# Troubleshooting¶

## Symbol aliases¶

SymPy treats symbols with different assumptions as different symbols even if they have the same name. To reduce this confusion, Lcapy assumes that symbol names are not aliased. It achieves this by maintaining a list of defined symbols for each circuit. However, it is unaware of symbols created by SymPy.

## Symbol assumptions¶

There can be difficulties with symbol assumptions when working with SymPy. By default SymPy creates symbols with few assumptions, for example,

>>> from sympy import Symbol
>>> R1 = Symbol('R')
>>> R1.assumptions0
{'commutative': True}

On the other hand, by default, Lcapy assumes that symbols are positive (unless explicitly defined otherwise). For example,

>>> from lcapy import symbol
>>> R2 = symbol('R')
>>> R2.assumptions0
{'commutative': True,
'complex': True,
'hermitian': True,
'imaginary': False,
'negative': False,
'nonnegative': True,
'nonpositive': False,
'nonzero': True,
'positive': True,
'real': True,
'zero': False}

Since R1 and R2 have different assumptions, SymPy considers them different symbols even though they are both defined with the same name R.

Note, every real symbol is also considered complex although with no imaginary part. The proper way to test assumptions is to use the attributes is_complex, is_real, etc. For example,

>>> t.is_real
True
>>> t.is_complex
False

## Zero substitution¶

Be careful with zero substitutions. For example, consider
>>> x = symbol('x')
>>> (x * (s + 1 / x)).subs(x, 0)
0

In general it is safer (but slower) to evaluate a limit at zero.

>>> x = symbol('x')
>>> (x * (s + 1 / x)).limit(x, 0)
1

Another approach is expand the expression to avoid the division:

>>> x = symbol('x')
>>> (x * (s + 1 / x)).expand().subs(x, 0)
1

## Computation speed¶

Lcapy can be slow for large problems due to the computational complexity of the algorithms. If speed is important, it is better to substitute symbolic values with numerical values.

The results from slow computations are cached to improve the speed.