{"id":1173,"date":"2016-07-09T13:07:18","date_gmt":"2016-07-09T10:07:18","guid":{"rendered":"http:\/\/java.mazurok.com\/?p=1173"},"modified":"2016-07-13T22:05:18","modified_gmt":"2016-07-13T19:05:18","slug":"quaternion","status":"publish","type":"post","link":"https:\/\/java.mazurok.com\/?p=1173","title":{"rendered":"Quaternion"},"content":{"rendered":"

\u0423\u0441\u043b\u043e\u0432\u0438\u0435<\/h1>\n

\u041a\u0432\u0430\u0442\u0435\u0440\u043d\u0438\u043e\u043d\u044b<\/b> (\u043e\u0442 \u043b\u0430\u0442.\u00a0quaterni<\/span><\/i>, \u043f\u043e \u0447\u0435\u0442\u044b\u0440\u0435<\/i>)\u00a0\u2014 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u0433\u0438\u043f\u0435\u0440\u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b, \u043e\u0431\u0440\u0430\u0437\u0443\u044e\u0449\u0430\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c\u044e \u0447\u0435\u0442\u044b\u0440\u0435 \u043d\u0430\u0434 \u043f\u043e\u043b\u0435\u043c \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b. \u041e\u0431\u044b\u0447\u043d\u043e \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0442\u0441\u044f \u0441\u0438\u043c\u0432\u043e\u043b\u043e\u043c \"H\". \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u044b \u0423\u0438\u043b\u044c\u044f\u043c\u043e\u043c \u0413\u0430\u043c\u0438\u043b\u044c\u0442\u043e\u043d\u043e\u043c \u0432 1843 \u0433\u043e\u0434\u0443.
\n\u041a\u0432\u0430\u0442\u0435\u0440\u043d\u0438\u043e\u043d\u044b \u0443\u0434\u043e\u0431\u043d\u044b \u0434\u043b\u044f \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u044f \u0438\u0437\u043e\u043c\u0435\u0442\u0440\u0438\u0439 \u0442\u0440\u0451\u0445- \u0438 \u0447\u0435\u0442\u044b\u0440\u0451\u0445\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u0435\u0432\u043a\u043b\u0438\u0434\u043e\u0432\u044b\u0445 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432, \u0438 \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u0448\u0438\u0440\u043e\u043a\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u0432 \u043c\u0435\u0445\u0430\u043d\u0438\u043a\u0435. \u0422\u0430\u043a\u0436\u0435 \u0438\u0445 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442 \u0432 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u0440\u0438 \u0441\u043e\u0437\u0434\u0430\u043d\u0438\u0438 \u0442\u0440\u0451\u0445\u043c\u0435\u0440\u043d\u043e\u0439 \u0433\u0440\u0430\u0444\u0438\u043a\u0438.
\n\u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a: \u041a\u0432\u0430\u0442\u0435\u0440\u043d\u0438\u043e\u043d\u044b — \u0412\u0438\u043a\u0438\u043f\u0435\u0434\u0438\u044f<\/a>.<\/p>\n

\u041a\u043e\u0434 \u043d\u0430 Java:<\/h1>\n

\u041e\u043f\u0438\u0441\u0430\u043d\u0438\u0435 \u043a\u043b\u0430\u0441\u0441\u0430:<\/h2>\n
