update wiki

Author: zzllrr

3d.html

@@ -34,7 +34,12 @@
 
     <script src="js/lib/legra.iife.js" defer></script>
     <script src="js/lib/rough.js" defer></script>
-    <script src="js/lib/math.js"></script>
+
+    <script src="js/lib/math.js" defer></script>
+    <script src="js/lib/infusion/fraction.js" defer></script>
+    <script src="js/lib/infusion/complex.js" defer></script>
+    <script src="js/lib/infusion/quaternion.js" defer></script>
+    <script src="js/lib/infusion/polynomial.js" defer></script>
 
     <!-- i18n -->
     <script src="js/i18n/en.js"></script>

culture.html

@@ -33,7 +33,12 @@
 
     <script src="js/lib/legra.iife.js" defer></script>
     <script src="js/lib/rough.js" defer></script>
-    <script src="js/lib/math.js"></script>
+  
+    <script src="js/lib/math.js" defer></script>
+    <script src="js/lib/infusion/fraction.js" defer></script>
+    <script src="js/lib/infusion/complex.js" defer></script>
+    <script src="js/lib/infusion/quaternion.js" defer></script>
+    <script src="js/lib/infusion/polynomial.js" defer></script>
 
     <!-- i18n -->
     <script src="js/i18n/en.js"></script>

document.html

@@ -33,7 +33,12 @@
 
     <script src="js/lib/legra.iife.js" defer></script>
     <script src="js/lib/rough.js" defer></script>
-    <script src="js/lib/math.js"></script>
+
+    <script src="js/lib/math.js" defer></script>
+    <script src="js/lib/infusion/fraction.js" defer></script>
+    <script src="js/lib/infusion/complex.js" defer></script>
+    <script src="js/lib/infusion/quaternion.js" defer></script>
+    <script src="js/lib/infusion/polynomial.js" defer></script>
 
     <!-- i18n -->
     <script src="js/i18n/en.js"></script>

doodle.html

@@ -37,7 +37,11 @@
     <script src="js/lib/rough.js" defer></script>
     <script src="js/lib/ztext.js" defer></script>
 
-    <script src="js/lib/math.js"></script>
+    <script src="js/lib/math.js" defer></script>
+    <script src="js/lib/infusion/fraction.js" defer></script>
+    <script src="js/lib/infusion/complex.js" defer></script>
+    <script src="js/lib/infusion/quaternion.js" defer></script>
+    <script src="js/lib/infusion/polynomial.js" defer></script>
 
     <!-- i18n -->
     <script src="js/i18n/en.js"></script>

editor.html

@@ -39,7 +39,11 @@
     <script src="js/lib/rough.js" defer></script>
     <script src="js/lib/ztext.js" defer></script>
 
-    <script src="js/lib/math.js"></script>
+    <script src="js/lib/math.js" defer></script>
+    <script src="js/lib/infusion/fraction.js" defer></script>
+    <script src="js/lib/infusion/complex.js" defer></script>
+    <script src="js/lib/infusion/quaternion.js" defer></script>
+    <script src="js/lib/infusion/polynomial.js" defer></script>
 
     <script src="js/lib/mathjax-tex-svg.js" defer></script>
 

explore.html

@@ -33,7 +33,12 @@
 
     <script src="js/lib/legra.iife.js" defer></script>
     <script src="js/lib/rough.js" defer></script>
-    <script src="js/lib/math.js"></script>
+    
+    <script src="js/lib/math.js" defer></script>
+    <script src="js/lib/infusion/fraction.js" defer></script>
+    <script src="js/lib/infusion/complex.js" defer></script>
+    <script src="js/lib/infusion/quaternion.js" defer></script>
+    <script src="js/lib/infusion/polynomial.js" defer></script>
 
