bug report solve

[Norbert Nitzsche]

this works (A)(although takes awfully long)

a,b,x,y,l1,l2=symbols('a b x y l1 l2')

eq = [l1*cos(a)+l2*cos(b)-x,l1*sin(a)+l2*sin(b)-y]

res = solve(eq,[a,b])

this does not (B):

a,b,x,y,l1,l2=symbols('a b x y l1 l2')

eq = [l1*cos(a)+l2*cos(a+b)-x,l1*sin(a)+l2*sin(a+b)-y]

res = solve(eq,[a,b])

solution from (A) could be used to find solution for (B) by a simple substitution, so, analytic solution exists, sympy, however, produces error

python 3.11.13

sympy 1.14.0

--------------------------------------------------------------------------- TypeError Traceback (most recent call last) Cell In[11], line 1 ----> 1 res2 = solve(eq,[a,b]) File ~\Documents\FH\Python\venv\control\Lib\site-packages\sympy\solvers\solvers.py:1170, in solve(f, *symbols, **flags) 1168 solution = _solve(f[0], *symbols, **flags) 1169 else: -> 1170 linear, solution = _solve_system(f, symbols, **flags) 1171 assert type(solution) is list 1172 assert not solution or type(solution[0]) is dict, solution File ~\Documents\FH\Python\venv\control\Lib\site-packages\sympy\solvers\solvers.py:1963, in _solve_system(exprs, symbols, **flags) 1961 for s in ok_syms: 1962 try: -> 1963 soln = _vsolve(eq2, s, **flags) 1964 except NotImplementedError: 1965 continue File ~\Documents\FH\Python\venv\control\Lib\site-packages\sympy\solvers\solvers.py:2638, in _vsolve(e, s, **flags) 2636 def _vsolve(e, s, **flags): 2637 """return list of scalar values for the solution of e for symbol s""" -> 2638 return [i[s] for i in _solve(e, s, **flags)] File ~\Documents\FH\Python\venv\control\Lib\site-packages\sympy\solvers\solvers.py:1743, in _solve(f, *symbols, **flags) 1738 result = [r for r in result if 1739 not any(checksol(d, r, **flags) 1740 for d in dens)] 1741 if check: 1742 # keep only results if the check is not False -> 1743 result = [r for r in result if 1744 checksol(f_num, r, **flags) is not False] 1745 return result File ~\Documents\FH\Python\venv\control\Lib\site-packages\sympy\solvers\solvers.py:1744, in <listcomp>(.0) 1738 result = [r for r in result if 1739 not any(checksol(d, r, **flags) 1740 for d in dens)] 1741 if check: 1742 # keep only results if the check is not False 1743 result = [r for r in result if -> 1744 checksol(f_num, r, **flags) is not False] 1745 return result File ~\Documents\FH\Python\venv\control\Lib\site-packages\sympy\solvers\solvers.py:354, in checksol(f, symbol, sol, **flags) 352 return val == 0 353 if numerical and val.is_number: --> 354 return (abs(val.n(18).n(12, chop=True)) < 1e-9) is S.true 356 if flags.get('warn', False): 357 warnings.warn("\n\tWarning: could not verify solution %s." % sol) File ~\Documents\FH\Python\venv\control\Lib\site-packages\sympy\core\decorators.py:248, in _SympifyWrapper.make_wrapped.<locals>._func(self, other) 246 if not isinstance(other, expectedcls): 247 return retval --> 248 return func(self, other) File ~\Documents\FH\Python\venv\control\Lib\site-packages\sympy\core\expr.py:400, in Expr.__lt__(self, other) 397 @sympify_return([('other', 'Expr')], NotImplemented) 398 def __lt__(self, other): 399 from .relational import StrictLessThan --> 400 return StrictLessThan(self, other) File ~\Documents\FH\Python\venv\control\Lib\site-packages\sympy\core\relational.py:850, in _Inequality.__new__(cls, lhs, rhs, **options) 848 raise TypeError("Invalid comparison of non-real %s" % me) 849 if me is S.NaN: --> 850 raise TypeError("Invalid NaN comparison") 851 # First we invoke the appropriate inequality method of `lhs` 852 # (e.g., `lhs.__lt__`). That method will try to reduce to 853 # boolean or raise an exception. It may keep calling (...) 857 # exception). In that case, it must call us with 858 # `evaluate=False` to prevent infinite recursion. 859 return cls._eval_relation(lhs, rhs, **options) TypeError: Invalid NaN comparison

[Chris Smith]

What substitution were you thinking? I would expand the 2nd set and rewrite in terms of exponentials and solve for them.

a,b,x,y,l1,l2=symbols('a b x y l1 l2')
eq = [l1*cos(a)+l2*cos(a+b)-x,l1*sin(a)+l2*sin(a+b)-y]

eq=[i.expand(trig=1).rewrite(exp).subs(exp(I*a),var('A')).subs(exp(I*b),var("B")).as_numer_denom()[0] for i in eq]
g = groebner(eq,(A,B))

solve(g,(A,B),simplify=0,verify=0)

which gives 3 solutions (but the one with A=0 is not valid, so just 2)

/c

[Chris Smith]

Nevermind...I suspect you just let b be called c in the first case and then let c = a+b in the second case. If you can solve for a and c you can solve for a and a+b, hence a and b in the second case.

/c

[Chris Smith]

I opened  solution for pair of equations in cos and sin · Issue #28804 · sympy/sympy