import java.util.*;\r\nimport java.lang.*;\r\nimport java.io.*;\r\n\r\nclass Quaternion {\r\n\tprivate double a;\r\n\tprivate double b;\r\n\tprivate double c;\r\n\tprivate double d;\r\n\t\r\n\tpublic Quaternion() {\r\n\t\ta = 0;\r\n\t\tb = 0;\r\n\t\tc = 0;\r\n\t\td = 0;\r\n\t}\r\n\tpublic Quaternion(double a) {\r\n\t\tthis.a = a;\r\n\t\tb = 0;\r\n\t\tc = 0;\r\n\t\td = 0;\r\n\t}\r\n\tpublic Quaternion(double a, double b, double c, double d) {\r\n\t\tthis.a = a;\r\n\t\tthis.b = b;\r\n\t\tthis.c = c;\r\n\t\tthis.d = d;\r\n\t}\r\n\t\r\n\tpublic Quaternion conjug() {\r\n\t\treturn new Quaternion(a, -b, -c, -d);\r\n\t}\r\n\tpublic double abs() {\r\n\t\treturn Math.sqrt(a * a  + b * b + c * c + d * d);\r\n\t}\r\n\tpublic Quaternion inverse() throws ArithmeticException {\r\n\t\treturn Quaternion.divide(this.conjug(), this.abs() * this.abs());\r\n\t}\r\n\tpublic boolean isZero() {\r\n\t\treturn (a == 0 && b == 0 && c == 0 && d == 0);\r\n\t}\r\n\t\r\n\tpublic static Quaternion sum(Quaternion a, Quaternion b) {\r\n\t\treturn new Quaternion(a.a + b.a, a.b + b.b, a.c + b.c, a.d + b.d);\r\n\t}\r\n\tpublic static Quaternion sub(Quaternion a, Quaternion b) {\r\n\t\treturn new Quaternion(a.a - b.a, a.b - b.b, a.c - b.c, a.d - b.d);\r\n\t}\r\n\tpublic static Quaternion mul(Quaternion a, double mult) {\r\n\t\treturn new Quaternion(a.a * mult, a.b * mult, a.c * mult, a.d * mult);\r\n\t}\r\n\tpublic static Quaternion mul(Quaternion a, Quaternion b) {\r\n\t\treturn new Quaternion(a.a * b.a - a.b * b.b - a.c * b.c - a.d * b.d,\r\n\t\t\t\t\t\t\t  a.a * b.b + a.b * b.a + a.c * b.d - a.d * b.c,\r\n\t\t\t\t\t\t\t  a.a * b.c - a.b * b.d + a.c * b.a + a.d * b.b,\r\n\t\t\t\t\t\t\t  a.a * b.d + a.b * b.c - a.c * b.b + a.d * b.a);\r\n\t}\r\n\tpublic static Quaternion divide(Quaternion a, double divider) throws ArithmeticException {\r\n\t\tif (divider == 0) throw new ArithmeticException(\"Zero divider\");\r\n\t\treturn new Quaternion(a.a \/ divider, a.b \/ divider, a.c \/ divider, a.d \/ divider);\r\n\t}\r\n\tpublic static Quaternion divide(Quaternion a, Quaternion b) throws ArithmeticException {\r\n\t\tif (b.isZero()) throw new ArithmeticException(\"Zero divider\");\r\n\t\treturn Quaternion.mul(a, b.inverse());\r\n\t}\r\n\t\r\n\tpublic String toString() {\r\n\t\treturn new String(a +\r\n\t\t\t\t\t\t  ((b < 0)? \" - \" : \" + \") + Math.abs(b) + \"*i\" +\r\n\t\t\t\t\t\t  ((c < 0)? \" - \" : \" + \") + Math.abs(c) + \"*j\" +\r\n\t\t\t\t\t\t  ((d < 0)? \" - \" : \" + \") + Math.abs(d) + \"*k\\n\");\r\n\t}\r\n}<\/pre>\n
\u0421\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/h3>\n
\u041a\u0432\u0430\u0442\u0435\u0440\u043d\u0438\u043e\u043d\u044b \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043a\u0430\u043a \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u0443\u044e \u0441\u0443\u043c\u043c\u0443 a + bi + cj + dk<\/strong>, \u0433\u0434\u0435 a, b, c, d<\/strong> \u2014 \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430, \u0430 i, j, k<\/strong> \u2014 \u043c\u043d\u0438\u043c\u044b\u0435 \u0435\u0434\u0438\u043d\u0438\u0446\u044b \u0441\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e\u043c: i2<\/sup> = j2<\/sup> = k2<\/sup> = ijk = \u22121<\/strong>.
