Oops

1 files changed, 44 insertions, 44 deletions

diff --git a/ga/n3.lyx b/ga/n3.lyx
index d3edbf2..55c0a6a 100644
--- a/ga/n3.lyx
+++ b/ga/n3.lyx
@@ -173,7 +173,7 @@ polinomios constantes
 \end_inset
 
  e 
-\begin_inset Formula $I[X]:=\{a_{0}+a_{1}X+\dots+a_{n}X^{n}\in A[X]\mid a_{0},\dots,a_{n}\in I\}$
+\begin_inset Formula $I[X]\coloneqq \{a_{0}+a_{1}X+\dots+a_{n}X^{n}\in A[X]\mid a_{0},\dots,a_{n}\in I\}$
 \end_inset
 
  son ideales de 
@@ -185,7 +185,7 @@ polinomios constantes
 
 \begin_layout Standard
 Dado 
-\begin_inset Formula $p:=\sum_{k\in\mathbb{N}}p_{k}X^{k}\in A[X]\setminus\{0\}$
+\begin_inset Formula $p\coloneqq \sum_{k\in\mathbb{N}}p_{k}X^{k}\in A[X]\setminus\{0\}$
 \end_inset
 
 , llamamos 
@@ -197,7 +197,7 @@ grado
 \end_inset
 
  a 
-\begin_inset Formula $\text{gr}(p):=\max\{k\in\mathbb{N}\mid p_{k}\neq0\}$
+\begin_inset Formula $\text{gr}(p)\coloneqq \max\{k\in\mathbb{N}\mid p_{k}\neq0\}$
 \end_inset
 
 , 
@@ -321,7 +321,7 @@ Sean
 \end_inset
 
  y 
-\begin_inset Formula $t:=\max\{m,n\}$
+\begin_inset Formula $t\coloneqq \max\{m,n\}$
 \end_inset
 
 , entonces 
@@ -901,7 +901,7 @@ función polinómica
 \end_inset
 
  dada por 
-\begin_inset Formula $\hat{p}(b):=S_{b}(p)$
+\begin_inset Formula $\hat{p}(b)\coloneqq S_{b}(p)$
 \end_inset
 
 .
@@ -1210,7 +1210,7 @@ status open
 Demostración:
 \series default
  Para la existencia, basta ver que 
-\begin_inset Formula $d:=\mathtt{dividir}$
+\begin_inset Formula $d\coloneqq \mathtt{dividir}$
 \end_inset
 
  termina y los valores 
@@ -1265,11 +1265,11 @@ Demostración:
 \end_inset
 
 , sea 
-\begin_inset Formula $p:=\frac{f_{n}}{g_{m}}X^{n-m}$
+\begin_inset Formula $p\coloneqq \frac{f_{n}}{g_{m}}X^{n-m}$
 \end_inset
 
 , 
-\begin_inset Formula $(q,r):=d(f,acc)=d(f-pg,acc+p)$
+\begin_inset Formula $(q,r)\coloneqq d(f,acc)=d(f-pg,acc+p)$
 \end_inset
 
 , pero como 
@@ -1570,7 +1570,7 @@ Para
 \end_inset
 
 , existe 
-\begin_inset Formula $m:=\max\{k\in\mathbb{N}\mid (X-a)^{k}\mid f\}$
+\begin_inset Formula $m\coloneqq \max\{k\in\mathbb{N}\mid (X-a)^{k}\mid f\}$
 \end_inset
 
 
@@ -1819,7 +1819,7 @@ status open
 Demostración:
 \series default
  Para 
-\begin_inset Formula $s:=\sum_{k=1}^{n}\alpha_{k}=1$
+\begin_inset Formula $s\coloneqq \sum_{k=1}^{n}\alpha_{k}=1$
 \end_inset
 
  es evidente.
@@ -2059,19 +2059,19 @@ Dado un anillo conmutativo
 derivada
 \series default
  de 
-\begin_inset Formula $P:=\sum_{k}a_{k}X^{k}\in A[X]$
+\begin_inset Formula $P\coloneqq \sum_{k}a_{k}X^{k}\in A[X]$
 \end_inset
 
  como 
-\begin_inset Formula $P':=D(P):=\sum_{k\geq1}ka_{k}X^{k-1}$
+\begin_inset Formula $P'\coloneqq D(P)\coloneqq \sum_{k\geq1}ka_{k}X^{k-1}$
 \end_inset
 
 , y escribimos 
-\begin_inset Formula $P^{(0)}:=P$
+\begin_inset Formula $P^{(0)}\coloneqq P$
 \end_inset
 
  y 
-\begin_inset Formula $P^{(n+1)}:=P^{(n)\prime}$
+\begin_inset Formula $P^{(n+1)}\coloneqq P^{(n)\prime}$
 \end_inset
 
 .
@@ -2455,7 +2455,7 @@ status open
 
 .
  En efecto, sea 
-\begin_inset Formula $D:=A[X]$
+\begin_inset Formula $D\coloneqq A[X]$
 \end_inset
 
