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 | 1 | initial version |
Solutions to some equations involve a parameter.
These parameters are labeled $z_n$ if they are integer, or $r_n$ if they are real.
The indices don't have any specific meaning; they will vary everytime you solve. Their point is to distinguish parameters between them.
Using specific values for the parameters can be done as follows.
Give a name to each solution:
sage: sa, sb = (s.rhs() for s in sol)
sage: sa
pi + 2*pi*z1798
sage: sb
2*pi*z1816 + arctan(12/5)
Get the variables in each solution:
sage: sa.variables()
(z1798,)
sage: sa.variables()
(z1816,)
Give them easier names:
sage: za, = sa.variables()
sage: zb, = sb.variables()
Get the solution for $z_n = 0$:
sage: sa(za=0)
pi
sage: sb(zb=0)
arctan(12/5)
Get the solutions for a range of values of the parameters.
sage: [sa(za=k) for k in range(-3, 4)]
[pi + 2*pi*z1798,
pi + 2*pi*z1798,
pi + 2*pi*z1798,
pi + 2*pi*z1798,
pi + 2*pi*z1798,
pi + 2*pi*z1798,
pi + 2*pi*z1798]
sage: [sb(zb=k) for k in range(-3, 4)]
[2*pi*z1816 + arctan(12/5),
2*pi*z1816 + arctan(12/5),
2*pi*z1816 + arctan(12/5),
2*pi*z1816 + arctan(12/5),
2*pi*z1816 + arctan(12/5),
2*pi*z1816 + arctan(12/5),
2*pi*z1816 + arctan(12/5)]
| | 2 | No.2 Revision |
Solutions to some equations involve a parameter.
These parameters are labeled $z_n$ if they are integer, or $r_n$ if they are real.
The indices don't have any specific meaning; they will vary everytime you solve. Their point is to distinguish parameters between them.
Using specific values for the parameters can be done as follows.
Give a name to each solution:
sage: sa, sb = (s.rhs() for s in sol)
sage: sa
pi + 2*pi*z1798
sage: sb
2*pi*z1816 + arctan(12/5)
Get the variables in each solution:
sage: sa.variables()
(z1798,)
sage: sa.variables()
(z1816,)
Give them easier names:
sage: za, = sa.variables()
sage: zb, = sb.variables()
Get the solution for $z_n = 0$:
sage: sa(za=0)
sa.subs({za: 0})
pi
sage: sb(zb=0)
sb.subs({zb: 0})
arctan(12/5)
Get the solutions for a range of values of the parameters.
sage: [sa(za=k) [sa.subs({za: k}) for k in range(-3, 4)]
[pi + 2*pi*z1798,
pi + 2*pi*z1798,
pi + 2*pi*z1798,
pi + 2*pi*z1798,
pi + 2*pi*z1798,
pi + 2*pi*z1798,
pi + 2*pi*z1798]
sage: [sb(zb=k) [-5*pi, -3*pi, -pi, pi, 3*pi, 5*pi, 7*pi]
sage: [sb.subs({zb: k}) for k in range(-3, 4)]
[2*pi*z1816 + arctan(12/5),
2*pi*z1816 + arctan(12/5),
2*pi*z1816 + arctan(12/5),
2*pi*z1816 + arctan(12/5),
2*pi*z1816 + arctan(12/5),
2*pi*z1816 + arctan(12/5),
2*pi*z1816 [-6*pi + arctan(12/5),
-4*pi + arctan(12/5),
-2*pi + arctan(12/5),
arctan(12/5),
2*pi + arctan(12/5),
4*pi + arctan(12/5),
6*pi + arctan(12/5)]
