- \n
- \u53d8\u91cf\u540d\u7ea6\u5b9a<\/a><\/li>\n
- \u7b49\u53f7
=<\/code>\u2248<\/code>\u2260<\/code>:=<\/code><\/a><\/li>\n- \u5e73\u65b9\u6839\u4e0e\u590d\u6570
\u221a<\/code>i<\/code><\/em><\/a><\/li>\n- \u70b9 & \u53c9
\u00b7<\/code>\u00d7<\/code>\u2218<\/code><\/a>\n- \n
- \u6807\u91cf\u4e58\u6cd5<\/a><\/li>\n
- \u5411\u91cf\u4e58\u6cd5<\/a><\/li>\n
- \u70b9\u4e58<\/a><\/li>\n
- \u53c9\u4e58<\/a><\/li>\n<\/ul>\n<\/li>\n
- \u897f\u683c\u739b
\u03a3<\/code><\/a> – \u6c42\u548c<\/em><\/li>\n- \u5927\u5199 Pi
\u03a0<\/code><\/a> – \u5e8f\u5217\u7684\u79ef<\/em><\/li>\n- \u7ba1\u9053
||<\/code><\/a>\n- \n
- \u7edd\u5bf9\u503c<\/a><\/li>\n
- \u6b27\u51e0\u91cc\u5f97\u6a21<\/a><\/li>\n
- \u884c\u5217\u5f0f<\/a><\/li>\n<\/ul>\n<\/li>\n
- \u5e3d\u5b50
\u00e2<\/code><\/strong><\/a> – \u5355\u4f4d\u5411\u91cf<\/em><\/li>\n- “\u5c5e\u4e8e”
\u2208<\/code>\u2209<\/code><\/a><\/li>\n- \u5e38\u89c1\u6570\u5b57\u96c6
\u211d<\/code>\u2124<\/code>\u211a<\/code>\u2115<\/code><\/a><\/li>\n- \u51fd\u6570
\u0192<\/code><\/a>\n- \n
- \u5206\u6bb5\u51fd\u6570<\/a><\/li>\n
- \u901a\u7528\u51fd\u6570<\/a><\/li>\n
- \u51fd\u6570\u7b26\u53f7
\u21a6<\/code>\u2192<\/code><\/a><\/li>\n<\/ul>\n<\/li>\n- \u6487\u53f7
\u2032<\/code><\/a><\/li>\n- \u5411\u4e0b\u53d6\u6574\u548c\u5411\u4e0a\u53d6\u6574\uff08floor & ceiling\uff09
\u230a<\/code>\u2309<\/code><\/a><\/li>\n- \u7bad\u5934<\/a>\n
- \n
- \u5b9e\u8d28\u8574\u542b\uff08material implication\uff09
\u21d2<\/code>\u2192<\/code><\/a><\/li>\n- \u7b49\u5f0f
<<\/code>\u2265<\/code>\u226b<\/code><\/a><\/li>\n- \u4e0e & \u6216
\u2227<\/code>\u2228<\/code><\/a><\/li>\n<\/ul>\n<\/li>\n- \u903b\u8f91\u975e
\u00ac<\/code>~<\/code>!<\/code><\/a><\/li>\n- \u533a\u95f4\uff08intervals\uff09<\/a><\/li>\n
- \u66f4\u591a…<\/a><\/li>\n<\/ul>\n
\u53d8\u91cf\u540d\u7ea6\u5b9a<\/h2>\n
\u6709\u5f88\u591a\u547d\u540d\u7ea6\u5b9a\u53d6\u51b3\u4e8e\u4e0a\u4e0b\u6587\u548c\u6240\u5b66\u9886\u57df\uff0c\u4ed6\u4eec\u5e76\u4e0d\u592a\u4e00\u81f4\u3002\u7136\u800c\u5728\u4e00\u4e9b\u6587\u732e\u4e2d\u4f60\u4f1a\u53d1\u73b0\u53d8\u91cf\u540d\u9075\u5faa\u4e00\u4e9b\u6a21\u5f0f\uff0c\u4f8b\u5982\uff1a<\/p>\n
- \n
- s<\/em> – \u659c\u4f53\u5c0f\u5199\u5b57\u6bcd\u7528\u505a\u6807\u91cf \uff08\u4f8b\u5982\u4e00\u4e2a\u6570\u5b57\uff09<\/li>\n
