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Hello.
I want to solve a system of equations for a straight line and a tangent to an ellipse.
A straight line: y - y1 = (y2 - y1) / (x2 - x1) * (x - x1) A tangent to an ellipse: x * x3 / a ^ 2 + y * y3 / b ^ 2 = 1
So I ran the following test code and it didn't finish.
Apparently the Rational.Simplify method is taking a long time.
My operating environment is as follows.
The dependent libraries are:
Is there any good solution to reduce the processing time?
Thank you.
using MathNet.Symbolics; using NUnit.Framework; using System; using System.Collections.Generic; using System.Threading.Tasks; namespace boilersGraphics.Test { using Expr = MathNet.Symbolics.Expression; [TestFixture] public class MathNetTest { [Test] public void Basic() { var x = Expr.Symbol("x"); var y = Expr.Symbol("y"); var x1 = Expr.Symbol("x1"); var y1 = Expr.Symbol("y1"); var x2 = Expr.Symbol("x2"); var y2 = Expr.Symbol("y2"); var x3 = Expr.Symbol("x3"); var y3 = Expr.Symbol("y3"); var a = Expr.Symbol("a"); var b = Expr.Symbol("b"); Expr left_line = y - y1; Expr right_line = (y2 - y1) / (x2 - x1) * (x - x1); Expr left_tangent = x * x3 / Expr.Pow(a, 2) + y * y3 / Expr.Pow(b, 2); Expr right_tangent = 1; Expr line_x = null; Expr tangent_x = null; Parallel.Invoke( () => { line_x = SolveSimpleRoot(x, left_line - right_line); }, () => { tangent_x = SolveSimpleRoot(x, left_tangent - right_tangent); } ); Expr cy = SolveSimpleRoot(y, line_x - tangent_x); Expr cx = Algebraic.Expand(Structure.Substitute(y, cy, line_x)); Console.WriteLine(Infix.Format(cx)); Console.WriteLine(Infix.Format(cy)); } // Quote from https://stackoverflow.com/questions/31223380/solving-system-of-linear-equations-using-mathdotnet Expr SolveSimpleRoot(Expr variable, Expr expr) { // try to bring expression into polynomial form Expr simple = Algebraic.Expand(Rational.Numerator(Rational.Simplify(variable, expr))); // extract coefficients, solve known forms of order up to 1 Expr[] coeff = MathNet.Symbolics.Polynomial.Coefficients(variable, simple); switch (coeff.Length) { case 1: return Expr.Zero.Equals(coeff[0]) ? variable : Expr.Undefined; case 2: return Rational.Simplify(variable, Algebraic.Expand(-coeff[0] / coeff[1])); //heavy code default: return Expr.Undefined; } } } }
The text was updated successfully, but these errors were encountered:
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Hello.
I want to solve a system of equations for a straight line and a tangent to an ellipse.
A straight line: y - y1 = (y2 - y1) / (x2 - x1) * (x - x1)
A tangent to an ellipse: x * x3 / a ^ 2 + y * y3 / b ^ 2 = 1
So I ran the following test code and it didn't finish.
Apparently the Rational.Simplify method is taking a long time.
My operating environment is as follows.
The dependent libraries are:
Is there any good solution to reduce the processing time?
Thank you.
The text was updated successfully, but these errors were encountered: