} & -\\frac{4344960}{18952537} & 1 & 0 & -\\frac{14007448}{18952537} & \\frac{142788}{18952537} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & \\frac{65040}{462257} & 0 & 1 & \\frac{89069}{462257} & \\frac{1594320}{462257} & 0 & 0 & -\\frac{177559200}{17103509} & \\frac{626080}{462257} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{235950}{462257} & 0 & 0 & \\frac{57665}{462257} & \\frac{171920}{462257} & 0 & 0 & \\frac{28902692}{17103509} & \\frac{91033000}{462257}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & 0 & -\\frac{1215251}{462257} & 0 & 0 & -\\frac{492833}{924514} & \\frac{2430480}{462257} & 0 & 0 & -\\frac{47595730}{17103509} & \\frac{9977945}{462257} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & -\\frac{4947543}{462257} & 1 & 0 & -\\frac{1835037}{924514} & \\frac{8557520}{462257} & 0 & 0 & -\\frac{290654546}{17103509} & \\frac{59074065}{462257} \\\\\n", "{x}_{3} & 0 & 0 & 1 & \\frac{5691}{462257} & 0 & 0 & -\\frac{203985}{924514} & \\frac{601760}{462257} & 0 & 0 & -\\frac{15536430}{17103509} & \\frac{13460235}{462257} \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{1338375}{462257} & 0 & 0 & \\frac{630087}{924514} & -\\frac{2680560}{462257} & 0 & 0 & \\frac{47990306}{17103509} & \\frac{1258645}{462257} \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & \\frac{41192}{462257} & 0 & 0 & -\\frac{143901}{462257} & -\\frac{2688320}{462257} & 0 & 1 & -\\frac{9810742}{462257} & \\frac{88346}{462257} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & \\frac{66576}{18952537} & 0 & 0 & -\\frac{232578}{18952537} & -\\frac{4344960}{18952537} & 1 & 0 & -\\frac{14007448}{18952537} & \\frac{142788}{18952537} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & \\frac{65040}{462257} & 0 & 1 & \\frac{89069}{462257} & \\frac{1594320}{462257} & 0 & 0 & -\\frac{177559200}{17103509} & \\frac{626080}{462257} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & \\frac{235950}{462257} & 0 & 0 & \\frac{57665}{462257} & \\frac{171920}{462257} & 0 & 0 & \\frac{28902692}{17103509} & \\frac{91033000}{462257}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[-------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------]\n", "[ x1| 1 0 0 -1215251/462257 0 0 -492833/924514 2430480/462257 0 0 -47595730/17103509| 9977945/462257]\n", "[ s1| 0 0 0 -4947543/462257 1 0 -1835037/924514 8557520/462257 0 0 -290654546/17103509| 59074065/462257]\n", "[ x3| 0 0 1 5691/462257 0 0 -203985/924514 601760/462257 0 0 -15536430/17103509| 13460235/462257]\n", "[ x2| 0 1 0 1338375/462257 0 0 630087/924514 -2680560/462257 0 0 47990306/17103509| 1258645/462257]\n", "[ s6| 0 0 0 41192/462257 0 0 -143901/462257 -2688320/462257 0 1 -9810742/462257| 88346/462257]\n", "[ s5| 0 0 0 66576/18952537 0 0 -232578/18952537 -4344960/18952537 1 0 -14007448/18952537| 142788/18952537]\n", "[ s2| 0 0 0 65040/462257 0 1 89069/462257 1594320/462257 0 0 -177559200/17103509| 626080/462257]\n", "[-------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------]\n", "[ Z| 0 0 0 235950/462257 0 0 57665/462257 171920/462257 0 0 28902692/17103509| 91033000/462257]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(5,10)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "v=matrix(QQ,1,nv,[0,-47/73,0,-(60/73)*(163/56),0,-202*163/(219*56),-(79/219)*(163/56)] ); R=-163/219;\n", "añadeRes(v,R) # hecho con la segunda mejora" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "cocientesD(4)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "cambio(4,6)" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.5", "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": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 4 }