Hi all,
Recent adopter, first time caller, bear with me if I have some newbish
misunderstandings about sympy.
I am working on a project where we are trying to use sympy to do a lot of
symbolic geometric computation. The project predates sympy, so I cannot
really change too much code to accomodate it.
Our calculations create matrices, and sometimes, the expressions can seem
large, like the one seen below. I know that this is actually supposed to
be a linear expression, and I need to get it into a linear form.
*Matrix([*
*[
1.0*leg1.beamwidth - (2.05432527401305e-33*leg1.beamwidth**3 +
0.166666666666667*leg1.beamwidth**2*total_length +
0.166666666666667*leg1.beamwidth**2*(1.23259516440783e-32*leg1.beamwidth +
total_length/2))/(6.16297582203915e-33*leg1.beamwidth**2 +
0.25*leg1.beamwidth*total_length +
0.5*leg1.beamwidth*(1.23259516440783e-32*leg1.beamwidth + total_length/2)),
1.0*leg1.beamwidth - (2.05432527401305e-33*leg1.beamwidth**3 +
0.166666666666667*leg1.beamwidth**2*total_length +
0.166666666666667*leg1.beamwidth**2*(1.23259516440783e-32*leg1.beamwidth +
total_length/2))/(6.16297582203915e-33*leg1.beamwidth**2 +
0.25*leg1.beamwidth*total_length +
0.5*leg1.beamwidth*(1.23259516440783e-32*leg1.beamwidth + total_length/2)),
1.0*leg1.beamwidth -
(2.05432527401305e-33*leg1.beamwidth**3 +
0.166666666666667*leg1.beamwidth**2*total_length +
0.166666666666667*leg1.beamwidth**2*(1.23259516440783e-32*leg1.beamwidth +
total_length/2))/(6.16297582203915e-33*leg1.beamwidth**2 +
0.25*leg1.beamwidth*total_length +
0.5*leg1.beamwidth*(1.23259516440783e-32*leg1.beamwidth + total_length/2)),
1.0*leg1.beamwidth -
(2.05432527401305e-33*leg1.beamwidth**3 +
0.166666666666667*leg1.beamwidth**2*total_length +
0.166666666666667*leg1.beamwidth**2*(1.23259516440783e-32*leg1.beamwidth +
total_length/2))/(6.16297582203915e-33*leg1.beamwidth**2 +
0.25*leg1.beamwidth*total_length +
0.5*leg1.beamwidth*(1.23259516440783e-32*leg1.beamwidth +
total_length/2))],*
*[-6.12323399573677e-17*leg1.beamwidth -
(-2.53215139886928e-65*leg1.beamwidth**3 +
0.0416666666666667*leg1.beamwidth*total_length**2 +
0.166666666666667*leg1.beamwidth*(1.23259516440783e-32*leg1.beamwidth +
total_length/2)*(1.23259516440783e-32*leg1.beamwidth +
total_length))/(6.16297582203915e-33*leg1.beamwidth**2 +
0.25*leg1.beamwidth*total_length +
0.5*leg1.beamwidth*(1.23259516440783e-32*leg1.beamwidth + total_length/2)),
6.12323399573677e-17*leg1.beamwidth + total_length/2 -
(-2.53215139886928e-65*leg1.beamwidth**3 +
0.0416666666666667*leg1.beamwidth*total_length**2 +
0.166666666666667*leg1.beamwidth*(1.23259516440783e-32*leg1.beamwidth +
total_length/2)*(1.23259516440783e-32*leg1.beamwidth +
total_length))/(6.16297582203915e-33*leg1.beamwidth**2 +
0.25*leg1.beamwidth*total_length +
0.5*leg1.beamwidth*(1.23259516440783e-32*leg1.beamwidth + total_length/2)),
total_length/2 - (-2.53215139886928e-65*leg1.beamwidth**3 +
0.0416666666666667*leg1.beamwidth*total_length**2 +
0.166666666666667*leg1.beamwidth*(1.23259516440783e-32*leg1.beamwidth +
total_length/2)*(1.23259516440783e-32*leg1.beamwidth +
total_length))/(6.16297582203915e-33*leg1.beamwidth**2 +
0.25*leg1.beamwidth*total_length +
0.5*leg1.beamwidth*(1.23259516440783e-32*leg1.beamwidth + total_length/2)),
-(-2.53215139886928e-65*leg1.beamwidth**3 +
0.0416666666666667*leg1.beamwidth*total_length**2 +
0.166666666666667*leg1.beamwidth*(1.23259516440783e-32*leg1.beamwidth +
total_length/2)*(1.23259516440783e-32*leg1.beamwidth +
total_length))/(6.16297582203915e-33*leg1.beamwidth**2 +
0.25*leg1.beamwidth*total_length +
0.5*leg1.beamwidth*(1.23259516440783e-32*leg1.beamwidth +
total_length/2))],*
*[
-1.0*leg1.beamwidth,
-1.0*leg1.beamwidth,
0,
0]])*
If I perform nsimplify on this with a tolerance = 1e-5, I get something
reasonable:
*Matrix([*
*[
leg1.beamwidth/2,
leg1.beamwidth/2, leg1.beamwidth/2, leg1.beamwidth/2],*
*[-612323399573677*leg1.beamwidth/10000000000000000000000000000000 -
total_length/4,
612323399573677*leg1.beamwidth/10000000000000000000000000000000 +
total_length/4, total_length/4, -total_length/4],*
*[
-leg1.beamwidth,
-leg1.beamwidth, 0, 0]])*
But I can't simplify it further for some reason. Even though
*-612323399573677*leg1.beamwidth/10000000000000000000000000000000
= -6e-17, *I can't seem to make that term disappear.
