I didn't take a deep look into this example. I just looked at the picture. On this picture, the theta can not return back, so the curve can not be closed from the right hand side. The only possibility for it to be closed is if turns to the left hand side and closes there. From the picture, it seems as if it reaches infinity soon, instead of turning to the left. In this particular example Maple's performance was not bad - it found a solution even with initial point being that close to a singularity and it plotted the solution that it found. I would rather call it 'very impressive' than unreliable (unless it is wrong, of course.) Did you see the ranges? Numerical calculations with real numbers (or integers, or integers mod p) of moderate ranges, using only elementary functions, are often correct in Maple (except, maybe, few specific algorithms.) That doesn't mean that they shouldn't be double or triple checked if possible, using various methods, but that is just a nature (or culture) of any mathematical work. In general, I think that Maple language is easy to use. It takes some time to learn it, but the same can be said about any other language. _________ Alec Mihailovs http://mihailovs.com/Alec/

I didn't take a deep look into this example. I just looked at the picture. On this picture, the theta can not return back, so the curve can not be closed from the right hand side. The only possibility for it to be closed is if turns to the left hand side and closes there. From the picture, it seems as if it reaches infinity soon, instead of turning to the left. In this particular example Maple's performance was not bad - it found a solution even with initial point being that close to a singularity and it plotted the solution that it found. I would rather call it 'very impressive' than unreliable (unless it is wrong, of course.) Did you see the ranges? Numerical calculations with real numbers (or integers, or integers mod p) of moderate ranges, using only elementary functions, are often correct in Maple (except, maybe, few specific algorithms.) That doesn't mean that they shouldn't be double or triple checked if possible, using various methods, but that is just a nature (or culture) of any mathematical work. In general, I think that Maple language is easy to use. It takes some time to learn it, but the same can be said about any other language. _________ Alec Mihailovs http://mihailovs.com/Alec/

'recent posts' link at the lhs is quite useful - if there is a new blog (or forum) post - it is usually there (except if the category is not specified.) __________ Alec Mihailovs http://mihailovs.com/Alec/

I found interesting that comp.soft-sys.matlab is listed there, but comp.soft-sys.math.maple - not. This site is also not listed. __________ Alec Mihailovs http://mihailovs.com/Alec/

soln(0.1);

Error, (in soln) cannot evaluate the solution further right of .59709089e-23, probably a singularity

soln(-0.1);

Error, (in soln) cannot evaluate the solution further left of -.59709089e-23, probably a singularity

Still, it can be plotted as

plot(R,-.59e-23..0.59e-23,coords=polar);

or

plots[polarplot](R,-.59e-23..0.59e-23);

__________ Alec Mihailovs http://mihailovs.com/Alec/

soln(0.1);

Error, (in soln) cannot evaluate the solution further right of .59709089e-23, probably a singularity

soln(-0.1);

Error, (in soln) cannot evaluate the solution further left of -.59709089e-23, probably a singularity

Still, it can be plotted as

plot(R,-.59e-23..0.59e-23,coords=polar);

or

plots[polarplot](R,-.59e-23..0.59e-23);

__________ Alec Mihailovs http://mihailovs.com/Alec/

If you provided a complete example, so that I could copy and paste it in Maple, I would post the right code (the same with animation - I am kinda busy at the moment). __________ Alec Mihailovs http://mihailovs.com/Alec/

If you provided a complete example, so that I could copy and paste it in Maple, I would post the right code (the same with animation - I am kinda busy at the moment). __________ Alec Mihailovs http://mihailovs.com/Alec/

HTML no longer allowed by file manager. __________ Alec Mihailovs http://mihailovs.com/Alec/

HTML no longer allowed by file manager. __________ Alec Mihailovs http://mihailovs.com/Alec/

Very similar,

_EnvAllSolutions:=true:
                     
_EnvExplicit:=true:

solve({seq(i,i=A.A-E),seq(i,i=B.B-E),seq(i,i=A.B+B.A)});