 , es claro que 
@@ -2734,7 +2734,7 @@ Si
 \end_inset
 
 , sean 
-\begin_inset Formula $a:=a_{0}+\dots+a_{n}X^{n},b:=b_{0}+\dots+b_{m}X^{m}\in D[X]$
+\begin_inset Formula $a\coloneqq a_{0}+\dots+a_{n}X^{n},b\coloneqq b_{0}+\dots+b_{m}X^{m}\in D[X]$
 \end_inset
 
  tales que 
@@ -2886,7 +2886,7 @@ Demostración:
 \end_inset
 
  múltiplo común de los denominadores en estos representantes, 
-\begin_inset Formula $g:=bG\in D[X]$
+\begin_inset Formula $g\coloneqq bG\in D[X]$
 \end_inset
 
 , y si hacemos lo mismo con 
@@ -2898,7 +2898,7 @@ Demostración:
 \end_inset
 
  con 
-\begin_inset Formula $h:=cH\in D[X]$
+\begin_inset Formula $h\coloneqq cH\in D[X]$
 \end_inset
 
 .
@@ -2936,16 +2936,16 @@ Demostración:
 \end_inset
 
 , podemos tomar 
-\begin_inset Formula $g':=(bc)^{-1}g$
+\begin_inset Formula $g'\coloneqq (bc)^{-1}g$
 \end_inset
 
  y 
-\begin_inset Formula $h':=h$
+\begin_inset Formula $h'\coloneqq h$
 \end_inset
 
 .
  Si 
-\begin_inset Formula $n:=\varphi(bc)>0$
+\begin_inset Formula $n\coloneqq \varphi(bc)>0$
 \end_inset
 
 , probado esto para 
@@ -3066,7 +3066,7 @@ status open
 \end_inset
 
 Primero vemos que todo 
-\begin_inset Formula $a:=a_{0}+\dots+a_{n}X^{n}\in D[X]$
+\begin_inset Formula $a\coloneqq a_{0}+\dots+a_{n}X^{n}\in D[X]$
 \end_inset
 
  con 
@@ -3127,7 +3127,7 @@ Primero vemos que todo
 
  es obvio.
  De lo contrario existen 
-\begin_inset Formula $b:=b_{0}+\dots+b_{m}X^{m},c:=c_{0}+\dots+c_{k}X^{k}\in D[X]$
+\begin_inset Formula $b\coloneqq b_{0}+\dots+b_{m}X^{m},c\coloneqq c_{0}+\dots+c_{k}X^{k}\in D[X]$
 \end_inset
 
  no invertibles ni unidades con 
@@ -3469,11 +3469,11 @@ Definimos
 \end_inset
 
  tal que, para 
-\begin_inset Formula $p:=\sum_{k\geq0}p_{k}X^{k}\in D[X]$
+\begin_inset Formula $p\coloneqq \sum_{k\geq0}p_{k}X^{k}\in D[X]$
 \end_inset
 
 , 
-\begin_inset Formula $c(p):=\{x\mid x=\text{mcd}_{k\geq0}p_{k}\}$
+\begin_inset Formula $c(p)\coloneqq \{x\mid x=\text{mcd}_{k\geq0}p_{k}\}$
 \end_inset
 
 , y para 
@@ -3489,7 +3489,7 @@ Definimos
 \end_inset
 
 , 
-\begin_inset Formula $c(p):=a^{-1}c(ap)$
+\begin_inset Formula $c(p)\coloneqq a^{-1}c(ap)$
 \end_inset
 
 .
@@ -3747,11 +3747,11 @@ Sea
 \end_inset
 
 , 
-\begin_inset Formula $n:=n_{i}:=\max_{k}n_{k}\geq1$
+\begin_inset Formula $n\coloneqq n_{i}\coloneqq \max_{k}n_{k}\geq1$
 \end_inset
 
 , 
-\begin_inset Formula $m:=\text{mcm}_{k}s_{k}$
+\begin_inset Formula $m\coloneqq \text{mcm}_{k}s_{k}$
 \end_inset
 
  y 
@@ -3874,7 +3874,7 @@ Lema de Gauss:
 Demostración:
 \series default
  
-\begin_inset Formula $f':=f/c(f)$
+\begin_inset Formula $f'\coloneqq f/c(f)$
 \end_inset
 
  es primitivo, pues 
@@ -3882,7 +3882,7 @@ Demostración:
 \end_inset
 
 , y análogamente 
-\begin_inset Formula $g':=g/c(g)$
+\begin_inset Formula $g'\coloneqq g/c(g)$
 \end_inset
 
  es primitivo, luego 
@@ -4286,11 +4286,11 @@ Si
 \end_inset
 
 , 
-\begin_inset Formula $f:=\sum_{k}a_{k}X^{k}\in D[X]$
+\begin_inset Formula $f\coloneqq \sum_{k}a_{k}X^{k}\in D[X]$
 \end_inset
 
  y 
-\begin_inset Formula $n:=\text{gr}(f)$
+\begin_inset Formula $n\coloneqq \text{gr}(f)$
 \end_inset
 
