I am solving a 9x9 system of ordinary differential equations. In simple terms, I need to get the equilibrium expressions for the system. I am using the solve command in sage, but I get an error whose cause I don't know. Kindly help.
Declare variables
mu_h,beta,alpha,gamma_r,gamma_s,omega,mu_m,epsilon,theta,N_h,S_h,I_hr,I_hs,I_hsr,R_h,N_m,S_m,I_mr,I_ms,I_msr = var('mu_h,beta,alpha,gamma_r,gamma_s,omega,mu_m,epsilon,theta,N_h,S_h,I_hr,I_hs,I_hsr,R_h,N_m,S_m,I_mr,I_ms,I_msr')
System of equations.
````dI_hrdt = (beta*S_h*I_mr) - (mu_h*I_hr) - (gamma_r*I_hr) - (alpha*I_hr)*(I_ms +I_msr)
````dI_hsdt = (beta*S_h*I_ms) - (mu_h*I_hs) - (gamma_s*I_hs) - (alpha*I_hs)*(I_mr +I_msr)
````dI_hsrdt = (beta*S_h*I_msr) - (mu_h*I_hsr) - (gamma_r*I_hsr) + (alpha*I_hr)*(I_ms +I_msr) + (alpha*I_hs)*(I_mr +I_msr)
````dR_hdt = (gamma_r*I_hr) + (gamma_s*I_hs) + (gamma_r*I_hsr) -(mu_h*R_h)- (omega*R_h)
````dS_mdt = (mu_m*N_m) - (epsilon*S_m)*(I_hr + I_hs +I_hsr) - (mu_m*S_m)
````dI_mrdt = (epsilon*S_m*I_hr) - (mu_m*I_mr) - (theta*I_mr)*(I_hs +I_hsr)
````dI_msdt = (epsilon*S_m*I_hs) - (mu_m*I_ms) - (theta*I_ms)*(I_hr +I_hsr)
````dI_msrdt = (epsilon*S_m*I_hsr) - (mu_m*I_msr) - (theta*I_mr)*(I_hs +I_hsr) - (theta*I_ms)*(I_hr +I_hsr)
##finding the equilibria
````soln = solve([dS_hdt==0,dI_hrdt==0,dI_hsdt==0,dI_hsrdt==0,dR_hdt==0,dS_mdt==0,dI_mrdt==0,dI_msdt==0,dI_msrdt==0],[S_h,I_hr,I_hs,I_hsr,R_h,S_m,I_mr,I_ms,I_msr])
````show(soln)
That is my code, I expected expressions for my variables, [S_h,I_hr,I_hs,I_hsr,R_h,S_m,I_mr,I_ms,I_msr], but instead I get an error. the error is given below.
`RuntimeError Traceback (most recent call last)
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/interface.py in __init__(self, parent, value, is_name, name)
717 try:
--> 718 self._name = parent._create(value, name=name)
719 except (TypeError, RuntimeError, ValueError) as x:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/maxima_lib.py in _create(self, value, name)
603 else:
--> 604 self.set(name, value)
605 except RuntimeError as error:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/maxima_lib.py in set(self, var, value)
511 cmd = '%s : %s$'%(var, value.rstrip(';'))
--> 512 self.eval(cmd)
513
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/maxima_lib.py in _eval_line(self, line, locals, reformat, **kwds)
457 if statement:
--> 458 maxima_eval("#$%s$" % statement)
459 if not reformat:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/libs/ecl.pyx in sage.libs.ecl.EclObject.__call__ (build/cythonized/sage/libs/ecl.c:8609)()
852 """
--> 853 lispargs = EclObject(list(args))
854 return ecl_wrap(ecl_safe_apply(self.obj,(<EclObject>lispargs).obj))
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/libs/ecl.pyx in sage.libs.ecl.EclObject.__init__ (build/cythonized/sage/libs/ecl.c:8072)()
713 elif len(args) == 1:
--> 714 self.set_obj(python_to_ecl(args[0], True))
715 elif len(args) == 2:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/libs/ecl.pyx in sage.libs.ecl.python_to_ecl (build/cythonized/sage/libs/ecl.c:7058)()
487 else:
--> 488 L = cl_cons(python_to_ecl(pyobj[0], read_strings),Cnil)
489 ptr = L
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/libs/ecl.pyx in sage.libs.ecl.python_to_ecl (build/cythonized/sage/libs/ecl.c:6695)()
463 if read_strings:
--> 464 return ecl_safe_funcall(read_from_string_clobj, o)
465 else:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/libs/ecl.pyx in sage.libs.ecl.ecl_safe_funcall (build/cythonized/sage/libs/ecl.c:5665)()
346
--> 347 ecl_sig_on()
348 ret = safe_cl_funcall(&error,func,arg)
RuntimeError: Aborted
During handling of the above exception, another exception occurred:
TypeError Traceback (most recent call last)
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/interface.py in __call__(self, x, name)
308 try:
--> 309 result = self._coerce_impl(x, use_special=False)
310 return result if name is None else result.name(new_name=name)
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/interface.py in _coerce_impl(self, x, use_special)
357 else:
--> 358 w = self(v)
359 A.append(w.name())
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/interface.py in __call__(self, x, name)
301 # new element.