\n\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \u0431\u0430\u0437\u0438\u0441\u043d\u044b\u0445 \u043a\u0432\u0430\u0442\u0435\u0440\u043d\u0438\u043e\u043d\u043e\u0432\u00a0\u2014 1, i, j, k<\/strong>\u00a0\u2014 \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0442\u0430\u043a:<\/p>\n\n\n\n\n\n\n\n
\u00d7<\/strong><\/td>\n1<\/strong><\/td>\ni<\/strong><\/td>\nj<\/strong><\/td>\nk<\/strong><\/td>\n<\/tr>\n
1<\/strong><\/td>\n1<\/td>\ni<\/td>\nj<\/td>\nk<\/td>\n<\/tr>\n
i<\/strong><\/td>\ni<\/td>\n-1<\/td>\nk<\/td>\n-j<\/td>\n<\/tr>\n
j<\/strong><\/td>\nj<\/td>\n-k<\/td>\n-1<\/td>\ni<\/td>\n<\/tr>\n
k<\/strong><\/td>\nk<\/td>\nj<\/td>\n-1<\/td>\n-1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\u0421\u043e\u043f\u0440\u044f\u0436\u0435\u043d\u0438\u0435<\/h3>\n
\u0414\u043b\u044f \u043a\u0432\u0430\u0442\u0435\u0440\u043d\u0438\u043e\u043d\u0430 q<\/strong> \u0441\u043e\u043f\u0440\u044f\u0436\u0451\u043d\u043d\u044b\u043c \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f:
\n\"conj(q)<\/p>\n
\u041c\u043e\u0434\u0443\u043b\u044c<\/h3>\n
\u0422\u0430\u043a \u0436\u0435, \u043a\u0430\u043a \u0438 \u0434\u043b\u044f \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b,
\n\"abs(q)
\n\u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043c\u043e\u0434\u0443\u043b\u0435\u043c<\/em> q<\/strong>.<\/p>\n
\u041e\u0431\u0440\u0430\u0449\u0435\u043d\u0438\u0435 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f (\u0434\u0435\u043b\u0435\u043d\u0438\u0435)<\/h3>\n
\u041a\u0432\u0430\u0442\u0435\u0440\u043d\u0438\u043e\u043d, \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439 \u043f\u043e \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044e \u043a  q<\/span><\/strong>, \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u0430\u043a:
\n\"q^-1.<\/p>\n
\u041e\u0441\u043d\u043e\u0432\u043d\u0430\u044f \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0430:<\/h2>\n
class Main {\r\n\tpublic static void main (String[] args) {\r\n\t\tQuaternion qt1 = new Quaternion();\r\n\t\tQuaternion qt2 = new Quaternion(5);\r\n\t\tQuaternion qt3 = new Quaternion(1, 2, 3, 4);\r\n\t\tQuaternion qt4 = new Quaternion(0.1, 1.4, -2.5, -1.7);\r\n\t\tif (!qt1.isZero()) {\r\n\t\t\tSystem.out.print(Quaternion.sum(qt3, qt4));\r\n\t\t} else {\r\n\t\t\tSystem.out.print(Quaternion.mul(qt3, qt4));\r\n\t\t}\r\n\t\tdo {\r\n\t\t\tqt2 = Quaternion.sub(qt2, qt3);\r\n\t\t\tSystem.out.print(qt2);\r\n\t\t\tSystem.out.print(qt2.conjug());\r\n\t\t\tSystem.out.print(qt2.inverse());\r\n\t\t} while (qt2.isZero());\r\n\t\ttry {\r\n\t\t\tSystem.out.print(Quaternion.divide(qt3, qt4));\r\n\t\t} catch (ArithmeticException e) {\r\n\t\t\tSystem.out.print(e.getMessage());\r\n\t\t}\r\n\t\tSystem.out.print(Quaternion.mul(qt3, 17.2));\r\n\t}\r\n}<\/pre>\n
\u0425\u043e\u0434 \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f<\/h2>\n
\u041f\u0440\u0438 \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u0438 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043a\u043b\u0430\u0441\u0441\u0430: \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0445, \u0430\u0440\u0438\u0444\u043c\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445, \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u044f \u043e\u0431\u044a\u0435\u043a\u0442\u043e\u0432, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043e\u0442 \u0438\u0441\u0445\u043e\u0434\u043d\u043e\u0433\u043e (\u0442\u0430\u043a\u0438\u0445, \u043a\u0430\u043a \u0441\u043e\u043f\u0440\u044f\u0436\u0435\u043d\u043d\u043e\u0435 \u0438 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435), \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0442\u0440\u043e\u043a\u043e\u0432\u043e\u0433\u043e \u043e\u0442\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u043e\u0431\u044a\u0435\u043a\u0442\u0430.<\/p>\n
\u0412\u044b\u0432\u043e\u0434 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u044b:<\/h2>\n
11.600000000000001 + 6.5*i + 6.8*j - 10.499999999999998*k\r\n4.0 - 2.0*i - 3.0*j - 4.0*k\r\n4.0 + 2.0*i + 3.0*j + 4.0*k\r\n0.08888888888888888 + 0.04444444444444444*i + 0.06666666666666665*j + 0.08888888888888888*k\r\n-1.026102610261026 - 0.5490549054905489*i - 0.5580558055805579*j + 1.017101710171017*k\r\n17.2 + 34.4*i + 51.599999999999994*j + 68.8*k<\/pre>\n
\u0421\u0441\u044b\u043b\u043a\u0438:<\/h1>\n
\u0420\u0430\u0431\u043e\u0447\u0438\u0439 \u043a\u043e\u0434 \u0434\u043b\u044f \u0442\u0435\u0441\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043d\u0430 Ideone.com: Ideone.com<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
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