5.10

template.typ

@@ -4,12 +4,6 @@
 
 #import "@preview/lemmify:0.1.4": *
 #import "@preview/commute:0.2.0": node, arr, commutative-diagram
-#let (
-  theorem, lemma, corollary,
-  remark, proposition, example, definition,
-  proof, rules: thm-rules
-) = default-theorems("thm-group", lang: "en")
-#let (answer) = default-theorems("thm-group-a", lang: "en")
 $1 + 1$
 #let TODO = [#text("TODO", fill: red)]
 #let der(y, x) = $(d #y) / (d #x)$
@@ -29,7 +23,7 @@ $1 + 1$
 #let Gal = math.op("Gal")
 #let HomoCoor = math.vec.with(delim: "[")
 #let autoHomoCoor3 = autoVec3.with(delim: "[")
-#let Det(arr) = mat(delim: "|", ..arr)
+#let Det = math.mat.with(delim: "|")
 #let Hom = math.op("Hom")
 #let Proj = math.op("Proj")
 #let Spec = math.op("Spec")
@@ -54,7 +48,7 @@ $1 + 1$
 #let ei(x) = $e^(i #x)$
 #let eiB(x) = $e^(#x i)$ // i Behind
 #let sgn = math.op("sgn")
-#let Res = math.op("Res")
+#let Res(f, i) = $op("Res") (#f \; #i)$
 #let lcm = math.op("lcm")
 #let Der = math.op("Der")
 #let Arg = math.op("Arg")
@@ -176,6 +170,8 @@ $1 + 1$
       parbreak()
     }
   )
+
+
 #let noneNameChecker(name) = {
   if name == [] {
     none
@@ -184,14 +180,31 @@ $1 + 1$
     name
 }
 }
-#let theo = theorem
-#let lem = lemma
-#let cor = corollary
-#let prop = proposition
-#let def = definition
-#let ex = example
-#let rem = remark
-#let pr = proof
+#let (
+  theorem: theo, lemma: lem, corollary: cor,
+  remark: rem, proposition: prop, example:ex , definition:def,
+  proof: pr, rules: thm-rules
+) = default-theorems("thm-group", lang: "en")
+#let (
+  theorem: theo1, lemma: lem1, corollary: cor1,
+  remark: rem1, proposition: prop1, example:ex1 , definition:def1,
+  proof: pr1, rules: thm-rules1
+) = default-theorems("thm-group-linear", lang: "en", thm-numbering: thm-numbering-linear)
+#let my-ans-style(
+  thm-type, name, number, body
+) = block(spacing: 11.5pt, {
+  set enum(numbering: "Step 1.1.")
+  body
+  linebreak()
+  h(1fr)
+  box(scale(160%, origin: bottom + right, sym.square.stroked))
+})
+#let my-styling = (
+  thm-styling: my-ans-style,
+  thm-numbering: thm-numbering-linear
+)
+#let (answer, rules:ans-rules) = new-theorems("thm-ans", ("answer": "Answer"), ..my-styling)
+
 #let _convert(f, name, body) = f(name: noneNameChecker(name))[
   #body
   #parbreak()
@@ -209,9 +222,23 @@ $1 + 1$
 ]
   #linebreak()
 ]
-#let lemma1 = lem.with(
-  numbering: none
-)
+
+
+
+#let theoremLinear(name, body) = _convert(theo1, name, body)
+#let lemmaLinear(name, body) = _convert(lem1, name, body)
+#let corollaryLinear(name, body) = _convert(cor1, name, body)
+#let propositionLinear(name, body) = _convert(prop1, name, body)
+#let exampleLinear(name, body) = _convert(ex1, name, body)
+#let remarkLinear(name, body) = _convert(rem1, name, body)
+#let definitionLinear(name, body) = _convert(def1, name, body)
+#let proofLinear(body) = [#pr1[
+  #set text(size: 10pt)
+  #body
+]
+  #linebreak()
+]
+
 //#let theorem = base_env.with(
 //  type: "Theorem",
 //  fg: blue,
@@ -271,19 +298,6 @@ $1 + 1$
 //  h(1fr)
 //  box(scale(160%, origin: bottom + right, sym.square.stroked))
 //})
-#let my-ans-style(
-  thm-type, name, number, body
-) = block(spacing: 11.5pt, {
-  set enum(numbering: "Step 1.1.")
-  body
-  linebreak()
-  h(1fr)
-  box(scale(160%, origin: bottom + right, sym.square.stroked))
-})
-#let my-styling = (
-  thm-styling: my-ans-style
-)
-#let (answer, rules:ans-rules) = new-theorems("thm-ans", ("answer": "Answer"), ..my-styling)
 