This was a simple case, but in more complex cases, sympy fails to cancel
out terms and the solution becomes highly nonlinear. As an example, this
won't simplify with nsimplify for some reason, even though certain terms
clearly dominate others:
*(leg1.beamwidth*total_length*(24492935982947*leg2.beamwidth/200000000000000000000000000000
+ total_length/2)**2/2 -
306161699786839*leg2.beamwidth*total_length**2*(24492935982947*leg2.beamwidth/200000000000000000000000000000
+ total_length/2)/10000000000000000000000000000000 +
153080849893419*total_length**3*(24492935982947*leg2.beamwidth/200000000000000000000000000000
+
total_length/2)/10000000000000000000000000000000)/(total_length*(24492935982947*leg2.beamwidth/200000000000000000000000000000
+ total_length/2)**2)*
Lastly, things sometimes get worse. If I try to play around with simplify,
N, and nsimplify to try to "force" it to simplify things, I sometimes get
the error attached.
Is there a proper way to get do the simplifications I need? And, why would
I get that value error I displayed attached.
Thanks for any and all help,
Andy S.
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math.nsimplify(math.simplify(math.N(math.transpose(face.get2DCoords()))), 1e-5)
CAUSES:
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
/home/aespielberg/ppr2/ppr/svggen/api/proto_conversion3.pyc in <module>()
----> 1
math.nsimplify(math.simplify(math.N(math.transpose(face.get2DCoords()))), 1e-5)
/usr/local/lib/python2.7/dist-packages/sympy-0.7.5-py2.7.egg/sympy/simplify/simplify.pyc
in nsimplify(expr, constants, tolerance, full, rational)
3837 expr = sympify(expr)
3838 if rational or expr.free_symbols:
-> 3839 return _real_to_rational(expr, tolerance)
3840
3841 # SymPy's default tolerance for Rationals is 15; other numbers may
have
/usr/local/lib/python2.7/dist-packages/sympy-0.7.5-py2.7.egg/sympy/simplify/simplify.pyc
in _real_to_rational(expr, tolerance)
3792 r = Integer(0)
3793 reps[key] = r
-> 3794 return p.subs(reps, simultaneous=True)
3795
3796
/usr/local/lib/python2.7/dist-packages/sympy-0.7.5-py2.7.egg/sympy/core/basic.pyc
in subs(self, *args, **kwargs)
966 for old, new in sequence:
967 d = C.Dummy(commutative=new.is_commutative)
--> 968 rv = rv._subs(old, d, **kwargs)
969 reps[d] = new
970 if not isinstance(rv, Basic):
/usr/local/lib/python2.7/dist-packages/sympy-0.7.5-py2.7.egg/sympy/core/cache.pyc
in wrapper(*args, **kw_args)
91 except (KeyError, TypeError):
92 pass
---> 93 r = func(*args, **kw_args)
94 try:
95 func_cache_it_cache[k] = r
/usr/local/lib/python2.7/dist-packages/sympy-0.7.5-py2.7.egg/sympy/core/basic.pyc
in _subs(self, old, new, **hints)
1088 rv = self._eval_subs(old, new)
1089 if rv is None:
-> 1090 rv = fallback(self, old, new)
1091 return rv
1092
/usr/local/lib/python2.7/dist-packages/sympy-0.7.5-py2.7.egg/sympy/core/basic.pyc
in fallback(self, old, new)
1065 args[i] = arg
1066 if hit:
-> 1067 rv = self.func(*args)
1068 hack2 = hints.get('hack2', False)
1069 if hack2 and self.is_Mul and not rv.is_Mul: # 2-arg
hack
/usr/local/lib/python2.7/dist-packages/sympy-0.7.5-py2.7.egg/sympy/matrices/immutable.pyc
in __new__(cls, *args, **kwargs)
46
47 def __new__(cls, *args, **kwargs):
---> 48 return cls._new(*args, **kwargs)
49
50 @property
/usr/local/lib/python2.7/dist-packages/sympy-0.7.5-py2.7.egg/sympy/matrices/immutable.pyc
in _new(cls, *args, **kwargs)
39 if len(args) == 1 and isinstance(args[0], ImmutableMatrix):
40 return args[0]
---> 41 rows, cols, flat_list = cls._handle_creation_inputs(*args,
**kwargs)
42 rows = Integer(rows)
43 cols = Integer(cols)
/usr/local/lib/python2.7/dist-packages/sympy-0.7.5-py2.7.egg/sympy/matrices/matrices.pyc
in _handle_creation_inputs(cls, *args, **kwargs)
144 if len(args) == 3:
145 rows = as_int(args[0])
--> 146 cols = as_int(args[1])
147
148 # Matrix(2, 2, lambda i, j: i+j)
/usr/local/lib/python2.7/dist-packages/sympy-0.7.5-py2.7.egg/sympy/core/compatibility.pyc
in as_int(n)
388 raise TypeError
389 except TypeError:
--> 390 raise ValueError('%s is not an integer' % n)
391 return result
392
ValueError: -_Dummy_518 is not an integer
