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</o:shapelayout></xml><![endif]--></head><body lang=ES-CO link=blue vlink=purple style='tab-interval:35.4pt'><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;color:#1F497D;mso-fareast-language:EN-US'>Hola Ricardo, facilítame la vida, indícame quien está mal con respecto a las <u>matemática</u>, las calculadoras o Python, espero que la respuesta no sea “ninguna” porque entonces tendría que afirmar que sabía más antes de preguntar.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;color:#1F497D;mso-fareast-language:EN-US'>Saludos, Johnny Alonso<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><a name="_MailOriginal"><b><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-font-family:"Times New Roman";mso-ansi-language:ES'>De:</span></b></a><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-fareast-font-family:"Times New Roman";mso-ansi-language:ES'> Python-es [mailto:python-es-bounces+johnny.alonso.quintero=gmail.com@python.org] <b>En nombre de </b>Miguel Manzano<br><b>Enviado el:</b> domingo, 25 de diciembre de 2016 1:55 a. m.<br><b>Para:</b> La lista de python en castellano<br><b>Asunto:</b> Re: [Python-es] Python 3.5.2<o:p></o:p></span></span></p><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>Ricardo y David. Nunca pensé que iba a disfrutar tanto de una conversación sobre precedencia de operadores. ;P<o:p></o:p></span></p><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>Saludos.<o:p></o:p></span></p></div></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>El 25/12/2016 7:15, "Ricardo Cárdenes" <</span><a href="mailto:ricardo.cardenes@gmail.com"><span style='mso-bookmark:_MailOriginal'>ricardo.cardenes@gmail.com</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'>> escribió:<o:p></o:p></span></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;mso-border-left-alt:solid #CCCCCC .75pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-right:0cm'><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>Añado, al respecto de calculadoras: en una normal, <b>donde no se pueden introducir expresiones aritméticas</b>, sino que lo que hay en pantalla se toma siempre como un operando completo, hubiese esperado lo contrario, ya que estoy solicitando explícitamente elevar al cuadrado el número -2 y entonces no hay ningún tipo de duda de que el resultado será "4" y no "-4"<o:p></o:p></span></p><div><div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>2016-12-24 20:05 GMT-10:00 Ricardo Cárdenes <</span><a href="mailto:ricardo.cardenes@gmail.com" target="_blank"><span style='mso-bookmark:_MailOriginal'>ricardo.cardenes@gmail.com</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'>>:<o:p></o:p></span></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;mso-border-left-alt:solid #CCCCCC .75pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-right:0cm'><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>Mire señor Alonso, yo no le he respondido a la ligera.<o:p></o:p></span></p><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>Primero, como le dije, el caso de Python no es una excepción, sino *la regla* en cuanto a lenguajes de programación *que implementan la exponenciación* en su sintaxis - es decir, la precedencia está dictada por el propio lenguaje. Es decir, no lo busque en C, o en C++, o en Java, etc. De hecho, me molesté en documentarme brevemente antes de responder. Y mira que no hay muchos lenguajes que implementen la exponenciación en su sintaxise, pero le dejo una lista (no exhaustiva), sin irme a casos demasiado exóticos:<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'> - ADA: los operadores de MAYOR precedencia son abs (valor absoluto), not (negación lógica) y ** (exponenciación). Dos niveles por encima de los operadores unarios, y uno por encima de la multiplicación/división.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'> - D: El operador ^^ (exponenciación) está un nivel por encima de los unarios<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'> - FORTRAN: El operador ** tiene la precedencia más alta<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'> - Haskell: Los operadores ^, ^^ y ** (todos de exponenciación) están por debajo sólo de "!!", que se usa para acceder a los índices de arrays<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'> - PHP: ** está por encima de todos los demás operadores aritméticos (y mira que le tengo tirria a este lenguaje, pero por una vez...)<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'> - Python (pero esto ya lo sabíamos): ** está, como viene siendo habitual, por encima de los unarios, pero por debajo de los operadores de indización<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'> - R: ^ (exponenciación), está justo por encima de + y - unarios<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'> - Ruby: ** está justo por encima del - unario (pero justo por debajo del + unario, cosas de la vida)<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>Casos que conozco donde la precedencia de los unarios está por encima: Prolog, JavaScript y algunos casos patológicos como Excel (véase más abajo).<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>En cuanto a calculadoras, he usado la que tengo más a mano (en mi teléfono móvil) y:<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'> -4^2 = -16<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'> (-4)^2 = 16<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>tal como esperaba.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>Y en el caso de las matemáticas, don Aurelio Baldor (al que no conocía, por cierto) podrá cantar misa en Latín, pero cualquier de mis profesores de matemáticas me hubiera tirado de las orejas si se ocurre interpretar que:<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'> -x^n = (-x)^n<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>Aunque claro, siempre me animaron a usar paréntesis para que no cupiera duda.