You could use contourplot command. For example, as

E:=-sqrt(5-Pi)*r*(cos(2*phi)-sin(2*phi));
eval(E,[r=sqrt(x^2+y^2),phi=arctan(y,x)]);
contourplot(%,x=-1..1,y=-1..1);

Alec

I waited for Alejandro to see whether that works in Maple V Release 5.1. In Maple 12 it gives

                                        (-b)
                         h(t) := ln(1/t)


                                                              1/2
                             _c[1]                       _c[1]    x
  u(t, x) = _C1 exp(-1/2 -------------) exp(a t) _C2 exp(----------)
                                   b 2                    1/2  1/2
                         b (ln(1/t) )                    c    b

                            _c[1]
           _C1 exp(-1/2 -------------) exp(a t) _C3
                                  b 2
                        b (ln(1/t) )
         + ----------------------------------------
                                1/2
                           _c[1]    x
                       exp(----------)
                            1/2  1/2
                           c    b

Alec

I waited for Alejandro to see whether that works in Maple V Release 5.1. In Maple 12 it gives

                                        (-b)
                         h(t) := ln(1/t)


                                                              1/2
                             _c[1]                       _c[1]    x
  u(t, x) = _C1 exp(-1/2 -------------) exp(a t) _C2 exp(----------)
                                   b 2                    1/2  1/2
                         b (ln(1/t) )                    c    b

                            _c[1]
           _C1 exp(-1/2 -------------) exp(a t) _C3
                                  b 2
                        b (ln(1/t) )
         + ----------------------------------------
                                1/2
                           _c[1]    x
                       exp(----------)
                            1/2  1/2
                           c    b

Alec

That is for the cases when you can guess - like in the original example - when you are trying to find whether one of numerical constants can be expressed in some simple way through others.

By the way, the example with sqrt(71) works without guessing with

Digits:=50;

Alec

That is for the cases when you can guess - like in the original example - when you are trying to find whether one of numerical constants can be expressed in some simple way through others.

By the way, the example with sqrt(71) works without guessing with

Digits:=50;

Alec

Here is an example where it is working,

a:=evalf(2*sqrt(71)+sqrt(3));
                           a := 18.58435036
identify(a);
                             18.58435036

identify(a,extension=[sqrt(71)]);

                             1/2       1/2
                            3    + 2 71

Alec

Here is an example where it is working,

a:=evalf(2*sqrt(71)+sqrt(3));
                           a := 18.58435036
identify(a);
                             18.58435036

identify(a,extension=[sqrt(71)]);

                             1/2       1/2
                            3    + 2 71

Alec

Various numerical algorithms, such as Newton's method and its modifications, need to have some starting point for calculations. If you don't provide it, then the system is using some standard ones for which the method might be divergent. So the general idea is that if fsolve doesn't give a solution, one might try to enter some starting point values. I entered just some more or less random values satisfying the conditions you gave, and that gave a solution.

Another use of starting points is for cases with more than one solution. Some starting points give one of solutions, other starting points give another one etc.

Alec

Various numerical algorithms, such as Newton's method and its modifications, need to have some starting point for calculations. If you don't provide it, then the system is using some standard ones for which the method might be divergent. So the general idea is that if fsolve doesn't give a solution, one might try to enter some starting point values. I entered just some more or less random values satisfying the conditions you gave, and that gave a solution.

Another use of starting points is for cases with more than one solution. Some starting points give one of solutions, other starting points give another one etc.

Alec

(u(t, x) = _F1(t) _F2(x)) &where [{

                             (-1 - 2 b)
        d             ln(1/t)           _F1(t) _c[1]
        -- _F1(t) = - ------------------------------ + a _F1(t),
        dt                          t

         2
        d            _c[1] _F2(x)
        --- _F2(x) = ------------}]
          2              c b
        dx

Alec

(u(t, x) = _F1(t) _F2(x)) &where [{

                             (-1 - 2 b)
        d             ln(1/t)           _F1(t) _c[1]
        -- _F1(t) = - ------------------------------ + a _F1(t),
        dt                          t

         2
        d            _c[1] _F2(x)
        --- _F2(x) = ------------}]
          2              c b
        dx

Alec

In this particular example, that can be done as

l:=[op(indets(f,'float'))];

  l := [-1.751336299, -0.5457363063736358, -0.3611166740,
        -0.2061949348454455, 0.2467414433]

IntegerRelations:-LinearDependency(map(log@abs,l));

                           [1, 0, -1, 1, 0]

In general, identify with option extension could be used, but it seems to be broken - at least I couldn't add list l or parts of it using this option.

Alec

In this particular example, that can be done as

l:=[op(indets(f,'float'))];

  l := [-1.751336299, -0.5457363063736358, -0.3611166740,
        -0.2061949348454455, 0.2467414433]

IntegerRelations:-LinearDependency(map(log@abs,l));

                           [1, 0, -1, 1, 0]

In general, identify with option extension could be used, but it seems to be broken - at least I couldn't add list l or parts of it using this option.

Alec

Model function should be chosen very carefully though.

Trying to fit A*exp(B*x) + C*exp(E*x^2), for example, will go into an infinite loop that couldn't be stopped by hitting the Interrupt button. Eventually, after some time, that would crash not only Maple, but Windows as well.

Alec

Model function should be chosen very carefully though.

Trying to fit A*exp(B*x) + C*exp(E*x^2), for example, will go into an infinite loop that couldn't be stopped by hitting the Interrupt button. Eventually, after some time, that would crash not only Maple, but Windows as well.

Alec