- x<\/strong> – \u7c97\u4f53\u5c0f\u5199\u5b57\u6bcd\u7528\u505a\u5411\u91cf \uff08\u4f8b\u5982\u4e00\u4e2a2D\u70b9\uff09<\/li>\n
- A<\/strong> – \u7c97\u4f53\u5927\u5199\u5b57\u6bcd\u7528\u505a\u77e9\u9635 \uff08\u4f8b\u5982\u4e00\u4e2a3D\u53d8\u6362\uff09<\/li>\n
- \u03b8<\/em> – \u659c\u4f53\u5c0f\u5199\u5e0c\u814a\u5b57\u6bcd\u7528\u505a\u5e38\u91cf\u548c\u7279\u6b8a\u53d8\u91cf \uff08\u4f8b\u5982 \u6b27\u62c9\u89d2 \u03b8<\/em>, theta<\/em><\/a>)<\/li>\n<\/ul>\n
\u672c\u6587\u4e5f\u57fa\u4e8e\u8fd9\u4e2a\u683c\u5f0f\u3002<\/p>\n
\u7b49\u53f7<\/h2>\n
\u6709\u5f88\u591a\u7b26\u53f7\u5f88\u50cf\u7b49\u53f7
=<\/code> \u3002\u8fd9\u91cc\u6709\u4e9b\u5e38\u89c1\u7684\u4f8b\u5b50\uff1a<\/p>\n- \n
=<\/code> \u8868\u793a\u76f8\u7b49 \uff08\u503c\u76f8\u540c\uff09<\/li>\n\u2260<\/code> \u8868\u793a\u4e0d\u76f8\u7b49 \uff08\u503c\u4e0d\u540c\uff09<\/li>\n\u2248<\/code> \u8868\u793a\u7ea6\u7b49\u4e8e \uff08\u03c0 \u2248 3.14159<\/code>\uff09<\/li>\n:=<\/code> \u8868\u793a\u5b9a\u4e49 \uff08A \u88ab\u5b9a\u4e49\u4e3a B\uff09<\/li>\n<\/ul>\n\u5728 JavaScript \u4e2d:<\/p>\n
\/\/ \u76f8\u7b49\n2 === 3\n\n\/\/ \u4e0d\u76f8\u7b49\n2 !== 3\n\n\/\/ \u7ea6\u7b49\u4e8e\nalmostEqual(Math.PI, 3.14159, 1e-5)\n\nfunction almostEqual(a, b, epsilon) {\n return Math.abs(a - b) <= epsilon\n}\n<\/code><\/pre>\n\u4f60\u4e5f\u8bb8\u770b\u8fc7
:=<\/code>\uff0c=:<\/code> \u548c=<\/code> \u7b26\u53f7\u7528\u6765\u8868\u793a \u5b9a\u4e49<\/em>\u3002[1]<\/sup><\/p>\n\u4f8b\u5982\uff0c\u4e0b\u8fb9\u5b9a\u4e49 x<\/em> \u4e3a 2kj<\/em> \u7684\u522b\u540d\u3002<\/p>\n
<\/p>\n
<\/p>\n
\u5728 JavaScript \u4e2d\uff0c\u6211\u4eec\u7528
var<\/code> \u6765 \u5b9a\u4e49<\/em> \u53d8\u91cf\u548c\u63d0\u4f9b\u522b\u540d\uff1a<\/p>\nvar x = 2 * k * j\n<\/code><\/pre>\n\u7136\u800c\uff0c\u8fd9\u91cc\u7684x\u503c\u662f\u53ef\u53d8\u7684\uff0c\u4ec5\u662f\u5f53\u65f6\u7684\u4e00\u4e2a\u5feb\u7167\u3002\u5728\u67d0\u4e9b\u6709\u9884\u5904\u7406\u5668\u8bed\u8a00\u4e2d\u7684
#define<\/code> \u8bed\u53e5\u624d\u6bd4\u8f83\u63a5\u8fd1\u4e8e\u6570\u5b66\u4e2d\u7684 \u5b9a\u4e49<\/em>\u3002<\/p>\n\u5728JavaScript (ES6) \u4e2d\uff0c\u66f4\u7cbe\u786e\u7684 \u5b9a\u4e49<\/em> \uff0c\u5e94\u8be5\u6709\u70b9\u7c7b\u4f3c\u8fd9\u6837\uff1a<\/p>\n