 , todas las raíces de 
@@ -4519,11 +4519,11 @@ En particular, si
 \end_inset
 
  es primo, 
-\begin_inset Formula $f:=\sum_{k}a_{k}X^{k}\in\mathbb{Z}[X]$
+\begin_inset Formula $f\coloneqq \sum_{k}a_{k}X^{k}\in\mathbb{Z}[X]$
 \end_inset
 
  es primitivo, 
-\begin_inset Formula $n:=\text{gr}(f)$
+\begin_inset Formula $n\coloneqq \text{gr}(f)$
 \end_inset
 
 , 
@@ -4559,11 +4559,11 @@ Criterio de Eisenstein:
 \end_inset
 
  un DFU, 
-\begin_inset Formula $f:=\sum_{k}a_{k}X^{k}\in D[X]$
+\begin_inset Formula $f\coloneqq \sum_{k}a_{k}X^{k}\in D[X]$
 \end_inset
 
  primitivo y 
-\begin_inset Formula $n:=\text{gr}f$
+\begin_inset Formula $n\coloneqq \text{gr}f$
 \end_inset
 
 , si existe un irreducible 
@@ -4596,7 +4596,7 @@ status open
 Demostración:
 \series default
  Sean 
-\begin_inset Formula $g:=b_{0}+\dots+b_{m}X^{m},h:=c_{0}+\dots+c_{k}X^{k}\in D[X]$
+\begin_inset Formula $g\coloneqq b_{0}+\dots+b_{m}X^{m},h\coloneqq c_{0}+\dots+c_{k}X^{k}\in D[X]$
 \end_inset
 
  con 
@@ -4641,7 +4641,7 @@ Demostración:
 \end_inset
 
 , luego existe 
-\begin_inset Formula $i:=\min\{j\mid p\nmid b_{j}\}$
+\begin_inset Formula $i\coloneqq \min\{j\mid p\nmid b_{j}\}$
 \end_inset
 
  y entonces 
@@ -4761,7 +4761,7 @@ de 1
 \end_inset
 
 , donde 
-\begin_inset Formula $\Phi_{n}(X):=X^{n-1}+X^{n-2}+\dots+X+1$
+\begin_inset Formula $\Phi_{n}(X)\coloneqq X^{n-1}+X^{n-2}+\dots+X+1$
 \end_inset
 
  es el 
@@ -4876,7 +4876,7 @@ anillo de polinomios
 \end_inset
 
  como 
-\begin_inset Formula $A[X_{1},\dots,X_{n}]:=A[X_{1},\dots,X_{n-1}][X_{n}]$
+\begin_inset Formula $A[X_{1},\dots,X_{n}]\coloneqq A[X_{1},\dots,X_{n-1}][X_{n}]$
 \end_inset
 
 .
@@ -4984,7 +4984,7 @@ Dados
 \end_inset
 
  e 
-\begin_inset Formula $i:=(i_{1},\dots,i_{n})\in\mathbb{N}^{n}$
+\begin_inset Formula $i\coloneqq (i_{1},\dots,i_{n})\in\mathbb{N}^{n}$
 \end_inset
 
 , llamamos a 
@@ -5259,7 +5259,7 @@ homomorfismo de sustitución
 \end_inset
 
  viene dado por 
-\begin_inset Formula $p(b_{1},\dots,b_{n}):=S(p):=\sum_{i\in\mathbb{N}^{n}}p_{i}b_{1}^{i_{1}}\cdots b_{n}^{i_{n}}$
+\begin_inset Formula $p(b_{1},\dots,b_{n})\coloneqq S(p)\coloneqq \sum_{i\in\mathbb{N}^{n}}p_{i}b_{1}^{i_{1}}\cdots b_{n}^{i_{n}}$
 \end_inset
 
 .
@@ -5312,7 +5312,7 @@ Sean
 \end_inset
 
  con inversa 
-\begin_inset Formula $\tau:=\sigma^{-1}$
+\begin_inset Formula $\tau\coloneqq \sigma^{-1}$
 \end_inset
 
 , tomando 
@@ -5355,7 +5355,7 @@ Todo homomorfismo de anillos conmutativos
 \end_inset
 
  dado por 
-\begin_inset Formula $\hat{f}(p):=\sum_{i\in\mathbb{N}^{n}}f(p_{i})X_{1}^{i_{1}}\cdots X_{n}^{i_{n}}$
+\begin_inset Formula $\hat{f}(p)\coloneqq \sum_{i\in\mathbb{N}^{n}}f(p_{i})X_{1}^{i_{1}}\cdots X_{n}^{i_{n}}$
 \end_inset
 
 .