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>Si es cuestión de sacar referencias, pues nada. Citemos Wikipedia, que a su vez usa como referencias "Elementary Algebra for College Students" (Angel Allen) y "Taschebuch der Mathematik" (Grosche, Ziegler y Ziegler):<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><blockquote style='margin-left:30.0pt;margin-right:0cm'><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><span style='font-size:9.5pt;font-family:"Arial","sans-serif";color:black'>There exist differing conventions concerning the unary operator − (usually read "minus"). <b>In written or printed mathematics</b>, the expression −3</span></span><span style='mso-bookmark:_MailOriginal'><sup><span style='font-size:7.5pt;font-family:"Arial","sans-serif";color:black'>2</span></sup></span><span style='mso-bookmark:_MailOriginal'><span style='font-size:9.5pt;font-family:"Arial","sans-serif";color:black'> is interpreted to mean 0 − (3</span></span><span style='mso-bookmark:_MailOriginal'><sup><span style='font-size:7.5pt;font-family:"Arial","sans-serif";color:black'>2</span></sup></span><span style='mso-bookmark:_MailOriginal'><span style='font-size:9.5pt;font-family:"Arial","sans-serif";color:black'>) = −9,</span></span><span style='mso-bookmark:_MailOriginal'><span style='font-size:7.5pt;font-family:"Arial","sans-serif";color:black'> </span></span><span style='mso-bookmark:_MailOriginal'><span style='font-size:9.5pt;font-family:"Arial","sans-serif";color:black'>but in some applications and programming languages, notably Microsoft Office Excel (and other spreadsheet applications) and the programming language bc [...]</span><o:p></o:p></span></p></div></blockquote><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>Las negritas son mías, pero vamos, que la norma la que decimos nosotros, aunque algunos lenguajes de programación han escogido usar la convención contraria. Y Baldor, según vd., aunque la única copia a la que tenido acceso es una edición de 1985-86, en la que el capítulo XV no empieza hasta la página 155 y no aparece un sólo número negativo.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>Saludos,<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>Ricardo<o:p></o:p></span></p></div></div><div><div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'>2016-12-24 6:52 GMT-10:00 Johnny Alonso <</span><a href="mailto:johnny.alonso.quintero@gmail.com" target="_blank"><span style='mso-bookmark:_MailOriginal'>johnny.alonso.quintero@gmail.com</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'>>:<o:p></o:p></span></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;mso-border-left-alt:solid #CCCCCC .75pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-right:0cm'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Hola Ricardo y Armando, si las expresiones que muestran son código Python, lamento decirles que están bastante lejos de la realidad.</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Están comparando expresiones con operadores diferentes y que el resultado en ocasiones les coincida es mera casualidad.<br>En Python el operador ** es potenciación y ^ equivale a la operación XOR entre bist.<br>>>> -2**2<br>-4<br>>>> -(2^2)<br>0<br>Armando ni siquiera coinciden los resultados, dándote el beneficio de la duda, y utilizas el ^ como operador de potenciación, entonces:<br>La expresión -(2^2) en Python equivale a:<br>>>> -(2**2)<br>-4<br>Aquí los resultados con el operador ** coinciden, -4 en ambos casos, y lo acepto como correcto desde el punto de vista del lenguaje, pero no desde el punto de vista matemático, pues matemáticamente las expresión </span>-2² </span><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>es diferente a </span></span><span style='mso-bookmark:_MailOriginal'><span style='font-family:"Liberation Serif","serif"'>-(2²)</span></span><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>.</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Los desarrolladores de lenguajes son libres de incorporar lo que desean, esto también aplica para la precedencia de operadores y el sentido de evaluación de las expresiones matemáticas, pero de igual forma lo documentan para que los usuarios no incurramos en errores asumiendo que todos cumplen las reglas de evaluación matemática al pie de la letra.</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Conjetura: Python no implementa el operador menos unario, pero si el binario el cual tiene menor precedencia que el de potenciación, así:</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>-x**n es interpretado en Python como 0-x**n.</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>>>> -2**2</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>-4</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>>>> 0 - 2**2</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>-4</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Saludos, Johnny Alonso</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-outline-level:1'><span style='mso-bookmark:_MailOriginal'><b><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>De:</span></b></span><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'> Python-es [mailto:</span></span><a href="mailto:python-es-bounces%2Bjohnny.alonso.quintero" target="_blank"><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>python-es-bounces+johnny.alonso.quintero</span></span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>=</span></span><a href="mailto:gmail.com@python.org" target="_blank"><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>gmail.com@python.org</span></span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>] <b>En nombre de </b>Armando Ortega<br><b>Enviado el:</b> sábado, 24 de diciembre de 2016 6:24 a. m.