Can maple 10 do graph pattern matching or find a repeating cycle in an equation/graph tia sal2

Discussion in 'Maple' started by temp, May 29, 2006.

  1. temp

    temp Guest

    Greetings All.

    I'm trying to find out where this graph starts to repeat its cycle. I
    think it's called graph pattern matching but I could be wrong. I looked up
    in the help and the only thing that was close was stringtools but I can't
    use that because I'm using an equation/graph. Is there a command that will
    do graph pattern matching in maple 10 so I can know where a graph repeats?

    tia sal2

    a1 := x -> sin(x)

    a2 := x -> 2 sin(2 x)

    a4 := x -> 4 sin(4 x)

    a8 := x -> 8 sin(8 x)

    a7 := x -> 7 sin(7 x)

    a5 := x -> 5 sin(5 x)

    plot([a1 + a2 + a4 + a8 + a7 + a5], 0 .. 16, color = [black])
     
    temp, May 29, 2006
    #1
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  2. It has nothing to do with graphs. You have a function and you want
    to find its minimal period. Here's one possibility that might work
    (it does in your example with sines):
    solve(identity(F(x+T)=F(x), x));

    2 Pi _Z1~

    So the answer is 2 Pi.

    Robert Israel
    Department of Mathematics http://www.math.ubc.ca/~israel
    University of British Columbia Vancouver, BC, Canada
     
    Robert Israel, May 29, 2006
    #2
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  3. temp

    Mladen Guest


    I have a question, regarding similar problem of plotting multiple plots
    in same window (example: y(x) = C*x^2, C= {1..30} ) -> familiy of
    parabolas


    how to write a "for C 1 to 30 do" loop in implicitplot or plot
    function?

    TIA

    Mladen
     
    Mladen, May 30, 2006
    #3
  4. temp

    Peter Pein Guest

    try
    plot({c*x^2$c=1..30},x=-1..1);
     
    Peter Pein, May 30, 2006
    #4
  5. temp

    Mladen Guest

    Peter Pein je napisao/la:
    /.../
    Danke!

    Please do tell me what is this operator ("$") called. I would like to
    see its definition and examples.

    Mladen
     
    Mladen, May 31, 2006
    #5
  6. It's the dollar operator, which forms a sequence of expressions.
    To display its help page, enter ?$ (or ?dollar, if you prefer).

    A common application is the entry of higher derivatives:
    diff(cos(3*x),x$5);
    is more readable and saves some keystrokes as compared to
    diff(cos(3*x),x,x,x,x,x);

    Note that Maple 10 can also find many derivatives of symbolic
    (unspecified) order: diff(cos(3*x),x$n);
     
    Thomas Richard, May 31, 2006
    #6
  7. Be careful with the dollar operator: it evaluates the left hand
    side -once- and takes that result and evaluates it for each
    value specified on the right. For example,
    427419669081, 427419669081, 427419669081, 427419669081, 427419669081
    321110693270, 343633073697, 474256143563, 558458718976, 746753830538
    SQUARE(1), SQUARE(2), SQUARE(3), SQUARE(4), SQUARE(5)
    1, 4, 9, 16, 25
     
    Walter Roberson, May 31, 2006
    #7
  8. temp

    Mladen Guest

    Thanks for the tips!

    But Maple resists to accept 'dollar' in implicitplot function. :(
    (or I don't know the syntax? :) )
    And unfortunately, 'dollar' doesn't have a 'step' - like 'for' loop
    does.
    Only half of a problem is solved, because the field is too dense for
    bigger C :(

    The truth is I need to plot orthogonal trajectories:
    for example family of parabolas y= a*x^2 and family of ellipses x^2 +
    2y^2 = c

    is there maybe another way of solving the problem?

    Mladen
     
    Mladen, May 31, 2006
    #8
  9. temp

    Peter Pein Guest

    Do you want sth. like this:
    clist:=[1/8,1/4,1/2,1,2,4]:plot(map(c->c*x^2,clist),x=-3/2..3/2,y=0..2);
    or that:
    plot(map(c->[c*cos(t),c/sqrt(2)*sin(t),t=0..2*Pi],clist),scaling=constrained);
    ?
     
    Peter Pein, Jun 1, 2006
    #9
  10. temp

    Mladen Guest

    Peter Pein je napisao/la:
    Yes! That's it!
    Thanks a lot!
    But can this be plotted in a single window?
    If not, I'll figure something out with photoshop... ;)
     
    Mladen, Jun 1, 2006
    #10
  11. temp

    Peter Pein Guest

    Try it! ;-)

    It displays all curves which belong to the parameter-list into a single plot.
     
    Peter Pein, Jun 2, 2006
    #11
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