tarea-1.pdf - \u00c1lgebra computacional Tarea 1 Fecha l\u00edmite Universidad de El Salvador ciclo impar 2019 Ejercicio 1 Implemente en Macaulay2 la funci\u00f3n

tarea-1.pdf - Álgebra computacional Tarea 1 Fecha límite...

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Álgebra computacional. Tarea 1. Fecha límite: 21/03/2019 Universidad de El Salvador, ciclo impar 2019 Ejercicio 1. Implemente en Macaulay2 la función mcd( f , g ) que calcula el máximo común divisor de f , g k [ x ] usando el algoritmo de Euclides. (Para el resto de división, use el operador % .) Ejercicio 2. Demuestre que sobre los polinomios en una variable k [ x ] hay un solo orden monomial que viene dado por 1 x x 2 x 3 ≺ ··· ; es decir, x m x n ⇐⇒ m < n . Ejercicio 3. Demuestre que lex , grlex , grevlex son órdenes monomiales. Ejercicio 4. Consideremos la siguiente propiedad: para cualesquiera α , β existe un número finito de mo- nomios x γ tales que x α x γ x β . ¿Para cuáles órdenes monomiales entre lex , grlex y grevlex esto es cierto? Ejercicio 5. Fijemos algún orden monomial sobre k [ x 1 ,..., x n ] . Sean f , g k [ x 1 ,..., x n ] polinomios no nulos. Demuestre las siguientes propiedades.
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