--> 302 result = self._coerce_from_special_method(x)
303 return result if name is None else result.name(new_name=name)
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/maxima_lib.py in _coerce_from_special_method(self, x)
384 else:
--> 385 return MaximaAbstract._coerce_from_special_method(self,x)
386
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/interface.py in _coerce_from_special_method(self, x)
329 try:
--> 330 return (x.__getattribute__(s))(self)
331 except AttributeError:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression._maxima_ (build/cythonized/sage/symbolic/expression.cpp:8014)()
1023 else:
-> 1024 return super(Expression, self)._interface_(session)
1025
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/structure/sage_object.pyx in sage.structure.sage_object.SageObject._interface_ (build/cythonized/sage/structure/sage_object.c:5759)()
691 raise NotImplementedError("coercion of object %s to %s not implemented:\n%s\n%s" % (repr(self), I))
--> 692 X = I(s)
693 if c:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/interface.py in __call__(self, x, name)
294 if isinstance(x, str):
--> 295 return cls(self, x, name=name)
296 try:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/interface.py in __init__(self, parent, value, is_name, name)
719 except (TypeError, RuntimeError, ValueError) as x:
--> 720 raise TypeError(x)
721
TypeError: Aborted
During handling of the above exception, another exception occurred:
RuntimeError Traceback (most recent call last)
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/interface.py in __init__(self, parent, value, is_name, name)
717 try:
--> 718 self._name = parent._create(value, name=name)
719 except (TypeError, RuntimeError, ValueError) as x:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/maxima_lib.py in _create(self, value, name)
603 else:
--> 604 self.set(name, value)
605 except RuntimeError as error:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/maxima_lib.py in set(self, var, value)
511 cmd = '%s : %s$'%(var, value.rstrip(';'))
--> 512 self.eval(cmd)
513
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/maxima_lib.py in _eval_line(self, line, locals, reformat, **kwds)
457 if statement:
--> 458 maxima_eval("#$%s$" % statement)
459 if not reformat:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/libs/ecl.pyx in sage.libs.ecl.EclObject.__call__ (build/cythonized/sage/libs/ecl.c:8609)()
852 """
--> 853 lispargs = EclObject(list(args))
854 return ecl_wrap(ecl_safe_apply(self.obj,(<EclObject>lispargs).obj))
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/libs/ecl.pyx in sage.libs.ecl.EclObject.__init__ (build/cythonized/sage/libs/ecl.c:8072)()
713 elif len(args) == 1:
--> 714 self.set_obj(python_to_ecl(args[0], True))
715 elif len(args) == 2:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/libs/ecl.pyx in sage.libs.ecl.python_to_ecl (build/cythonized/sage/libs/ecl.c:7058)()
487 else:
--> 488 L = cl_cons(python_to_ecl(pyobj[0], read_strings),Cnil)
489 ptr = L
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/libs/ecl.pyx in sage.libs.ecl.python_to_ecl (build/cythonized/sage/libs/ecl.c:6695)()
463 if read_strings:
--> 464 return ecl_safe_funcall(read_from_string_clobj, o)
465 else:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/libs/ecl.pyx in sage.libs.ecl.ecl_safe_funcall (build/cythonized/sage/libs/ecl.c:5665)()
346
--> 347 ecl_sig_on()
348 ret = safe_cl_funcall(&error,func,arg)
RuntimeError: Aborted
During handling of the above exception, another exception occurred:
TypeError Traceback (most recent call last)
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/interface.py in __call__(self, x, name)
312 try:
--> 313 return cls(self, str(x), name=name)
314 except TypeError:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/interface.py in __init__(self, parent, value, is_name, name)
719 except (TypeError, RuntimeError, ValueError) as x:
--> 720 raise TypeError(x)
721
TypeError: Aborted
During handling of the above exception, another exception occurred:
TypeError Traceback (most recent call last)
<ipython-input-10-5fd138375d76> in <module>
17
18 ##finding the equilibria
---> 19 soln = solve([dS_hdt==Integer(0),dI_hrdt==Integer(0),dI_hsdt==Integer(0),dI_hsrdt==Integer(0),dR_hdt==Integer(0),dS_mdt==Integer(0),dI_mrdt==Integer(0),dI_msdt==Integer(0),dI_msrdt==Integer(0)],[S_h,I_hr,I_hs,I_hsr,R_h,S_m,I_mr,I_ms,I_msr])
20 show(soln)
21
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/symbolic/relation.py in solve(f, *args, **kwds)
1104
1105 from sage.calculus.calculus import maxima
-> 1106 m = maxima(f)
1107
1108 try:
/opt/sagemath-9.3/local/lib/python3.7/site-packages/sage/interfaces/interface.py in __call__(self, x, name)
313 return cls(self, str(x), name=name)
314 except TypeError:
--> 315 raise TypeError(msg)
316
317 def _coerce_from_special_method(self, x):
TypeError: Aborted
`