# Making my own special type of variable

I want to create an object that I can take formal products and sums of, and also that remembers some extra data. I'd like to use sage's symbolic tools to do it without reimplementing multiplication, etc. For example, I'd like to make a class myVar that behaves something like this:

sage: a = myVar("some data about a")
sage: b = myVar("other important stuff")
sage: p = ((a + b)^2).expand()
a^2 + 2*a*b + b^2

sage: p.operands()
[a^2, 2a*b, b^2]

sage: p.operands()[0].operands[0]
a

sage: p.operands()[0].operands[0].get_data()
"some data about a"


I've tried subclassing Expression, but it seems like whenever I try to do some sums or products it just turns my thing into an Expression and forgets that it was a myVar.

Is something like this possible in sage?

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I think my syntax is probably bad in the example-- I need to be more careful about the variable names, probably, but I hope it is clear what I am trying to do.

( 2011-05-11 08:16:30 -0500 )edit

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You can't solve your problem by subclassing Expression, this requires you to assign data to every expression. Whats the data associated to the Expression a+b?

Since you only want to associate something to variables, you can just use a dictionary:

sage: var('a, b')
(a, b)
mydata = { a:'foo', b:'bar' }
sage: p = ((a + b)^2).expand()
a^2 + 2*a*b + b^2
sage: p.operands()[0].operands()[0]
a
sage: mydata[_]
'foo'

more

I have thought about using a dictionary, but it is kind of awkward when I want to pass these things into functions and between modules, and also I sometimes want variables with the same name but different data.

( 2011-05-21 10:39:44 -0500 )edit

Also, I am ok if a+b is just an Expression, I just want to be able to extract 'a' using operands() and then get a myVar object out.

( 2011-05-21 10:40:46 -0500 )edit

This is not a complete answer, but here are some useful methods of the symbolic ring and elements for retrieving wrapped python objects:

sage: a=SR(Mod(8,3))
sage: a
2
sage: type(a)
<type 'sage.symbolic.expression.Expression'>
sage: type(a.pyobject())
<type 'sage.rings.finite_rings.integer_mod.IntegerMod_int'>
sage: b=SR._force_pyobject('test')
sage: b
'test'
sage: type(b)
<type 'sage.symbolic.expression.Expression'>
sage: type(b.pyobject())
<type 'str'>

more

This is along the lines of what I want, but if I force my object into SR, then I can't add them together because the addition is not defined for them. I want to just inherit the addition and multiplication of the Symbolic Ring somehow without reimplementing.

( 2011-05-21 10:42:26 -0500 )edit