 #let note(title: "Note title", author: "Name", logo: none, date: none,
           preface: none, code_with_line_number: true, withOutlined: true, withTitle: true, withHeadingNumbering: true, body) = {
@@ -307,22 +321,22 @@ $1 + 1$
   }
   show: thm-rules
   show: ans-rules
+  show: thm-rules1
   show math.equation: set text(font: ("Noto Serif CJK SC", "New Computer Modern Math"))
   set math.equation(numbering: "(1)")
-
+  set math.equation(numbering: num =>
+      "(" + (counter(heading).get() + (num,)).map(str).join(".") + ")") if withHeadingNumbering == true
+  let headingfunc = (it => it)
   if withHeadingNumbering == false {
     set math.equation(numbering: "(1)")
   }
   else {
-    show heading: it => {
+    headingfunc = (it => {
         counter(math.equation).update(0)
         it
-    }
-    set math.equation(numbering: "1.")
-    set math.equation(numbering: num =>
-      "(" + (counter(heading).get() + (num,)).map(str).join(".") + ")")
-    set math.equation(numbering: "(1)")
+    })
   }
+  show heading: headingfunc
   // set ref(supplement: it => {
   // let eq = math.equation
   // let el = it
@@ -386,6 +400,7 @@ $1 + 1$
   set par(justify: true, first-line-indent: 22pt)
 
   set heading(numbering: "1.")
+  set heading(numbering: none) if withHeadingNumbering == false
 
   // Code
   show raw.where(block: false): box.with(

代数学二/main.typ

@@ -2560,7 +2560,7 @@
     ]
     #proof[
       定义 $l(M)$ 是 $M$ 的合成列中的最小长度
-      #lemma1[
+      #lemmaLinear[][
         设 $N$ 是 $M$ 的真子模，则 $l(N) < l(M)$
       ]
       #proof[
@@ -2575,7 +2575,7 @@
         因此这些商模要么是 $0$，要么是单模。去掉所有的 $0$ 之后便成为长度为 $l' <= l(M)$ 的合成列\
         同时，假设 $l=  l(M)$，表明上面的 $N_(i-1) quo N_i tilde.eq M_(i-1) quo M_i$，可以递归证明 $M_i = N_i$，这是荒谬的
       ]
-      #lemma1[
+      #lemmaLinear[][
         $M$ 中任何一个子模链的长度不超过 $l(M)$
       ]
       #proof[
@@ -3386,7 +3386,7 @@
     #proof[
       首先，$Sigma$ 非空（可以取 $(0, 0)$），且满足 Zoun 引理条件，进而存在极大元\
       设 $B$ 是一个极大元
-      #lemma1[
+      #lemmaLinear[][
          $B$ 是局部环，且 $m = ker(f)$ 是极大理想
       ]
       #proof[
@@ -3396,7 +3396,7 @@
         $
         当然 $f$ 可以延拓到 $B_m$ 上，而由极大性得 $B_m = B$，证毕
       ]
-      #lemma1[
+      #lemmaLinear[][
         任取 $x in k - {0}, B[x] subset k, m[x] := m B[x]$ ，则以下两者至少有一个成立：
         - $m[x] subset.not B[x]$
         - $m[Inv(x)] subset.not B[Inv(x)]$
@@ -3498,13 +3498,13 @@
       + $exists x in A$ 使得每个非零理想都形如 $(x^k), k >= 0$
     ]
     #proof[
-      #lemma1[
+      #lemmaLinear[][
         设 $I$ 是非平凡理想，则存在 $n > 0, m^n subset I$
       ]
       #proof[
         注意到 $sqrt(I)$ 是包含 $I$ 的所有素理想的交，由 $dim A = 1$ 知它就是 $m$，再由 Noether 知 $m$ 有限生成，考虑生成元不难发现结论成立
       ]
-      #lemma1[
+      #lemmaLinear[][
         $m^k != m^(k+1)$
       ]
       #proof[
@@ -4131,7 +4131,7 @@
         - 若 $G(M)$ 诺特，则 $M$ 诺特
       ]
       #proof[
-        #lemma1[
+        #lemmaLinear[][
           设 $phi: A -> B$ 是 filtered 群间的同态，诱导 $hat(phi): hat(A) -> hat(B), G(phi) : G(A)  -> G(B)$，则：
           - $G(phi)$ 是单射给出 $hat(phi)$ 是单射
           - $G(phi)$ 是满射给出 $hat(phi)$ 是满射

