MaplePrimes - answers and comments on Question, intersection point of two plots

intersection point

Robert Israel — Fri, 03 Jul 2009 21:14:55 Z

Because you left out a multiplication sign, your d1 is interpreted as sec(I*(x^2-2)) (which is real-valued). Putting the multiplication sign in, you get an expression that is real only when x is a multiple of Pi.

Now I'm not sure what you mean by "intersection point". Are you trying to solve d1 = d2? That won't have any real solutions.

Graphical intersection

Christopher2222 — Fri, 03 Jul 2009 21:40:47 Z

I think he means what are the points where the lines cross as viewed from the plot and how can it be calculated.

Following Robert Israel's

gulliet — Sat, 04 Jul 2009 00:15:20 Z

Following Robert Israel's hints and suggestion about the d1 expression, we can see that the plot contains d2 only.

> restart;
> d1 := sec(I*(x^2-2))*(exp(I*x)*sin(2*x)+cos(I*(2*x-3)));

                  / 2    \                                    
              sech\x  - 2/ (exp(I x) sin(2 x) + cosh(2 x - 3))

> d2 := 1/2;
                                      1
                                      -
                                      2


> plot([d1, d2], x = -5 .. 5);
Warning, unable to evaluate 1 of the 2 functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

Note that you can look for the zeroes of d1-d2 thanks to the function RootFinding:-Analytic and you can also get plot of the complex expression with plots:-complexplot.

> RootFinding:-Analytic(d1-d2, x, re = -4 .. 4, im = -10 .. 10);

                 0.692769566066800 + 0.716998844038150 I, 

                   0.233941585379303 - 0.856174437455665 I, 

                   2.02176105726006 + 1.30134684099697 I

> plots:-complexplot(d1, x = -10 .. 10);

HTH, -- Jean-Marc