const f = (k, j) => 2 * k * j\n<\/code><\/pre>\n\u4e0e\u6b64\u4e0d\u540c\u7684\u662f\uff0c\u4e0b\u8fb9\u8fd9\u53e5\u8868\u793a\u7684\u662f\u76f8\u7b49\uff1a<\/p>\n
<\/p>\n
<\/p>\n
\u4e0a\u8fb9\u7684\u7b49\u5f0f\u4e5f\u53ef\u4ee5\u89e3\u91ca\u4e3a\u4e00\u4e2a \u65ad\u8a00<\/a>:<\/p>\n
console.assert(x === (2 * k * j))\n<\/code><\/pre>\n\u5e73\u65b9\u6839\u4e0e\u590d\u6570<\/h2>\n
\u4e00\u4e2a\u5e73\u65b9\u6839\u8fd0\u7b97\u662f\u8fd9\u79cd\u5f62\u5f0f:<\/p>\n
<\/p>\n
<\/p>\n
\u5728\u7f16\u7a0b\u8bed\u8a00\u4e2d\u6211\u4eec\u4f7f\u7528
sqrt<\/code> \u51fd\u6570\uff0c \u50cf\u8fd9\u6837\uff1a<\/p>\nvar x = 9;\nconsole.log(Math.sqrt(x));\n\/\/=> 3\n<\/code><\/pre>\n\u590d\u6570\u662f
\u5f62\u5f0f\u7684\u8868\u8fbe\u5f0f\uff0c \u5176\u4e2d
\u662f\u5b9e\u6570\u90e8\u5206\uff0c
\u662f\u865a\u6570\u90e8\u5206\u3002 \u865a\u6570
\u7684\u5b9a\u4e49\u4e3a\uff1a<\/p>\n
.
\n<\/p>\nJavaScript\u6ca1\u6709\u5185\u7f6e\u590d\u6570\u7684\u529f\u80fd\uff0c\u4f46\u6709\u4e00\u4e9b\u5e93\u652f\u6301\u590d\u6570\u7b97\u6cd5\u3002\u4f8b\u5982\uff0c mathjs<\/a>:<\/p>\n
var math = require('mathjs')\n\nvar a = math.complex(3, -1)\n\/\/=> { re: 3, im: -1 }\n\nvar b = math.sqrt(-1)\n\/\/=> { re: 0, im: -1 }\n\nconsole.log(math.multiply(a, b).toString())\n\/\/=> '1 + 3i'\n<\/code><\/pre>\n\u8fd9\u4e2a\u5e93\u8fd8\u652f\u6301\u5b57\u7b26\u4e32\u8868\u8fbe\u5f0f\u6c42\u503c\uff0c \u6240\u4ee5\u4e0a\u8fb9\u7684\u53ef\u4ee5\u5199\u4e3a\uff1a<\/p>\n
console.log(math.eval('(3 - i) * i').toString())\n\/\/=> '1 + 3i'\n<\/code><\/pre>\n\u5176\u4ed6\u5b9e\u73b0\uff1a<\/p>\n
- \n
- immutable-complex<\/a><\/li>\n
- complex-js<\/a><\/li>\n
- Numeric-js<\/a><\/li>\n<\/ul>\n
\u70b9 & \u53c9<\/h2>\n
\u70b9
\u00b7<\/code> \u548c\u53c9\u00d7<\/code> \u7b26\u53f7\u6839\u636e\u4e0a\u4e0b\u6587\u7684\u4e0d\u540c\u6709\u4e0d\u540c\u7684\u7528\u6cd5\u3002<\/p>\n\u4ed6\u4eec\u53ef\u80fd\u770b\u4e0a\u53bb\u5f88\u660e\u663e\uff0c\u4f46\u5728\u8fdb\u5165\u4e0b\u4e00\u90e8\u5206\u4e4b\u524d\uff0c\u7406\u89e3\u4ed6\u4eec\u4e4b\u95f4\u5fae\u5999\u7684\u4e0d\u540c\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002<\/p>\n
\u6807\u91cf\u4e58\u6cd5<\/h4>\n
\u4e24\u4e2a\u7b26\u53f7\u90fd\u53ef\u4ee5\u8868\u793a\u7b80\u5355\u7684\u6807\u91cf\u4e4b\u95f4\u7684\u4e58\u6cd5\u3002\u4e0b\u8fb9\u7684\u5199\u6cd5\u610f\u601d\u76f8\u540c\uff1a<\/p>\n
<\/p>\n
<\/p>\n
\u5728\u7f16\u7a0b\u8bed\u8a00\u4e2d\uff0c\u6211\u4eec\u503e\u5411\u7528\u661f\u53f7\u8868\u793a\u76f8\u4e58\uff1a<\/p>\n
var result = 5 * 4\n<\/code><\/pre>\n\u901a\u5e38\uff0c\u4f7f\u7528\u4e58\u6cd5\u7b26\u53f7\u53ea\u662f\u4e3a\u4e86\u907f\u514d\u610f\u4e49\u6a21\u7cca\uff08\u4f8b\u5982\u4e24\u4e2a\u6570\u5b57\u4e4b\u95f4\u7684\uff09\u3002\u8fd9\u91cc\uff0c\u6211\u4eec\u53ef\u4ee5\u5b8c\u5168\u7701\u7565\uff1a<\/p>\n
<\/p>\n
<\/p>\n
\u5982\u679c\u8fd9\u4e9b\u53d8\u91cf\u8868\u793a\u7684\u662f\u6807\u91cf\uff0c\u5219\u4ee3\u7801\u5e94\u8be5\u8fd9\u6837\u5199:<\/p>\n
var result = 3 * k * j\n<\/code><\/pre>\n\u5411\u91cf\u4e58\u6cd5<\/h4>\n
\u8868\u793a\u5411\u91cf\u548c\u6807\u91cf\u4e4b\u95f4\u76f8\u4e58\uff0c\u6216\u4e24\u5411\u91cf\u7684\u9010\u5143\u7d20\u76f8\u4e58\uff08element-wise multiplication\uff09\uff0c\u6211\u4eec\u4e0d\u7528\u70b9
\u00b7<\/code> \u6216\u53c9\u00d7<\/code> \u7b26\u53f7\u3002 \u8fd9\u4e9b\u7b26\u53f7\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\u6709\u4e0d\u540c\u7684\u610f\u601d\uff0c\u540e\u8fb9\u8ba8\u8bba\u3002<\/p>\n\u8ba9\u6211\u4eec\u7528\u4e4b\u524d\u7684\u4f8b\u5b50\uff0c\u4f46\u7528\u5728\u5411\u91cf\u4e0a\u3002\u5bf9\u4e8e\u5411\u91cf\u7684\u9010\u5143\u7d20\u76f8\u4e58\uff08element-wise vector multiplication\uff09\u6765\u8bf4\uff0c\u4f60\u53ef\u80fd\u4f1a\u770b\u5230\u7528\u4e00\u4e2a\u7a7a\u5fc3\u70b9\u6765\u8868\u793a Hadamard product<\/a>\u3002[2]<\/sup><\/p>\n
<\/p>\n
<\/p>\n
\u67d0\u4e9b\u65f6\u5019\uff0c\u4f5c\u8005\u53ef\u80fd\u4f1a\u663e\u5f0f\u5b9a\u4e49\u4e00\u4e2a\u4e0d\u540c\u7684\u7b26\u53f7\uff0c\u4f8b\u5982\u5706\u4e2d\u70b9
\u2299<\/code> \u6216\u5b9e\u5fc3\u5708\u25cf<\/code> \u3002[3]<\/sup><\/p>\n\u8fd9\u662f\u5bf9\u5e94\u7684\u4ee3\u7801\uff0c\u4f7f\u7528\u6570\u7ec4
[x, y]<\/code> \u6765\u8868\u793a2D\u5411\u91cf\u3002<\/p>\nvar s = 3\nvar k = [ 1, 2 ]\nvar j = [ 2, 3 ]\n\nvar tmp = multiply(k, j)\nvar result = multiplyScalar(tmp, s)\n\/\/=> [ 6, 18 ]\n<\/code><\/pre>\nmultiply<\/code> \u548cmultiplyScalar<\/code> \u51fd\u6570\u5e94\u8be5\u8fd9\u6837:<\/p>\nfunction multiply(a, b) {\n return [ a[0] * b[0], a[1] * b[1] ]\n}\n\nfunction multiplyScalar(a, scalar) {\n return [ a[0] * scalar, a[1] * scalar ]\n}\n<\/code><\/pre>\n\u540c\u6837\u7684\uff0c\u77e9\u9635\u76f8\u4e58\u4e5f\u4e0d\u7528