代数学二/matin test.typ

@@ -0,0 +1,11 @@
+#import "../template.typ": note
+// Take a look at the file `template.typ` in the file panel
+// to customize this template and discover how it works.
+#show: note.with(
+  title: "代数学二",
+  author: "YHTQ",
+  date: none,
+  logo: none,
+)
+#include "章节/上半学期.typ"
+#include "章节/下半学期.typ"

代数学二/作业/hw3.typ

@@ -1,4 +1,4 @@
-#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemma1
+#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemmaLinear[]
 #import "../../template.typ": *
 #import "@preview/commute:0.2.0": node, arr, commutative-diagram
 
@@ -247,7 +247,7 @@
   P = union.big_i im(z_i)
   $
   \
-  #lemma1[
+  #lemmaLinear[][
     $
     ker g = union_i y_i (ker g_i)
     $

代数学二/作业/hw4.typ

@@ -1,4 +1,4 @@
-#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemma1
+#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemmaLinear[]
 #import "../../template.typ": *
 #import "@preview/commute:0.2.0": node, arr, commutative-diagram
 
@@ -146,7 +146,7 @@
   证毕
 
   对于第二个事实，先证明：
-  #lemma1[
+  #lemmaLinear[][
     $S$ 是极大元当且仅当 $Inv(S) A$ 的幂零根是唯一的素理想
   ]
   #proof[

代数学二/作业/hw5.typ

@@ -1,4 +1,4 @@
-#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemma1, tensorProduct, directSum
+#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemmaLinear[], tensorProduct, directSum
 #import "../../template.typ": *
 #import "@preview/commute:0.2.0": node, arr, commutative-diagram
 
@@ -269,7 +269,7 @@
   id compose (X -> M') = pi compose sigma compose (X -> M') = pi compose  sigma' compose (X -> M') 
   $
   而 $pi compose sigma', id$ 都是模自同态，自由模的唯一性将给出 $pi compose  sigma' = id$\
-  #lemma1[
+  #lemmaLinear[][
     设 $g: M' -> M, f : M -> M'$，则有：
     $
     f compose g = id => M tilde.eq ker f directSum im g

代数学二/作业/hw6.typ

@@ -1,4 +1,4 @@
-#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemma1, tensorProduct, directSum, directLimit
+#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemmaLinear[], tensorProduct, directSum, directLimit
 #import "../../template.typ": *
 #import "@preview/commute:0.2.0": node, arr, commutative-diagram
 

代数学二/作业/hw7.typ

@@ -1,4 +1,4 @@
-#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemma1, tensorProduct, directSum, directLimit
+#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemmaLinear[], tensorProduct, directSum, directLimit
 #import "../../template.typ": *
 #import "@preview/commute:0.2.0": node, arr, commutative-diagram
 

代数学二/作业/hw8.typ

@@ -1,4 +1,4 @@
-#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemma1, tensorProduct, directSum, directLimit
+#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemmaLinear[], tensorProduct, directSum, directLimit
 #import "../../template.typ": *
 #import "@preview/commute:0.2.0": node, arr, commutative-diagram
 
@@ -99,7 +99,7 @@
       A quo (p sect A) subset C quo (p sect C) subset B quo p
       $
       且都是整环，由上题结论得 $overline(f), overline(g)$ 的所有系数落在 $A quo (p sect A)$ 的整闭包中，进而在其上整。\
-      #lemma1[
+      #lemmaLinear[][
         设 $x in B$ 且任取素理想 $p in Spec(B)$ 均有 $overline(x) in B quo p$ 在 $A quo (p sect A)$ 上整，则 $x$ 在 $A$ 上整
       ]
       #proof[

代数学二/作业/hw9.typ

@@ -1,4 +1,4 @@
-#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemma1, tensorProduct, directSum, directLimit
+#import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemmaLinear[], tensorProduct, directSum, directLimit
 #import "../../template.typ": *
 #import "@preview/commute:0.2.0": node, arr, commutative-diagram
 
@@ -68,7 +68,7 @@
     若这个事实成立，则极大理想 $alpha$ 对应的 $Z(alpha)$ 非空，结合极大性知只能是单点集，如此立得 $alpha = m_x$ 也即结论成立。\
     然而看起来上面的事实并不容易从上题结论推出（何况上题第二个结论已经利用了希尔伯特零点定理的结果）
   == 18
-    #lemma1[
+    #lemmaLinear[][
       设 $A$ 是唯一分解整环，则 $A$ 是整闭的
     ]
     #proof[