Symbolic Computation Guide

A skill for using computer algebra systems (CAS) in mathematical research. Covers symbolic differentiation, integration, equation solving, series expansion, linear algebra, and polynomial arithmetic using SymPy, SageMath, and Mathematica, with practical workflows for research mathematics.

SymPy Fundamentals

Symbolic Expressions and Manipulation

from sympy import (
    symbols, expand, factor, simplify, cancel, apart,
    sin, cos, exp, log, sqrt, pi, oo, I,
    Rational, Eq, solve, solveset, S
)

x, y, z, t, n, k = symbols("x y z t n k")
a, b, c = symbols("a b c", real=True)