     <!-- i18n -->
     <script src="js/i18n/en.js"></script>

graphic.html

@@ -32,8 +32,12 @@
     <script src="js/lib/desmos_geometry.js" defer></script>
 
     <script src="js/lib/legra.iife.js" defer></script>
-    <script src="js/lib/math.js"></script>
-    
+    <script src="js/lib/math.js" defer></script>
+    <script src="js/lib/infusion/fraction.js" defer></script>
+    <script src="js/lib/infusion/complex.js" defer></script>
+    <script src="js/lib/infusion/quaternion.js" defer></script>
+    <script src="js/lib/infusion/polynomial.js" defer></script>
+
     <!-- i18n -->
     <script src="js/i18n/en.js"></script>
     <script src="js/i18n/zh_cn.js"></script>

index.html

@@ -41,6 +41,10 @@
 
 
 	<script src="js/lib/math.js" defer></script>
+	<script src="js/lib/infusion/fraction.js" defer></script>
+	<script src="js/lib/infusion/complex.js" defer></script>
+	<script src="js/lib/infusion/quaternion.js" defer></script>
+	<script src="js/lib/infusion/polynomial.js" defer></script>
 
 	<script src="js/lib/mathjax-tex-svg.js" defer></script>
 

js/htm/index/navhead/api.js

@@ -22,15 +22,16 @@
 						ZLR('katex echarts echarts-gl effects aframe aframe-ar zdog d3 geogebra desmos rough ztext'))),1),
 
 				detail(gM('Math'),
-					ul(Arrf(gitjs,
-						ZLR('math'))),1),
+					ul(Arrf(github,
+						ZLR('josdejong/mathjs '+zlr3('infusion/','Polynomial Fraction Complex Quaternion','.js')))),1),
 
 				href('./css/fonts','Fonts'),
 				detail('Icon Font',
 					ul(ZLR(zlr2('KaTeX MaterialIcons-Regular','.woff2'))),1)
 
 
 			].join(br)
+
 		,1);
 
 	}else{

js/htm/wiki/formula/equation/diophantus.js

@@ -772,38 +772,31 @@ detail(brA([ksc('x^2-ny^2=1')+'（'+gM2('Pell Equation')+'①）',
 
 
 
-
-detail(ksc('a^4+b^4+c^4=d^4')+' (Euler曾错误猜测无非平凡解：'+ksc('a_1^k+a_2^k+⋯+a_n^k=b^k ⇒ n ≥ k')+'其中整数n,k都>1）' ,
+detail('Euler幂和猜想（已被否证）Euler曾错误猜测无非平凡解：'+br+
+	ksc('a_1^k+a_2^k+⋯+a_n^k=b^k ⇒ n ≥ k')+'（其中整数n,k都>1）' ,
 
 
 	ksc([
-		
-		'2682440^4 + 15365639^4 + 18796760^4 = 20615673^4（Noam ~ Elkies 1986）',
-		'(85v^2 + 484v − 313)^4 + (68v^2 − 586v + 10)^4 + (2u)^4 = (357v^2 − 204v + 363)^4',
-		'其中u^2=22030 + 28849v − 56158v^2 + 36941v^3 − 31790v^4（可令v=-\\frac{31}{467}，代入上式化简）',
-		'95800^4 + 217519^4 + 414560^4 = 422481^4 （Roger Frye 1988）',
-
 
-		'a_1^k+a_2^k+⋯+a_n^k=b^k ⇒ n ≥ k （其中整数n,k>1，更一般的Euler幂和猜想，已被否证）',
 		'k=3时成立（因为费马大定理FLT成立，则可以用反证法得知此结论）',
 		'k=4、5时，不成立',
-		'k=5时的一些反例：',
-
-		'27^5 + 84^5 + 110^5 + 133^5 = 144^5 （Lander，Parkin, 1966）',
-		'(−220)^5 + 5027^5 + 6237^5 + 14068^5 = 14132^5 （Scher， Seidl 1996）',
-		'55^5 + 3183^5 + 28969^5 + 85282^5 = 85359^5 （Frye 2004）',
 
