Opened 10 years ago
Last modified 7 years ago
#11653 new defect
desolve failed to solve an ODE whose solution implies integration limits
Reported by: | JGuzman | Owned by: | burcin |
---|---|---|---|
Priority: | major | Milestone: | sage-6.4 |
Component: | calculus | Keywords: | maxima, at, desolve |
Cc: | kcrisman, nbruin | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
When trying to solve a simple ODE whose rhs contains a function, Sage fails to interpret the Maxima output if this contains integration limits.
A minimal example
sage: x=var('x') # independent variable sage: v=function('v', x) # dependent variable
if we now define a custom square pulse function
def pulse(tonset, tdur, amp): """ returns a square pulse as a function of x, f(x) the pulse is defined as follows: t onset -- start of pulse tdur -- duration of pulse amp -- amplitude of pulse """ f(x)= amp*(sign(x-tonset)/2-sign(x-tonset-tdur)/2) return f
now we create a pulse function
sage: mypulse = pulse(tonset=5, tdur=5, amp=2)
and define differential equation
sage: dvdx = diff(v, x)-x -mypulse == 0 # mypulse(x) is function
To get the evolution of v we can use desolve
myvolt = desolve(de=dvdx, ivar=x, dvar=v, ics=[0,0])
The error message is:
TypeError: unable to make sense of Maxima expression 'v(x)=-(2*(at(integrate(signum(x-5)-signum(x-13),x),[x=0,v(x)=0]))-2*int\egrate(signum(x-5)-signum(x-13),x)-x^2)/2' in Sage
desolve_laplace leads to similar error:
sage: desolve(de=dvdx, ivar=x, dvar=v, ics=[0,0])
TypeError: unable to make sense of Maxima expression 'ilt(((laplace(signum(x-5),x,?g2733)-laplace(signum(x-13),x,?g2733)+v(0)\ )*?g2733^2+1)/?g2733^3,?g2733,x)' in Sage
According to Nils Bruin, the problem is that Maxima 'at' function. As described in Ticket #385, this can be a problem with the implementation of 'at' for SR.
Expressions that work
And adding the sign function to the differential function does not affect the solution.
sage: dvdx = diff(v, x)-v -sign(x) == 0 sage: desolve(de=dvdx, ivar=x, dvar=v) sage: (c + integrate(e^(-x)*sgn(x), x))*e^x
However, adding initial conditions produces an output that Sage is not able to evaluate
sage: desolve(de = dvdx, ivar=x, dvar=v, ics=[0,0])
The output is:
TypeError: unable to make sense of Maxima expression 'v(x)=e^x*integrate(e^-x*signum(x),x)-e^x*(at(integrate(e^-x*signum(x),x),[x=0,v(x)=0]))' in Sage
I guess Sage is not able to interpret the integrations limits prompted by Maxima (e.g [t=0,v(t)=0]).
Detailed information (and a more realistic example) can be found here: http://groups.google.com/group/sage-support/browse_thread/thread/8cc67d39510faca2
Change History (16)
comment:1 Changed 10 years ago by
- Summary changed from desolve failed to solve an ODE with a to desolve failed to solve an ODE whose rhs contains a function
comment:2 Changed 10 years ago by
- Description modified (diff)
comment:3 Changed 10 years ago by
- Description modified (diff)
comment:4 Changed 10 years ago by
- Cc kcrisman nbruin added; sjm.guzman@… removed
- Keywords maxima at desolve added
comment:5 Changed 10 years ago by
- Description modified (diff)
comment:6 Changed 10 years ago by
As to the ticket, see the sage-support thread in question. The essential problem is that in laplace
and taylor
we take the answer from Maxima and send it to SR, which does parse the at
correctly via the Maxima string thingie in calculus/calculus.py, but in the desolve_*
functions we just coerce to .sage()
, which does not. Probably changing this would fix it.
comment:7 Changed 10 years ago by
- Description modified (diff)
I re-formatted the text according to kcrisman (thanks a lot for the suggestion!). I will have a look to the code soon. I am looking forward to implement it. If I understood correctly, the only thing to do is to make desolve_* take the answer from Maxima to SR.
comment:8 Changed 10 years ago by
- Description modified (diff)
- Owner changed from burcin to JGuzman
- Summary changed from desolve failed to solve an ODE whose rhs contains a function to desolve failed to solve an ODE whose solution implies integration limits
I changed the summary to delimit the error more carefully. Additional, a more detailed explanation is given of cases in which Sage is able to interpret Maxima output. I guess, the problem is that Sage is not able to interpret the integration limits prompted by the maxima expression.
comment:9 Changed 10 years ago by
- Description modified (diff)
- Owner changed from JGuzman to burcin
Change owner to burcin (I do not know why it changed last time !), and change the typesetting of TypeError?
comment:10 Changed 10 years ago by
- Description modified (diff)
comment:11 Changed 10 years ago by
- Description modified (diff)
comment:12 Changed 10 years ago by
There are several issues here, actually, so it may take a bit to solve this. We are apparently translating several things wrongly by not going through SR, but then there is also the 'general' variable ?g2733
which I remember being still undealt with... probably won't be fixed immediately :( just because of time constraints.
comment:13 Changed 8 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:14 Changed 8 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:15 Changed 7 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:16 Changed 7 years ago by
- Milestone changed from sage-6.3 to sage-6.4
Thanks, Jose! Just a few pointers: