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For symbolic computation: ASTs, mathematical expressions, code that manipulates code structure, expression transformations.
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Based on SOC occupation classification
| name | build-expression-tree |
| description | For symbolic computation: ASTs, mathematical expressions, code that manipulates code structure, expression transformations. |
Represent expressions as nested data structures (tuples, classes, or trees).
# Tuple representation
expr = ('+', ('*', 'x', 2), 1) # (x * 2) + 1
# Class representation
class Expr:
def __init__(self, op, *args):
self.op, self.args = op, args
def __add__(self, other):
return Expr('+', self, other)
def __mul__(self, other):
return Expr('*', self, other)
x = Expr('x')
expr = x * 2 + 1 # Builds expression tree
# Recursive evaluation
def evaluate(expr, env):
if isinstance(expr, str):
return env[expr] # Variable lookup
if isinstance(expr, (int, float)):
return expr
op, *args = expr if isinstance(expr, tuple) else (expr.op, *expr.args)
values = [evaluate(a, env) for a in args]
return {'+': lambda a,b: a+b, '*': lambda a,b: a*b}[op](*values)
class Expression:
"""A symbolic mathematical expression."""
def __init__(self, op, *args):
self.op, self.args = op, args
def __add__(self, other): return Expression('+', self, other)
def __radd__(self, other): return Expression('+', other, self)
def __mul__(self, other): return Expression('*', self, other)
def __rmul__(self, other): return Expression('*', other, self)
def __neg__(self): return Expression('-', self)
def __repr__(self):
if len(self.args) == 1:
return f"({self.op}{self.args[0]})"
return f"({self.args[0]} {self.op} {self.args[1]})"
class Function(Expression):
"""A function like sin or cos."""
def __call__(self, x):
return Expression(self, x)
# Create symbols and functions
x = Expression('x')
sin, cos = Function('sin'), Function('cos')
# Build expressions naturally
expr = sin(x) + cos(x) * 2
# Expression tree: (+ (sin x) (* (cos x) 2))
# Symbolic differentiation
def D(y, x=x):
"""Differentiate y with respect to x."""
if y == x: return 1
if not isinstance(y, Expression): return 0
op, args = y.op, y.args
if op == '+': return D(args[0], x) + D(args[1], x)
if op == '*': return D(args[0], x) * args[1] + args[0] * D(args[1], x)
if op == sin: return cos(args[0]) * D(args[0], x)
# ... more rules
2 + x not just x + 20 + x to x, etc.Conducts iterative deep research on any topic using web search, progressive exploration, and structured synthesis. Use when asked for comprehensive research, deep investigation, thorough analysis, or multi-source exploration of any topic. Triggers: research, investigate, deep dive, comprehensive analysis, explore thoroughly, find everything about.
For cross-cutting concerns: add behavior without modifying functions, caching, timing, logging, validation wrappers.
For performance work: measure before changing, profile to find bottlenecks, compare before and after.
For ordered processing: A* search, Dijkstra, event simulation, task scheduling. Efficient min/max extraction with heap-based queue.
For dynamic programming: overlapping subproblems, recursive solutions with repeated computations, memoization to avoid redundant work.
For persistent state: closures capture outer variables, alternative to classes for simple state, factory functions that remember context.