<\/a> \u2014 ayy+by+c=0 <\/p>\n <\/p>\n \u0415\u0441\u043b\u0438 \u044d\u043b\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043a\u0440\u0438\u0432\u0430\u044f \u0415 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u043a\u043e\u043b\u044c\u0446\u0430 \u0432\u044b\u0447\u0435\u0442\u043e\u0432 Z|n, \u0442\u043e \u0437\u0430\u0434\u0430\u0447\u0430 \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u044d\u043b\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043a\u0440\u0438\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0431\u043e\u043b\u0435\u0435 \u0441\u043b\u043e\u0436\u043d\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0435\u0439. \u2014 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u044b N a1 a2 a3 a4 a6<\/p>\n \u0414\u043b\u044f \u0440\u0430\u0431\u043e\u0442\u044b \u0441 \u043a\u044d\u0448\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u043c\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043b\u0435\u0432\u043e\u0439 \u0438 \u043f\u0440\u0430\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0435\u0439 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u044d\u043b\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043a\u0440\u0438\u0432\u043e\u0439 \u0415, \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c DBMS, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u043e\u0437\u0432\u043e\u043b\u0438\u0442 \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u043e\u043f\u0442\u0438\u043c\u0430\u043b\u044c\u043d\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u0440\u0430\u0431\u043e\u0442\u0443 \u043f\u043e \u0438\u043d\u0434\u0435\u043a\u0441\u0430\u0446\u0438\u0438 \u043a\u043e\u043b\u043e\u043d\u043e\u043a \u0442\u0430\u0431\u043b\u0438\u0446 \u0438 \u043e\u0431\u044a\u0435\u0434\u0438\u043d\u0435\u043d\u0438\u044e \u044d\u0442\u0438\u0445 \u0442\u0430\u0431\u043b\u0438\u0446.<\/p>\n t1 t2 t3 if(a1!=0 mod N) select t1.x,t2.y from t1, t2, t3 where (key1=key2+key3 or key1+N=key2+key3) and t1.x=t3.x and t2.y=t3.y \u2014 DBMS \u2014 SQLite <\/p>\n <\/p>\n \u0427\u0442\u043e \u0438 \u0442\u0440\u0435\u0431\u043e\u0432\u0430\u043b\u043e\u0441\u044c \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c<\/b><\/p>\n \u0418\u0441\u0445\u043e\u0434\u043d\u044b\u0435 \u043a\u043e\u0434\u044b \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c \u0434\u043e\u0441\u0442\u0443\u043f\u043d\u044b \u043f\u043e \u0430\u0434\u0440\u0435\u0441\u0443 https:\/\/github.com\/dprotopopov\/mssove3<\/a> <\/p>\n
\u2014 a=a(x)=1
\u2014 b=b(x)=a1*x+a3
\u2014 c=c(x)=-(x^3+a2*x^2+a4*x+a6)<\/p>\n
\u2014 D=bb-4ac
\u2014 y1=(-b-sqrt(D))\/(2a)
\u2014 y2=(-b+sqrt(D))\/(2a)<\/p>\n\u0420\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f<\/h3>\n
private void button1_Click(object sender, EventArgs e) { LockForm(); \/\/ \u041f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u044d\u043b\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043a\u0440\u0438\u0432\u043e\u0439 double a1 = GetA1(); double a2 = GetA2(); double a3 = GetA3(); double a4 = GetA4(); double a6 = GetA6(); \/\/ \u0414\u0438\u0430\u043f\u0430\u0437\u043e\u043d \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 X \u0438 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u043e\u0432 double xmin = GetXmin(); double xmax = GetXmax(); ulong n = GetN(); \/\/ http:\/\/stackoverflow.com\/questions\/10622674\/chart-creating-dynamically-in-net-c-sharp var series1 = new Series { Name = "Series1", Color = Color.Black, IsVisibleInLegend = false, IsXValueIndexed = true, ChartType = SeriesChartType.Line }; var series2 = new Series { Name = "Series2", Color = Color.Black, IsVisibleInLegend = false, IsXValueIndexed = true, ChartType = SeriesChartType.Line }; var sb = new StringBuilder(); var