In SymPy, trigonometric functions like sin, cos, and tan have an
.expand(trig=True) method. This method applies standard trigonometric
identities (like the addition formula).
However, there was a bug where these identities were being applied to
*non-commutative* symbols (like Matrices or Quantum Operators). In
non-commutative algebra, the standard identity:
$$\sin(A+B) = \sin(A)\cos(B) + \cos(A)\sin(B)$$
is *mathematically incorrect* because it assumes $AB = BA$. Applying this
expansion to non-commutative objects leads to wrong results in physics and
linear algebra.
*The Evidence*
If you define $A$ and $B$ as non-commutative, SymPy should "do nothing"
when asked to expand, but it was incorrectly simplifying them:
Python
A, B = symbols('A B', commutative=False) print(expand(sin(A + B), trig=True))
# BUGGY OUTPUT: sin(A)*cos(B) + sin(B)*cos(A) # CORRECT OUTPUT: sin(A + B)
*The Solution*
The fix involved adding a "Guard Clause" to the _eval_expand_trig method in
the sin, cos, and tan classes. This check ensures that if the argument is
non-commutative, the function returns itself instead of applying the
commutative identity.
*File:* sympy/functions/elementary/trigonometric.py
*The Fix:*
Python
def _eval_expand_trig(self, **hints): arg = self.args[0] # Check if symbols
commute. If not, standard identities do not apply. if arg.is_commutative is
False: return self # ... rest of the expansion logic ...
*Verification*
I wrote a comprehensive test suite to ensure the fix works across all
primary trig functions while ensuring that standard (commutative) math is
*not* broken:
1.
*Non-Commutative Test:* expand(sin(A+B)) returns sin(A+B) (Passed).
2.
*Commutative Test:* expand(sin(x+y)) still returns the standard
expansion (Passed).
3.
*Mixed Case:* expand(sin(A+x)) is recognized as non-commutative and
stays unexpanded (Passed).
*Impact*
This fix ensures mathematical consistency across SymPy. By making the
Trigonometry module respect the is_commutative flag (just like the
Exponential and Power modules already do), we prevent silent errors in
advanced mathematical computations.
should i make PR for this??
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