               2
         -1 + h                        2 h
  {g = - -------, b = 0, a = -1, c = - ---, h = h, d = 1, e = -h,
            f                           f

                                      2
                     2 h        -1 + h
        f = f}, {c = ---, g = - -------, b = 0, h = h, d = -1, a = 1,
                      f            f

        e = -h, f = f},

        {e = -1, h = 1, b = b, f = 0, g = 0, d = 0, c = 1/b, a = 0},

        {h = -1, b = b, e = 1, f = 0, g = 0, d = 0, c = 1/b, a = 0},

                                                    2 d
        {e = -1, h = 1, d = d, f = 0, a = -d, b = - ---,
                                                     g

                   2
            (-1 + d ) g
        c = -----------, g = g}, {h = -1, d = d, e = 1, f = 0, a = -d,
                2 d

                              2                          2
            2 d        (-1 + d ) g                 -1 + h
        b = ---, c = - -----------, g = g}, {g = - -------, b = b,
             g             2 d                        f

                                  b h + %1
        h = h, e = -h, f = f, d = --------,
                                     f

                                     2
            -2 (b h + %1) h - b + b h         b h + %1
        c = --------------------------, a = - --------}, {
                         2                       f
                        f

                    2
              -1 + h                                    b h - %1
        g = - -------, b = b, h = h, e = -h, f = f, d = --------,
                 f                                         f

                                     2
            -2 (b h - %1) h - b + b h         b h - %1
        c = --------------------------, a = - --------}
                         2                       f
                        f

          2    2 1/2
  %1 := (f  + b )

seq(eval(['A'=A,'B'=B],i),i=%);

       [ -1      0]                [ 1      0]
       [          ]                [         ]
  [A = [  2 h     ], B = %1], [A = [2 h      ], B = %1],
       [- ---    1]                [---    -1]
       [   f      ]                [ f       ]

             [ 0     b]      [-1    0]
        [A = [        ], B = [       ]],
             [1/b    0]      [ 0    1]

             [ 0     b]      [1     0]
        [A = [        ], B = [       ]],
             [1/b    0]      [0    -1]

             [                 2 d]
             [    -d         - ---]
             [                  g ]      [-1    0]
        [A = [                    ], B = [       ]],
             [       2            ]      [g     1]
             [(-1 + d ) g         ]
             [-----------      d  ]
             [    2 d             ]

             [                 2 d]
             [     -d          ---]
             [                  g ]      [1     0]
        [A = [                    ], B = [       ]],
             [         2          ]      [g    -1]
             [  (-1 + d ) g       ]
             [- -----------     d ]
             [      2 d           ]

             [          b h + %2                    ]
             [        - --------               b    ]
             [             f                        ]
             [                                      ]
        [A = [                         2            ], B = %1],
             [-2 (b h + %2) h - b + b h     b h + %2]
             [--------------------------    --------]
             [             2                   f    ]
             [            f                         ]

             [          b h - %2                    ]
             [        - --------               b    ]
             [             f                        ]
             [                                      ]
        [A = [                         2            ], B = %1]
             [-2 (b h - %2) h - b + b h     b h - %2]
             [--------------------------    --------]
             [             2                   f    ]
             [            f                         ]

        [   -h        f]
        [              ]
  %1 := [        2     ]
        [  -1 + h      ]
        [- -------    h]
        [     f        ]

          2    2 1/2
  %2 := (f  + b )

__________ Alec Mihailovs http://mihailovs.com/Alec/

Very similar,

_EnvAllSolutions:=true:
                     
_EnvExplicit:=true:

solve({seq(i,i=A.A-E),seq(i,i=B.B-E),seq(i,i=A.B+B.A)});

               2
         -1 + h                        2 h
  {g = - -------, b = 0, a = -1, c = - ---, h = h, d = 1, e = -h,
            f                           f