 		'k>5时，是否成立未知unknown',
 
 		'其它非反例的例子：',
-		'30^4 + 120^4 + 272^4 + 315^4 = 353^4 （Norrie 1911，最小例子）',
-		'19^5 + 43^5 + 46^5 + 47^5 + 67^5 = 72^5 （Lander, Parkin, Selfridge, 1967 最小例子）',
+		'k=4时',
+		'30^4 + 120^4 + 272^4 + 315^4 = 353^4 （\\text{Norrie 1911}，最小例子）',
+
+		'k=5时',
+		'19^5 + 43^5 + 46^5 + 47^5 + 67^5 = 72^5 （\\text{Lander, Parkin, Selfridge, 1967} 最小例子）',
 
-		'7^5 + 43^5 + 57^5 + 80^5 + 100^5 = 107^5（Sastry 1934，第三小的例子）',
+		'7^5 + 43^5 + 57^5 + 80^5 + 100^5 = 107^5（\\text{Sastry 1934}，第三小的例子）',
 
-		'127^7 + 258^7 + 266^7 + 413^7 + 430^7 + 439^7 + 525^7 = 568^7 （Dodrill 1999）',
+		'k=7时',
+		'127^7 + 258^7 + 266^7 + 413^7 + 430^7 + 439^7 + 525^7 = 568^7 （\\text{Dodrill 1999}）',
 
-		'90^8 + 223^8 + 478^8 + 524^8 + 748^8 + 1088^8 + 1190^8 + 1324^8 = 1409^8 （Chase 2000）',
+		'k=8时',
+		'90^8 + 223^8 + 478^8 + 524^8 + 748^8 + 1088^8 + 1190^8 + 1324^8 = 1409^8 （\\text{Chase 2000}）',
 
 	]).join(br)+
 	refer([
@@ -814,23 +807,51 @@ detail(ksc('a^4+b^4+c^4=d^4')+' (Euler曾错误猜测无非平凡解：'+ksc('a_
 ),
 
 
+detail('Euler幂和猜想的反例',
+
+	
+	ksc([
+		'k=4时的一些反例：',
+		'（参见方程a^3+b^3+c^3=d^4）',
+
+		'k=5时的一些反例：',
+
+		'27^5 + 84^5 + 110^5 + 133^5 = 144^5 （\\text{Lander，Parkin, 1966}）',
+		'(−220)^5 + 5027^5 + 6237^5 + 14068^5 = 14132^5 （\\text{Scher， Seidl 1996}）',
+		'55^5 + 3183^5 + 28969^5 + 85282^5 = 85359^5 （\\text{Frye 2004}）',
+
+		'k>5时，是否成立未知unknown',
+
+	
+	]).join(br)+
+	refer([
+		enwiki("Euler%27s_sum_of_powers_conjecture"),
+		
+
+	])
+),
+
 
 
-detail(ksc('a^3+b^3+c^3=d^3')+' 有无穷多组非平凡解，如(3,4,5,6)' ,
+detail(ksc('a^3+b^3+c^3=d^3')+' 有无穷多组非平凡解，如(3,4,5,6)=216（柏拉图数）' ,
 