</span><o:p></o:p></span></p><div><div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><br><b>Para:</b> La lista de python en castellano<br><b>Asunto:</b> Re: [Python-es] Python 3.5.2<o:p></o:p></span></p></div></div></div></div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'><span style='mso-bookmark:_MailOriginal'>Buenos días.<br><br>Ricardo tiene razón. <br><br>-2**2 = -(2^2) = -4<br>(-2)**2 = -2^2 = 4<br><br>Un saludo.<o:p></o:p></span></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>El 24/12/16 a las 04:54, Johnny Alonso escribió:<o:p></o:p></span></p></div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Hola Ricardo, Por definición “La potencia es resultado de tomar un número como factor 2 o más veces”. Aritmética de Baldor, capítulo XV, Elevación a potencias y sus operaciones inversas, página 152.</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>-2**2 = -2 * -2 </span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Leyes de la potenciación:</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Todo número elevado a la cero es igual a 1, x**0 = 1</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>-2**0 = 1</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Todo número elevado a un exponente par (múltiplo de 2) es positivo, en caso contrario se mantiene el signo del número.</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>-2**2 = 4</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>-2**3 = -8</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Lo anterior lo puedes verificar en la calculadora de un celular IPhone o Samsung, incluso en la de Windows.</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Es evidente que en Python es así, y lo acepto porque así está documentado, pero es algo para tener en cuenta cuando programas en él.</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Ricardo, con respecto a las matemáticas en este caso, estas equivocado.</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Saludos, Johnny Alonso</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-outline-level:1'><span style='mso-bookmark:_MailOriginal'><b><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>De:</span></b></span><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'> Python-es [</span></span><a href="mailto:python-es-bounces+johnny.alonso.quintero=gmail.com@python.org" target="_blank"><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>mailto:python-es-bounces+johnny.alonso.quintero=gmail.com@python.org</span></span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>] <b>En nombre de </b>Ricardo Cárdenes<br><b>Enviado el:</b> viernes, 23 de diciembre de 2016 5:04 p. m.<br><b>Para:</b> La lista de python en castellano<br><b>Asunto:</b> Re: [Python-es] Python 3.5.2</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>No, no es una excepción.<o:p></o:p></span></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>En matemáticas, la exponenciación tiene prioridad:<o:p></o:p></span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> -x^2 = -(x^2)<o:p></o:p></span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>Los lenguajes de programación que implementan este operador, suelen adherirse a la regla (Python, PHP, D, Ruby, ...). Luego tienes disidentes como JavaScript, pero bueno...<o:p></o:p></span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>Así que no, Python no es "una excepción a las reglas algebraicas".<o:p></o:p></span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>Saludos,<o:p></o:p></span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>Ricardo<o:p></o:p></span></p></div></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>2016-12-23 5:31 GMT-10:00 Johnny Alonso <</span><a href="mailto:johnny.alonso.quintero@gmail.com" target="_blank"><span style='mso-bookmark:_MailOriginal'>johnny.alonso.quintero@gmail.com</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'>>:<o:p></o:p></span></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Gracias Kiko, me queda claro, es excepción a las reglas algebraicas en Python.</span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-outline-level:1'><span style='mso-bookmark:_MailOriginal'><b><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>De:</span></b></span><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'> Python-es [mailto:</span></span><a href="mailto:python-es-bounces%2Bjohnny.alonso.quintero" target="_blank"><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>python-es-bounces+johnny.alonso.quintero</span></span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>=</span></span><a href="mailto:gmail.com@python.org" target="_blank"><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>gmail.com@python.org</span></span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><span lang=ES style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ansi-language:ES'>] <b>En nombre de </b>Kiko<br><b>Enviado el:</b> viernes, 23 de diciembre de 2016 10:08 a. m.<br><b>Para:</b> La lista de python en castellano<br><b>Asunto:</b> Re: [Python-es] Python 3.5.2</span><o:p></o:p></span></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>El 23 de diciembre de 2016, 16:05, Kiko <</span><a href="mailto:kikocorreoso@gmail.com" target="_blank"><span style='mso-bookmark:_MailOriginal'>kikocorreoso@gmail.com</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'>> escribió:<o:p></o:p></span></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt'><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'><span class=m-5921671789812374157m7382936169412308917m6101987704969579672m6604706889916089023gmail->El 23 de diciembre de 2016, 15:06, Johnny Alonso <</span></span><a href="mailto:johnny.alonso.quintero@gmail.com" target="_blank"><span style='mso-bookmark:_MailOriginal'>johnny.alonso.quintero@gmail.com</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><span class=m-5921671789812374157m7382936169412308917m6101987704969579672m6604706889916089023gmail->> escribió:</span><o:p></o:p></span></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>Hola todos, estoy iniciándome en Python y creo que se presenta un fallo de precedencia con el operador menos unario:<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>>>> -2**2 # probable error<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>-4<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>>>> -2 * -2 # Ok<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>4<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>>>> pow(-2, 2) # Ok<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>4<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>>>> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>Por favor, si alguien sabe si esto está documentado podría indicarme en donde lo encuentro, de lo contrario, podrían reportarlo a la fundación, yo no lo se hacer.