gistfile1.txt

[ins] In [1]: import sympy

[ins] In [2]: x=sympy.Function('x')
         ...: t=sympy.Function('t')
         ...: s=sympy.Symbol('s',real=True)
         ...: de_system=(sympy.Eq(x(s).diff(s),t(s).diff(s)), sympy.Eq(t(s).diff(s),1))
         ...: sympy.dsolve(de_system,funcs=(x,t),t=s,ics={x(0):1,t(0):0})
---------------------------------------------------------------------------
NotAlgebraic                              Traceback (most recent call last)
Input In [2], in <cell line: 5>()
      3 s=sympy.Symbol('s',real=True)
      4 de_system=(sympy.Eq(x(s).diff(s),t(s).diff(s)), sympy.Eq(t(s).diff(s),1))
----> 5 sympy.dsolve(de_system,funcs=(x,t),t=s,ics={x(0):1,t(0):0})

File /usr/lib/python3.10/site-packages/sympy/solvers/ode/ode.py:559, in dsolve(eq, func, hint, simplify, ics, xi, eta, x0, n, **kwargs)
    553 # This may have to be changed in future
    554 # when we have weakly and strongly
    555 # connected components. This have to
    556 # changed to show the systems that haven't
    557 # been solved.
    558 try:
--> 559     sol = dsolve_system(eq, funcs=func, ics=ics, doit=True)
    560     return sol[0] if len(sol) == 1 else sol
    561 except NotImplementedError:

File /usr/lib/python3.10/site-packages/sympy/solvers/ode/systems.py:2131, in dsolve_system(eqs, funcs, t, ics, doit, simplify)
   2129 if ics:
   2130     constants = Tuple(*sol).free_symbols - variables
-> 2131     solved_constants = solve_ics(sol, funcs, constants, ics)
   2132     sol = [s.subs(solved_constants) for s in sol]
   2134 if simplify:

File /usr/lib/python3.10/site-packages/sympy/solvers/ode/ode.py:793, in solve_ics(sols, funcs, constants, ics)
    791 # TODO: Use solveset here
    792 try:
--> 793     solved_constants = solve(subs_sols, constants, dict=True)
    794 except NotImplementedError:
    795     solved_constants = []

File /usr/lib/python3.10/site-packages/sympy/solvers/solvers.py:1108, in solve(f, *symbols, **flags)
   1106     solution = _solve(f[0], *symbols, **flags)
   1107 else:
-> 1108     solution = _solve_system(f, symbols, **flags)
   1110 #
   1111 # postprocessing
   1112 ###########################################################################
   1113 # Restore masked-off objects
   1114 if non_inverts:

File /usr/lib/python3.10/site-packages/sympy/solvers/solvers.py:1768, in _solve_system(exprs, symbols, **flags)
   1766 subsyms = list(sorted(subsyms, key = lambda x: sym_indices[x]))
   1767 flags['_split'] = False  # skip split step
-> 1768 subsol = _solve_system(subexpr, subsyms, **flags)
   1769 if not isinstance(subsol, list):
   1770     subsol = [subsol]

File /usr/lib/python3.10/site-packages/sympy/solvers/solvers.py:1799, in _solve_system(exprs, symbols, **flags)
   1796     failed.append(g)
   1797     continue
-> 1799 poly = g.as_poly(*symbols, extension=True)
   1801 if poly is not None:
   1802     polys.append(poly)

File /usr/lib/python3.10/site-packages/sympy/core/expr.py:1116, in Expr.as_poly(self, *gens, **args)
   1113 from sympy.polys.polytools import Poly
   1115 try:
-> 1116     poly = Poly(self, *gens, **args)
   1118     if not poly.is_Poly:
   1119         return None

File /usr/lib/python3.10/site-packages/sympy/polys/polytools.py:181, in Poly.__new__(cls, rep, *gens, **args)
    179     return cls._from_poly(rep, opt)
    180 else:
--> 181     return cls._from_expr(rep, opt)

File /usr/lib/python3.10/site-packages/sympy/polys/polytools.py:311, in Poly._from_expr(cls, rep, opt)
    309 """Construct a polynomial from an expression. """
    310 rep, opt = _dict_from_expr(rep, opt)
--> 311 return cls._from_dict(rep, opt)

File /usr/lib/python3.10/site-packages/sympy/polys/polytools.py:255, in Poly._from_dict(cls, rep, opt)
    252 domain = opt.domain
    254 if domain is None:
--> 255     domain, rep = construct_domain(rep, opt=opt)
    256 else:
    257     for monom, coeff in rep.items():

File /usr/lib/python3.10/site-packages/sympy/polys/constructor.py:367, in construct_domain(obj, **args)
    364     coeffs = [obj]
    366 coeffs = list(map(sympify, coeffs))
--> 367 result = _construct_simple(coeffs, opt)
    369 if result is not None:
    370     if result is not False:

File /usr/lib/python3.10/site-packages/sympy/polys/constructor.py:65, in _construct_simple(coeffs, opt)
     62 max_prec = max(c._prec for c in float_numbers) if float_numbers else 53
     64 if algebraics:
---> 65     domain, result = _construct_algebraic(coeffs, opt)
     66 else:
     67     if floats and complexes:

File /usr/lib/python3.10/site-packages/sympy/polys/constructor.py:105, in _construct_algebraic(coeffs, opt)
    102 trees = build_trees(coeffs)
    103 exts = list(ordered(exts))
--> 105 g, span, H = primitive_element(exts, ex=True, polys=True)
    106 root = sum([ s*ext for s, ext in zip(span, exts) ])
    108 domain, g = QQ.algebraic_field((g, root)), g.rep.rep

File /usr/lib/python3.10/site-packages/sympy/polys/numberfields/subfield.py:365, in primitive_element(extension, x, ex, polys)
    362         return cls(g), coeffs
    364 gen, coeffs = extension[0], [1]
--> 365 f = minimal_polynomial(gen, x, polys=True)
    366 K = QQ.algebraic_field((f, gen))  # incrementally constructed field
    367 reps = [K.unit]  # representations of extension elements in K

File /usr/lib/python3.10/site-packages/sympy/polys/numberfields/minpoly.py:701, in minimal_polynomial(ex, x, compose, polys, domain)
    697     raise GeneratorsError("the variable %s is an element of the ground "
    698                           "domain %s" % (x, domain))
    700 if compose:
--> 701     result = _minpoly_compose(ex, x, domain)
    702     result = result.primitive()[1]
    703     c = result.coeff(x**degree(result, x))

File /usr/lib/python3.10/site-packages/sympy/polys/numberfields/minpoly.py:618, in _minpoly_compose(ex, x, dom)
    616     res = _minpoly_rootof(ex, x)
    617 else:
--> 618     raise NotAlgebraic("%s doesn't seem to be an algebraic element" % ex)
    619 return res

NotAlgebraic: Integral(1, (s, 0)) doesn't seem to be an algebraic element