                                      2
                     2 h        -1 + h
        f = f}, {c = ---, g = - -------, b = 0, h = h, d = -1, a = 1,
                      f            f

        e = -h, f = f},

        {e = -1, h = 1, b = b, f = 0, g = 0, d = 0, c = 1/b, a = 0},

        {h = -1, b = b, e = 1, f = 0, g = 0, d = 0, c = 1/b, a = 0},

                                                    2 d
        {e = -1, h = 1, d = d, f = 0, a = -d, b = - ---,
                                                     g

                   2
            (-1 + d ) g
        c = -----------, g = g}, {h = -1, d = d, e = 1, f = 0, a = -d,
                2 d

                              2                          2
            2 d        (-1 + d ) g                 -1 + h
        b = ---, c = - -----------, g = g}, {g = - -------, b = b,
             g             2 d                        f

                                  b h + %1
        h = h, e = -h, f = f, d = --------,
                                     f

                                     2
            -2 (b h + %1) h - b + b h         b h + %1
        c = --------------------------, a = - --------}, {
                         2                       f
                        f

                    2
              -1 + h                                    b h - %1
        g = - -------, b = b, h = h, e = -h, f = f, d = --------,
                 f                                         f

                                     2
            -2 (b h - %1) h - b + b h         b h - %1
        c = --------------------------, a = - --------}
                         2                       f
                        f

          2    2 1/2
  %1 := (f  + b )

seq(eval(['A'=A,'B'=B],i),i=%);

       [ -1      0]                [ 1      0]
       [          ]                [         ]
  [A = [  2 h     ], B = %1], [A = [2 h      ], B = %1],
       [- ---    1]                [---    -1]
       [   f      ]                [ f       ]

             [ 0     b]      [-1    0]
        [A = [        ], B = [       ]],
             [1/b    0]      [ 0    1]

             [ 0     b]      [1     0]
        [A = [        ], B = [       ]],
             [1/b    0]      [0    -1]

             [                 2 d]
             [    -d         - ---]
             [                  g ]      [-1    0]
        [A = [                    ], B = [       ]],
             [       2            ]      [g     1]
             [(-1 + d ) g         ]
             [-----------      d  ]
             [    2 d             ]

             [                 2 d]
             [     -d          ---]
             [                  g ]      [1     0]
        [A = [                    ], B = [       ]],
             [         2          ]      [g    -1]
             [  (-1 + d ) g       ]
             [- -----------     d ]
             [      2 d           ]

             [          b h + %2                    ]
             [        - --------               b    ]
             [             f                        ]
             [                                      ]
        [A = [                         2            ], B = %1],
             [-2 (b h + %2) h - b + b h     b h + %2]
             [--------------------------    --------]
             [             2                   f    ]
             [            f                         ]

             [          b h - %2                    ]
             [        - --------               b    ]
             [             f                        ]
             [                                      ]
        [A = [                         2            ], B = %1]
             [-2 (b h - %2) h - b + b h     b h - %2]
             [--------------------------    --------]
             [             2                   f    ]
             [            f                         ]

        [   -h        f]
        [              ]
  %1 := [        2     ]
        [  -1 + h      ]
        [- -------    h]
        [     f        ]

          2    2 1/2
  %2 := (f  + b )

__________ Alec Mihailovs http://mihailovs.com/Alec/

Well, you can catch it using lasterror. Something like

try soln(100000) catch: lasterror[-1] end;
 
                              0.90133000

That should work well together with stop_cond, as Allan Wittkopf suggested. It should be written more carefully though. __________ Alec Mihailovs http://mihailovs.com/Alec/

Well, you can catch it using lasterror. Something like

try soln(100000) catch: lasterror[-1] end;
 
                              0.90133000

That should work well together with stop_cond, as Allan Wittkopf suggested. It should be written more carefully though. __________ Alec Mihailovs http://mihailovs.com/Alec/

I would choose the value of t where soln stops,

f(.90133);
                                             -5
                      0.727908994686135296 10

It is already close enough to 0 for the precision of your initial conditions. __________ Alec Mihailovs http://mihailovs.com/Alec/