\u00b7<\/code> \u6216\u00d7<\/code> \u7b26\u53f7\u3002 \u77e9\u9635\u4e58\u6cd5\u4f1a\u5728\u540e\u8fb9\u7ae0\u8282\u63d0\u5230.<\/p>\n\u70b9\u4e58<\/h4>\n
\u70b9\u7b26\u53f7
\u00b7<\/code> \u53ef\u7528\u6765\u8868\u793a\u4e24\u5411\u91cf\u4e4b\u95f4\u7684 \u70b9\u4e58<\/em><\/a> \u3002 \u7531\u4e8e\u5176\u503c\u662f\u4e00\u4e2a\u6807\u91cf\uff0c\u901a\u5e38\u88ab\u53eb\u505a \u6807\u91cf\u79ef\uff08scalar product\uff09<\/em> \u3002<\/p>\n<\/p>\n
<\/p>\n
\u8fd9\u5728\u7ebf\u6027\u4ee3\u6570\u548c3D\u5411\u91cf\u4e2d\u662f\u975e\u5e38\u5e38\u89c1\u7684\uff0c\u4ee3\u7801\u7c7b\u4f3c\u8fd9\u6837\uff1a<\/p>\n
var k = [ 0, 1, 0 ]\nvar j = [ 1, 0, 0 ]\n\nvar d = dot(k, j)\n\/\/=> 0\n<\/code><\/pre>\n\u7ed3\u679c\u4e3a
0<\/code> \u544a\u8bc9\u6211\u4eec\u4e24\u5411\u91cf\u4e92\u76f8\u5782\u76f4. \u8fd9\u662f3\u5143\u7d20\u5411\u91cf\u7684\u70b9\u4e58<\/code> \u51fd\u6570:<\/p>\nfunction dot(a, b) {\n return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]\n}\n<\/code><\/pre>\n\u53c9\u4e58<\/h4>\n
\u53c9\u4e58\u7b26\u53f7
\u00d7<\/code> \u53ef\u4ee5\u7528\u6765\u8868\u793a\u4e24\u5411\u91cf\u7684 \u53c9\u4e58<\/em><\/a>\u3002<\/p>\n<\/p>\n
<\/p>\n
\u5728\u4ee3\u7801\u4e2d\uff0c\u5e94\u8be5\u662f\u8fd9\u6837:<\/p>\n
var k = [ 0, 1, 0 ]\nvar j = [ 1, 0, 0 ]\n\nvar result = cross(k, j)\n\/\/=> [ 0, 0, -1 ]\n<\/code><\/pre>\n\u8fd9\u91cc\u5f97\u5230\u7ed3\u679c\u4e3a
[ 0, 0, -1 ]<\/code>\uff0c\u8fd9\u4e2a\u5411\u91cf\u540c\u65f6\u5782\u76f4\u4e8e k<\/strong> \u548c j<\/strong> \u3002<\/p>\n\u6211\u4eec\u7684\u53c9\u4e58
cross<\/code> \u51fd\u6570\uff1a<\/p>\nfunction cross(a, b) {\n var ax = a[0], ay = a[1], az = a[2],\n bx = b[0], by = b[1], bz = b[2]\n\n var rx = ay * bz - az * by\n var ry = az * bx - ax * bz\n var rz = ax * by - ay * bx\n return [ rx, ry, rz ]\n}\n<\/code><\/pre>\n\u5411\u91cf\u4e58\u6cd5\uff0c\u53c9\u4e58\uff0c\u70b9\u4e58\u7684\u5176\u4ed6\u5b9e\u73b0\uff1a<\/p>\n
- complex-js<\/a><\/li>\n
- x<\/strong> – \u7c97\u4f53\u5c0f\u5199\u5b57\u6bcd\u7528\u505a\u5411\u91cf \uff08\u4f8b\u5982\u4e00\u4e2a2D\u70b9\uff09<\/li>\n
- \u7b49\u5f0f
- \u901a\u7528\u51fd\u6570<\/a><\/li>\n
- \u6b27\u51e0\u91cc\u5f97\u6a21<\/a><\/li>\n
- \u5411\u91cf\u4e58\u6cd5<\/a><\/li>\n
- \u7b49\u53f7