| Developer(s) | Independent group of people |
|---|---|
| Initial release | 2007, 4–5 years ago |
| Stable release | 0.7.1 / July 29, 2011 |
| Development status | Active |
| Written in | Python |
| Operating system | Cross-platform |
| Type | Computer algebra system |
| License | New BSD license |
| Website | sympy.org |
SymPy is a Python library for symbolic computation. The stated goals of the library are to become a full-featured computer algebra system and to keep a simple code base to promote extensibility and comprehensibility. SymPy is written in Python.
SymPy is free software. The lead developers are Ondřej Čertík and Aaron Meurer.
Contents |
The SymPy library is split into a core with many optional modules.
Currently, the core of SymPy has around 13,000 lines of code (including comments and docstrings) and its capabilities include:
a*b*b + 2*b*a*b → 3*a*b**2)(a+b)**2 → a**2 + 2*a*b + b**2)exp(I*x).expand(complex=True) → cos(x)+I*sin(x))x → ln(x), or sin → cos)The complete set of SymPy modules (which are 73,000 lines including documentation) are specialised for performing the following tasks:
limit(x*log(x), x, 0) → 0)Sympy includes tools for applications in quantum physics, Fourier series, differential geometry, and relativity. There are also a set of self-tests (15,000 lines in 142 files) for most features in SymPy.
Sympy allows outputs to be formatted into a more appealing format through the pprint function. Alternatively, the init_printing() method will enable pretty printing, so pprint need not be called. Pretty printing will use unicode symbols when available in the current environment, otherwise it will fall back to ASCII characters.
>>> from sympy import pprint, init_printing, Symbol, sin, cos, exp, sqrt, series, Integral, Function >>> >>> x = Symbol("x") >>> y = Symbol("y") >>> f = Function('f') >>> # pprint will default to unicode if available >>> pprint( x**exp(x) ) ⎛ x⎞ ⎝ℯ ⎠ x >>> # An output without unicode >>> pprint(Integral(f(x), x), use_unicode=False) / | | f(x) dx | / >>> # Compare with same expression but this time unicode is enabled >>> pprint(Integral(f(x), x), use_unicode=True) ⌠ ⎮ f(x) dx ⌡ >>> # Alternatively, you can call init_printing() once and pretty print without the pprint function. >>> init_printing() >>> sqrt(sqrt(exp(x))) x ─ 4 ℯ >>> (1/cos(x)).series(x, 0, 10) 2 4 6 8 x 5⋅x 61⋅x 277⋅x ⎛ 10⎞ 1 + ── + ──── + ───── + ────── + O⎝x ⎠ 2 24 720 8064
>>> from sympy import init_printing, Symbol, expand >>> init_printing() >>> >>> a = Symbol('a') >>> b = Symbol('b') >>> e = (a + b)**5 >>> e 5 (a + b) >>> e.expand() 5 4 3 2 2 3 4 5 a + 5⋅a ⋅b + 10⋅a ⋅b + 10⋅a ⋅b + 5⋅a⋅b + b
>>> from sympy import Rational, pprint >>> >>> e = Rational(2)**50 / Rational(10)**50 >>> pprint(e) 1/88817841970012523233890533447265625
>>> from sympy import init_printing, symbols, ln, diff >>> init_printing() >>> x,y = symbols('x y') >>> f = x**2 / y + 2 * x - ln(y) >>> diff(f,x) 2⋅x ─── + 2 y >>> diff(f,y) 2 x 1 - ── - ─ 2 y y >>> diff(diff(f,x),y) -2⋅x ──── 2 y
>>> from sympy import symbols, Plot, cos >>> x,y = symbols('x y') >>> Plot(cos(x*3)*cos(y*5)-y) [0]: -y + cos(3*x)*cos(5*y), 'mode=cartesian'
>>> from sympy import init_printing, Symbol, limit, sqrt, oo >>> init_printing() >>> >>> x = Symbol('x') >>> limit(sqrt(x**2 - 5*x + 6) - x, x, oo) -5/2 >>> limit(x*(sqrt(x**2 + 1) - x), x, oo) 1/2 >>> limit(1/x**2, x, 0) ∞ >>> limit(((x - 1)/(x + 1))**x, x, oo) -2 ℯ
>>> from sympy import init_printing, Symbol, Function, Eq, dsolve, sin, diff >>> init_printing() >>> >>> x = Symbol("x") >>> f = Function("f") >>> >>> eq = Eq(f(x).diff(x), f(x)) >>> eq d ──(f(x)) = f(x) dx >>> >>> dsolve(eq, f(x)) x f(x) = C₁⋅ℯ >>> >>> eq = Eq(x**2*f(x).diff(x), -3*x*f(x) + sin(x)/x) >>> eq 2 d sin(x) x ⋅──(f(x)) = -3⋅x⋅f(x) + ────── dx x >>> >>> dsolve(eq, f(x)) C₁ - cos(x) f(x) = ─────────── 3 x
>>> from sympy import init_printing, integrate, Symbol, exp, cos, erf >>> init_printing() >>> x = Symbol('x') >>> # Polynomial Function >>> f = x**2 + x + 1 >>> f 2 x + x + 1 >>> integrate(f,x) 3 2 x x ── + ── + x 3 2 >>> # Rational Function >>> f = x/(x**2+2*x+1) >>> f x ──────────── 2 x + 2⋅x + 1 >>> integrate(f, x) 1 log(x + 1) + ───── x + 1 >>> # Exponential-polynomial functions >>> f = x**2 * exp(x) * cos(x) >>> f 2 x x ⋅ℯ ⋅cos(x) >>> integrate(f, x) 2 x 2 x x x x ⋅ℯ ⋅sin(x) x ⋅ℯ ⋅cos(x) x ℯ ⋅sin(x) ℯ ⋅cos(x) ──────────── + ──────────── - x⋅ℯ ⋅sin(x) + ───────── - ───────── 2 2 2 2 >>> # A non-elementary integral >>> f = exp(-x**2) * erf(x) >>> f 2 -x ℯ ⋅erf(x) >>> integrate(f, x) ___ 2 ╲╱ π ⋅erf (x) ───────────── 4
>>> from sympy import Symbol, cos, sin, pprint >>> x = Symbol('x') >>> e = 1/cos(x) >>> pprint(e) 1 ────── cos(x) >>> pprint(e.series(x, 0, 10)) 2 4 6 8 x 5⋅x 61⋅x 277⋅x ⎛ 10⎞ 1 + ── + ──── + ───── + ────── + O⎝x ⎠ 2 24 720 8064 >>> e = 1/sin(x) >>> pprint(e) 1 ────── sin(x) >>> pprint(e.series(x, 0, 4)) 3 1 x 7⋅x ⎛ 4⎞ ─ + ─ + ──── + O⎝x ⎠ x 6 360
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