improve desolve_system initial condition documentation

[rhinton]

Edit: See comments for the actual issue.

---

desolve_system apparently ignores initial conditions. Notice the identical results in the two calls in the following example.

sage: t = var('t')
sage: epsilon = var('epsilon')
sage: x1 = function('x1', t)
sage: x2 = function('x2', t)
sage: de1 = diff(x1,t) == epsilon
sage: de2 = diff(x2,t) == -2
sage: desolve_system([de1, de2], [x1, x2], ivar=t)
[x1(t) == epsilon*t + x1(0), x2(t) == -2*t + x2(0)]
sage: desolve_system([de1, de2], [x1, x2], ics=[1,1], ivar=t)
[x1(t) == epsilon*t + x1(0), x2(t) == -2*t + x2(0)] 

CC: @robert-marik

Component: calculus

Keywords: maxima, symbolics

Author: Sergey Bykov

Branch/Commit: dfbad1c

Reviewer: Karl-Dieter Crisman

Issue created by migration from https://trac.sagemath.org/ticket/9824

[robert-marik]

comment:1

As I observed from documentation, the ics have to be in the form [x0,x1(x0),x2(x0)]

The following works.

sage: t = var('t')
sage: epsilon = var('epsilon')
sage: x1 = function('x1', t)
sage: x2 = function('x2', t)
sage: de1 = diff(x1,t) == epsilon
sage: de2 = diff(x2,t) == -2
sage: desolve_system([de1, de2], [x1, x2], ivar=t)
[x1(t) == epsilon*t + x1(0), x2(t) == -2*t + x2(0)]
sage: desolve_system([de1, de2], [x1, x2], ics=[0,1,1], ivar=t)
[x1(t) == epsilon*t + 1, x2(t) == -2*t + 1]

O.K. what to do with this?

Update documentation to mention this explicitly?

Assume (silently or with a warning) that ivar=0 for initial condition whenever the number of dependent variables equals the number of initial conditions?

[rhinton]

comment:2

Thanks for pointing out my mistake!

I think updating the documentation is a great idea. I think we should raise a ValueError exception if ics is incomplete. Assuming an initial value of 0 is not horrible, but Python and Sage seem to prefer explicit-ness.

Replying to @robert-marik:

As I observed from documentation, the ics have to be in the form [x0,x1(x0),x2(x0)]

The following works.

sage: t = var('t')
sage: epsilon = var('epsilon')
sage: x1 = function('x1', t)
sage: x2 = function('x2', t)
sage: de1 = diff(x1,t) == epsilon
sage: de2 = diff(x2,t) == -2
sage: desolve_system([de1, de2], [x1, x2], ivar=t)
[x1(t) == epsilon*t + x1(0), x2(t) == -2*t + x2(0)]
sage: desolve_system([de1, de2], [x1, x2], ics=[0,1,1], ivar=t)
[x1(t) == epsilon*t + 1, x2(t) == -2*t + 1]

O.K. what to do with this?

Update documentation to mention this explicitly?

Assume (silently or with a warning) that ivar=0 for initial condition whenever the number of dependent variables equals the number of initial conditions?

[kcrisman]

comment:3

I agree that we should be explicit here. There is no obvious default for a diffeq; initial condition of zero is not the same as starting to count at 0 or 1. Yes, updating the documentation would be great for this.

[kcrisman]

Description changed:

--- 
+++ 
@@ -1,3 +1,8 @@
+Edit: See comments for the actual issue.
+
+---
+
+
 desolve_system apparently ignores initial conditions.  Notice the identical results in the two calls in the following example.
 
 ```