Question

I want to convert a Sage symoblic expression like:

y = 5*x + 7^x + 3*x^2

to a string which I can access by subscripting ( y[0] = ‘5’, y[1] = ‘*’, etc.

I need to do that because I want to calculate the number of occurrence of a specific variable in an expression. In above example the variable ‘X’ occures 3 times.

I would also appreciate if someone knew another way to achieve that.

Answer 1

I think everyone’s misreading the problem — we’re starting from a Sage symbolic expression.

sage: y = 5*x + 7^x + 3*x^2
sage: y
7^x + 3*x^2 + 5*x
sage: type(y)
<type 'sage.symbolic.expression.Expression'>

I would write a little recursive walker using operands() and operator():

def var_counter(someexpr, v):
    tor = someexpr.operator()
    if tor is None:
        return int(v in someexpr.variables())
    else:
        return sum(var_counter(operand, v) for operand in someexpr.operands())

which seems to work:

sage: x, x2, x3 = var("x x2 x3")
sage: y = 5*x + 7^x + 3*x^2 + x2**(x3+3*sin(x))
sage: var_counter(y, x)
4
sage: var_counter(y, x2)
1
sage: var_counter(y, x3)
1

And if you want to convert the expression to a string, simply call str:

sage: str(y)
'7^x + 3*x^2 + 5*x + x2^(x3 + 3*sin(x))'
sage: str(y)[2]
'x'
sage: str(y)[6]
'3'