sb1 = new StringBuilder(); sb.AppendLine("y^2+a1*x*y+a3*y = x^3+a2*x^2+a4*x+a6"); sb.AppendLine("a1=" + a1); sb.AppendLine("a2=" + a2); sb.AppendLine("a3=" + a3); sb.AppendLine("a4=" + a4); sb.AppendLine("a6=" + a6); sb.AppendLine(); sb.AppendLine("# X Y1 Y2"); sb1.AppendLine("# X Y1 Y2"); for (ulong i = 0; i <= n; i++) { double x = (xmin*(n - i) + xmax*i)\/n; \/\/ \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u043c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u0434\u0430\u043d\u043d\u043e\u0433\u043e X const double a = 1; double b = a1*x + a3; double c = -(x*x*x + a2*x*x + a4*x + a6); \/\/ \u041f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u0437\u0430 \u0448\u0435\u0441\u0442\u043e\u0439 \u043a\u043b\u0430\u0441\u0441 \u0441\u0440\u0435\u0434\u043d\u0435\u0439 \u0448\u043a\u043e\u043b\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f double d = b*b - 4*a*c; if (d < 0) continue; double y1 = (-b - Math.Sqrt(d))\/(2*a); double y2 = (-b + Math.Sqrt(d))\/(2*a); series1.Points.AddXY(x, y1); series2.Points.AddXY(x, y2); sb.AppendLine(x + " " + y1 + " " + y2); sb1.AppendLine(x + " " + y1 + " " + y2); } \/\/ \u0412\u044b\u0434\u0430\u0451\u043c \u043e\u0442\u0447\u0451\u0442 \u043e \u043f\u0440\u043e\u0434\u0435\u043b\u0430\u043d\u043d\u043e\u0439 \u0440\u0430\u0431\u043e\u0442\u0435 SetChart(series1, series2); SetReport(sb.ToString()); SetReport1(sb1.ToString()); UnlockForm(); ActivatePage(2); } <\/code><\/pre>\n\u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442<\/h3>\n
![\"\u042d\u043b\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f](\"https:\/\/raw.githubusercontent.com\/dprotopopov\/mssove3\/master\/EllipticR.jpg\")
<\/p>\n\u042d\u043b\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043a\u0440\u0438\u0432\u0430\u044f \u0415 \u0432 \u043a\u043e\u043b\u044c\u0446\u0435 \u0432\u044b\u0447\u0435\u0442\u043e\u0432 Z|n<\/h2>\n
\u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0438\u0442\u044c \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u0439 \u043b\u0435\u0433\u043a\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u0443\u0435\u043c\u044b\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c rendezvous \u0441\u043e\u0435\u0434\u0438\u043d\u0435\u043d\u0438\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u043b\u0435\u0432\u043e\u0439 \u0438 \u043f\u0440\u0430\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0435\u0439 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u044d\u043b\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043a\u0440\u0438\u0432\u043e\u0439 \u0415:<\/p>\n\n
x key1 = x^3+a2*x^2+a4*x+a6 mod N
1\u2026
2\u2026
3\u2026
\u2026
N rN<\/p>\n
y key2 = y^2+a3*y mod N
1\u2026
2\u2026
3\u2026
\u2026
N lN<\/p>\n
x y key3=a1*x*y mod N
1 1\u2026
1 2\u2026
\u2026
N N\u2026<\/p>\n
if(a1==0 mod N) select t1.x,t2.y from t1, t2 where key1=key2<\/p>\n\u0420\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f<\/h3>\n
private void button1_Click(object sender, EventArgs e) { LockForm(); \/\/ \u041f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u043a\u043e\u043b\u044c\u0446\u0430 \u0432\u044b\u0447\u0435\u0442\u043e\u0432 Z|n var n = GetN(); \/\/ \u041f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u044d\u043b\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043a\u0440\u0438\u0432\u043e\u0439 var a1 = GetA1(); var a2 = GetA2(); var a3 = GetA3(); var a4 = GetA4(); var a6 = GetA6(); \/\/ http:\/\/stackoverflow.com\/questions\/9173485\/how-can-i-create-an-in-memory-sqlite-database var connection = new SQLiteConnection("Data Source=:memory:"); connection.Open(); \/\/ \u0421\u043e\u0437\u0434\u0430\u0451\u043c \u0442\u0430\u0431\u043b\u0438\u0446\u044b string[] sqls1 = { "CREATE TABLE t1 (x INTEGER , key1 INTEGER )", "CREATE TABLE t2 (y INTEGER , key2 INTEGER )", "CREATE TABLE t3 (x INTEGER , y INTEGER , key3 INTEGER )" }; foreach (var sql in sqls1) new SQLiteCommand(sql, connection).ExecuteNonQuery(); \/\/ \u0417\u0430\u043f\u043e\u043b\u043d\u044f\u0435\u043c \u0442\u0430\u0431\u043b\u0438\u0446\u044b \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c\u0438 for (ulong x = 0; x < n; x++) { var x2 = (x*x)%n; var x3 = (x2*x)%n; var a2X2 = (a2*x2)%n; var a4X = (a4*x)%n; var key1 = (x3 + a2X2 + a4X + a6)%n; var sql = string.Format("INSERT INTO t1 (x, key1) VALUES ({0},{1})", x, key1); new SQLiteCommand(sql, connection).ExecuteNonQuery(); } for (ulong y = 0; y < n; y++) { var y2 = y*y%n; var a3Y = (a3*y)%n; var key2 = (y2 + a3Y)%n; var sql = string.Format("INSERT INTO t2 (y, key2) VALUES ({0},{1})", y, key2); new SQLiteCommand(sql, connection).ExecuteNonQuery(); } if ((a1%n) != 0) for (ulong x = 0; x < n; x++) { var a1X = (a1*x)%n; for (ulong y = 0; y < n; y++) { var key3 = (a1X*y)%n; var sql = string.Format("INSERT INTO t3 (x, y, key3) VALUES ({0},{1},{2})", x, y, key3); new SQLiteCommand(sql, connection).ExecuteNonQuery(); } } \/\/ \u0421\u043e\u0437\u0434\u0430\u0451\u043c \u0438\u043d\u0434\u0435\u043a\u0441\u044b \u0434\u043b\u044f \u0442\u0430\u0431\u043b\u0438\u0446 string[] sqls2 = { "CREATE INDEX t1key1 ON t1 (key1)", "CREATE INDEX t2key2 ON t2 (key2)", "CREATE INDEX t3key3 ON t3 (key3)", "CREATE UNIQUE INDEX t1x ON t1 (x)", "CREATE UNIQUE INDEX t2y ON t2 (y)", "CREATE INDEX t3x ON t3 (x)", "CREATE INDEX t3y ON t3 (y)" }; foreach (var sql in sqls2) new SQLiteCommand(sql, connection).ExecuteNonQuery(); \/\/ http:\/\/stackoverflow.com\/questions\/10622674\/chart-creating-dynamically-in-net-c-sharp var series1 = new Series { Name = "Series1", Color = Color.Black, IsVisibleInLegend = false, IsXValueIndexed = true, ChartType = SeriesChartType.Point }; \/\/ \u0412\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u043c JOIN \u0437\u0430\u043f\u0440\u043e\u0441 \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b \/\/ \u0427\u0435\u043c \u0434\u043e\u0440\u043e\u0436\u0435 DBMS \u0442\u0435\u043c \u043b\u0443\u0447\u0448\u0435 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u044b \u043e\u043d\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442 \u0434\u043b\u044f \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0437\u0430\u043f\u0440\u043e\u0441\u043e\u0432 var select = ((a1%n) == 0) ? "SELECT t1.x,t2.y FROM t1, t2 WHERE key1=key2" : "SELECT t1.x,t2.y FROM t1, t2, t3 WHERE (key1=key2+key3 or key1+" + n + "=key2+key3) AND t1.x=t3.x AND t2.y=t3.y"; var reader = new SQLiteCommand(select, connection).ExecuteReader(); var sb = new StringBuilder(); var sb1 = new StringBuilder(); sb.AppendLine("y^2+a1*x*y+a3*y = x^3+a2*x^2+a4*x+a6 mod n"); sb.AppendLine("n=" + n); sb.AppendLine("a1=" + a1); sb.AppendLine("a2=" + a2); sb.AppendLine("a3=" + a3); sb.AppendLine("a4=" + a4); sb.AppendLine("a6=" + a6); sb.AppendLine(); sb.AppendLine("# X Y"); sb1.AppendLine("# X Y"); while (reader.Read()) { var x = Convert.ToInt32(reader[0]); var y = Convert.ToInt32(reader[1]); series1.Points.AddXY(x, y); sb.AppendLine(x + " " + y); sb1.AppendLine(x + " " + y); } \/\/ \u0412\u044b\u0434\u0430\u0451\u043c \u043e\u0442\u0447\u0451\u0442 \u043e \u043f\u0440\u043e\u0434\u0435\u043b\u0430\u043d\u043d\u043e\u0439 \u0440\u0430\u0431\u043e\u0442\u0435 SetChart(series1); SetReport(sb.ToString()); SetReport1(sb1.ToString()); connection.Close(); UnlockForm(); ActivatePage(2); } <\/code><\/pre>\n\u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442<\/h3>\n
![\"\u042d\u043b\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f](\"https:\/\/raw.githubusercontent.com\/dprotopopov\/mssove3\/master\/EllipticZn.jpg\")
<\/p>\n