Improve documentation of how to access parts of the expression tree of a symbolic expression

[kcrisman]

sage: var('n')
n
sage: g=e^((n*pi-pi*2))

The desire is to have clear documentation on how to apply (e.g.) factor() to just some piece of this, such as the exponent.

CC: @sagetrac-rossk @mforets @slel

Component: symbolics

Keywords: expression tree, symbolic expression

Issue created by migration from https://trac.sagemath.org/ticket/9329

[mwhansen]

comment:1

Did you have something specific in mind? You can always get at the underlying tree with operand() and operands()

sage: var('n')
n
sage: g = e^((n*pi-pi*2))
sage: g.operator(), g.operands()
(exp, [-2*pi + pi*n])

This is what is done in expression_conversions.py

[kcrisman]

comment:2

I think the original request from a user was in order to access the whole tree at once as a "parsed tree", since here of course g.operands() is itself something with an operator and operands. Maybe there isn't such an object per se?

[jasongrout]

comment:3

See http://sagenb.org/home/pub/1760/ for a simple implementation.

def tree(expr): 
    if expr.operator() is None: 
        return expr 
    else: 
        return [expr.operator()]+map(tree, expr.operands()) 

[burcin]

comment:4

Here is the thread:

http://groups.google.com/group/sage-support/t/e4b769a26269b6ed

I think this is more of a documentation problem. We don't have any explanation of how to work with symbolic expressions, either traversing the tree using operator() and operands() or pattern matching with find() and match().

I don't think adding a function like Jason suggests in comment:3 would provide anything more than that is already there. Note that in the example worksheet Jason also doesn't use this function.

I suggest to close this ticket unless there is a more concrete suggestion.

[kcrisman]

comment:5

Well, this seems very reasonable; I certainly wouldn't have ever figured out the way you do it in that thread. This probably belongs either at the top of one of expression.pyx or in the documentation for SymbolicExpression, huh? It would be nice to do an example with simplification as well as substitution.

Changing ticket summary

[kcrisman]

Description changed:

--- 
+++ 
@@ -4,4 +4,4 @@
 n
 sage: g=e^((n*pi-pi*2))
 ```
-But there doesn't seem to be an easy (i.e. not via `fast_callable`) way to access the underlying expression tree.
+The desire is to have clear documentation on how to apply (e.g.) factor() to just some piece of this, such as the exponent.

[kcrisman]

comment:7

Resurrecting the original idea because I want this for my discrete math class in a couple days and realize that even having a very basic example of how to use Converter to make an expression tree - say one I could plot! - would be really useful. Right now I'm stuck with Jason's idea, which works but perhaps isn't as "Sage-ic".

sage: from sage.symbolic.random_tests import random_expr
sage: S = random_expr(20,nvars=2)
sage: S
sinh_integral(-sec(-4*abs(e))/((kronecker_delta(e, v1) - 52)*arctan(elliptic_kc(-2) - 2)))
sage: def tree(expr):
....:     if expr.operator() is None:
....:         return expr
....:     else:
....:         return [expr.operator()]+map(tree,expr.operands())
....:     
sage: tree(S)
[sinh_integral, [<built-in function mul>, [<built-in function pow>, [<built-in function add>, [kronecker_delta, [exp, 1], v1], -52], -1], [<built-in function pow>, [arctan, [<built-in function add>, [elliptic_kc, -2], -2]], -1], [sec, [<built-in function mul>, [abs, [exp, 1]], -4]], -1]]

I'm realizing it might even be useful to have a (binary) tree returned from a list of lists... but that wouldn't be here.

[jasongrout]

comment:8

By the way, http://interact.sagemath.org/node/76 might be a nice example too (that's an extremely simple expression->Java translator...)

[nbruin]

comment:9

Does

sage: S._maxima_lib_().ecl().python()

count?