 
 	ksc([
 		'3^3+4^3+5^3=6^3（令下式a=1,b=0即得）',
-		'(3a^{2}+5ab-5b^{2})^{3}+(4a^{2}-4ab+6b^{2})^{3}+(5a^{2}-5ab-3b^{2})^{3}=(6a^{2}-4ab+4b^{2})^{3}（拉马努金公式）',
+		'【1】(3a^{2}+5ab-5b^{2})^{3}+(4a^{2}-4ab+6b^{2})^{3}+(5a^{2}-5ab-3b^{2})^{3}=(6a^{2}-4ab+4b^{2})^{3}（拉马努金公式）',
 		'同一个二次项系数依次为（3,4,5,6），（5,-4,-5,-4），（-5,6,-3,4）',
-		'(3a^{2}-5ab-5b^{2})^{3}+(4a^{2}+4ab+6b^{2})^{3}+(5a^{2}+5ab-3b^{2})^{3}=(6a^{2}+4ab+4b^{2})^{3}（变体b→-b 或 a↔b）',
+		'',
+		'【2】(3a^{2}-5ab-5b^{2})^{3}+(4a^{2}+4ab+6b^{2})^{3}+(5a^{2}+5ab-3b^{2})^{3}=(6a^{2}+4ab+4b^{2})^{3}（变体b→-b 或 a↔b）',
 		'同一个二次项系数依次为（3,4,5,6），（-5,4,5,4），（-5,6,-3,4）',
-		
-		'b^{3}(a^{3}+b^{3})^{3}+a^{3}(a^{3}-2b^{3})^{3}+b^{3}(2a^{3}-b^{3})^{3}=a^{3}(a^{3}+b^{3})^{3}',
+		'',
+		'【3】b^{3}(a^{3}+b^{3})^{3}+a^{3}(a^{3}-2b^{3})^{3}+b^{3}(2a^{3}-b^{3})^{3}=a^{3}(a^{3}+b^{3})^{3}',
 		'括号中三次项系数，及括号外的项的底分别为（1,1,2,1；1,-2,-1,1；b,a,b,a）',
-		'a^{3}(a^{3}-b^{3})^{3}+b^{3}(a^{3}-b^{3})^{3}+b^{3}(2a^{3}+b^{3})^{3}=a^{3}(a^{3}+2b^{3})^{3}（变体b→-b或 a↔b）',
+
+		'',
+		'【4】a^{3}(a^{3}-b^{3})^{3}+b^{3}(a^{3}-b^{3})^{3}+b^{3}(2a^{3}+b^{3})^{3}=a^{3}(a^{3}+2b^{3})^{3}（变体b→-b或 a↔b）',
 		'括号中三次项系数，及括号外的项的底分别为（1,1,2,1；-1,-1,1,2；a,b,b,a）',
 
+		'',
 		'2100000可以用9种方法表示成3个立方数之和',
 
 
@@ -843,6 +864,21 @@ detail(ksc('a^3+b^3+c^3=d^3')+' 有无穷多组非平凡解，如(3,4,5,6)' ,
 	])
 ),
 
+detail(ksc('a^4+b^4+c^4=d^4')+' 有无穷多组非平凡解' ,
+	ksc([
+		'2682440^4 + 15365639^4 + 18796760^4 = 20615673^4（\\text{Noam ~ Elkies 1986}）',
+		'(85v^2 + 484v − 313)^4 + (68v^2 − 586v + 10)^4 + (2u)^4 = (357v^2 − 204v + 363)^4',
+		'其中u^2=22030 + 28849v − 56158v^2 + 36941v^3 − 31790v^4（可令v=-\\frac{31}{467}，代入上式化简）',
+		'95800^4 + 217519^4 + 414560^4 = 422481^4 （\\text{Roger Frye 1988}）',
+	]).join(br)+
+	refer([
+		enwiki("Euler%27s_sum_of_powers_conjecture"),
+		
+
+	])
+),
+
+
 detail(ksc('a^4=b^4+c^2')+'无正整数解'+br+
 	' (Fermat直角三角形定理，使用无限递降法证明) ' ,
 	refer([
@@ -1345,7 +1381,7 @@ detail(ksc('ax+by=c，其中(a,b)=1 有通解'),
 	])
 ),
 
-detail('ax^2+by^2+cxy+dx+ey+f=0', [
+detail(ksc('ax^2+by^2+cxy+dx+ey+f=0'), [
 		detail(ksc(piece(['x^2+1=kx 只有平凡整数解x=±1，即(1,2)，(-1,-2)',
 				'x^2-1=kx 只有平凡整数解x=±1，即(1,0)，(-1,0)'
 			])),