<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div></div></blockquote><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>Se evalúa antes el operador potencia: </span><a href="https://docs.python.org/3/reference/expressions.html#unary-arithmetic-and-bitwise-operations" target="_blank"><span style='mso-bookmark:_MailOriginal'>https://docs.python.org/3/reference/expressions.html#unary-arithmetic-and-bitwise-operations</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><o:p></o:p></span></p></div></div></div></div></blockquote><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>Antes he ido muy rápido: </span><a href="https://docs.python.org/3/reference/expressions.html#the-power-operator" target="_blank"><span style='mso-bookmark:_MailOriginal'>https://docs.python.org/3/reference/expressions.html#the-power-operator</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><br> <o:p></o:p></span></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt'><div><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'>Saludos, JohnnyAlonso<o:p></o:p></span></p></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'><span style='mso-bookmark:_MailOriginal'><br>_______________________________________________<br>Python-es mailing list<br></span><a href="mailto:Python-es@python.org" target="_blank"><span style='mso-bookmark:_MailOriginal'>Python-es@python.org</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><br></span><a href="https://mail.python.org/mailman/listinfo/python-es" target="_blank"><span style='mso-bookmark:_MailOriginal'>https://mail.python.org/mailman/listinfo/python-es</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><o:p></o:p></span></p></blockquote></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div></div></blockquote></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div></div></div></div></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'><span style='mso-bookmark:_MailOriginal'><br>_______________________________________________<br>Python-es mailing list<br></span><a href="mailto:Python-es@python.org" target="_blank"><span style='mso-bookmark:_MailOriginal'>Python-es@python.org</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><br></span><a href="https://mail.python.org/mailman/listinfo/python-es" target="_blank"><span style='mso-bookmark:_MailOriginal'>https://mail.python.org/mailman/listinfo/python-es</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><o:p></o:p></span></p></blockquote></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'><span style='mso-bookmark:_MailOriginal'><br style='mso-special-character:line-break'><![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'><![endif]><o:p></o:p></span></p><pre><span style='mso-bookmark:_MailOriginal'>_______________________________________________<o:p></o:p></span></pre><pre><span style='mso-bookmark:_MailOriginal'>Python-es mailing list<o:p></o:p></span></pre><pre><span style='mso-bookmark:_MailOriginal'></span><a href="mailto:Python-es@python.org" target="_blank"><span style='mso-bookmark:_MailOriginal'>Python-es@python.org</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><o:p></o:p></span></pre><pre><span style='mso-bookmark:_MailOriginal'></span><a href="https://mail.python.org/mailman/listinfo/python-es" target="_blank"><span style='mso-bookmark:_MailOriginal'>https://mail.python.org/mailman/listinfo/python-es</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><o:p></o:p></span></pre></blockquote><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='mso-bookmark:_MailOriginal'> <o:p></o:p></span></p></div></div></div></div><p class=MsoNormal style='margin-bottom:12.0pt'><span style='mso-bookmark:_MailOriginal'><br>_______________________________________________<br>Python-es mailing list<br></span><a href="mailto:Python-es@python.org" target="_blank"><span style='mso-bookmark:_MailOriginal'>Python-es@python.org</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><br></span><a href="https://mail.python.org/mailman/listinfo/python-es" target="_blank"><span style='mso-bookmark:_MailOriginal'>https://mail.python.org/mailman/listinfo/python-es</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><o:p></o:p></span></p></blockquote></div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div></div></div></blockquote></div><p class=MsoNormal><span style='mso-bookmark:_MailOriginal'><o:p> </o:p></span></p></div></div></div></div><p class=MsoNormal style='margin-bottom:12.0pt'><span style='mso-bookmark:_MailOriginal'><br>_______________________________________________<br>Python-es mailing list<br></span><a href="mailto:Python-es@python.org"><span style='mso-bookmark:_MailOriginal'>Python-es@python.org</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'><br></span><a href="https://mail.python.org/mailman/listinfo/python-es" target="_blank"><span style='mso-bookmark:_MailOriginal'>https://mail.python.org/mailman/listinfo/python-es</span><span style='mso-bookmark:_MailOriginal'></span></a><span style='mso-bookmark:_MailOriginal'></span><o:p></o:p></p></blockquote></div></div></div></body></html>