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Sage Reference Manual | |
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Module: sage.calculus.test_sympy
A Sample Session using Sympy
In this first part, we do all of the examples in the Sympy tutorial (http://code.google.com/p/sympy/wiki/Tutorial), but using Sage instead of Sympy.
sage: a = Rational((1,2)) sage: a 1/2 sage: a*2 1 sage: Rational(2)^50 / Rational(10)^50 1/88817841970012523233890533447265625 sage: 1.0/2 0.500000000000000 sage: 1/2 1/2 sage: pi^2 pi^2 sage: float(pi) 3.1415926535897931 sage: RealField(200)(pi) 3.1415926535897932384626433832795028841971693993751058209749 sage: float(pi + exp(1)) 5.85987448204883... sage: oo != 2 True
sage: var('x y')
(x, y)
sage: x + y + x - y
2*x
sage: (x+y)^2
(y + x)^2
sage: ((x+y)^2).expand()
y^2 + 2*x*y + x^2
sage: ((x+y)^2).subs(x=1)
(y + 1)^2
sage: ((x+y)^2).subs(x=y)
4*y^2
sage: limit(sin(x)/x, x=0) 1 sage: limit(x, x=oo) +Infinity sage: limit((5^x + 3^x)^(1/x), x=oo) 5
sage: diff(sin(x), x) cos(x) sage: diff(sin(2*x), x) 2*cos(2*x) sage: diff(tan(x), x) sec(x)^2 sage: limit((tan(x+y) - tan(x))/y, y=0) 1/cos(x)^2 sage: diff(sin(2*x), x, 1) 2*cos(2*x) sage: diff(sin(2*x), x, 2) -4*sin(2*x) sage: diff(sin(2*x), x, 3) -8*cos(2*x)
sage: cos(x).taylor(x,0,10) 1 - x^2/2 + x^4/24 - x^6/720 + x^8/40320 - x^10/3628800 sage: (1/cos(x)).taylor(x,0,10) 1 + x^2/2 + 5*x^4/24 + 61*x^6/720 + 277*x^8/8064 + 50521*x^10/3628800
sage: matrix([[1,0], [0,1]])
[1 0]
[0 1]
sage: var('x y')
(x, y)
sage: A = matrix([[1,x], [y,1]])
sage: A
[1 x]
[y 1]
sage: A^2
[x*y + 1 2*x]
[ 2*y x*y + 1]
sage: R.<x,y> = QQ[]
sage: A = matrix([[1,x], [y,1]])
sage: print A^10
[x^5*y^5 + 45*x^4*y^4 + 210*x^3*y^3 + 210*x^2*y^2 + 45*x*y + 1
10*x^5*y^4 + 120*x^4*y^3 + 252*x^3*y^2 + 120*x^2*y + 10*x]
[ 10*x^4*y^5 + 120*x^3*y^4 + 252*x^2*y^3 + 120*x*y^2 + 10*y x^5*y^5 +
45*x^4*y^4 + 210*x^3*y^3 + 210*x^2*y^2 + 45*x*y + 1]
sage: var('x y')
(x, y)
And here are some actual tests of sympy:
sage: from sympy import Symbol, cos, sympify, pprint sage: from sympy.abc import x
sage: e = sympify(1)/cos(x)**3; e cos(x)**(-3) sage: f = e.series(x, 0, 10); f 1 + 3*x**2/2 + 11*x**4/8 + 241*x**6/240 + 8651*x**8/13440 + O(x**10)
And the pretty-printer:
sage: pprint(e)
1
-------
3
cos (x)
sage: pprint(f)
2 4 6 8
3*x 11*x 241*x 8651*x
1 + ---- + ----- + ------ + ------- + O(x**10)
2 8 240 13440
And the functionality to convert from sympy format to Sage format:
sage: e._sage_()
1/cos(x)^3
sage: print e._sage_()
1
-------
3
cos (x)
sage: e._sage_().taylor(x._sage_(), 0, 8)
1 + 3*x^2/2 + 11*x^4/8 + 241*x^6/240 + 8651*x^8/13440
sage: f._sage_()
8651*x^8/13440 + 241*x^6/240 + 11*x^4/8 + 3*x^2/2 + 1
Mixing SymPy with Sage:
sage: import sympy
sage: sympy.sympify(var("y"))+sympy.Symbol("x")
x + y
sage: o = var("omega")
sage: s = sympy.Symbol("x")
sage: t1 = s + o
sage: t2 = o + s
sage: type(t1)
<class 'sage.calculus.calculus.SymbolicArithmetic'>
sage: type(t2)
<class 'sage.calculus.calculus.SymbolicArithmetic'>
sage: t1, t2
(x + omega, x + omega)
sage: e=sympy.sin(var("y"))+sage.all.cos(Symbol("x"))
sage: type(e)
<class 'sympy.core.add.Add'>
sage: e
cos(x) + sin(y)
sage: e=e._sage_()
sage: type(e)
<class 'sage.calculus.calculus.SymbolicArithmetic'>
sage: e
sin(y) + cos(x)
sage: e = sage.all.cos(var("y")**3)**4+var("x")**2
sage: e = e._sympy_()
sage: e
x**2 + cos(y**3)**4
sage: a = sympy.Matrix([1, 2, 3]) sage: a[1] 2
sage: sympify(1.5) 1.5 sage: sympify(2) 2 sage: sympify(-2) -2
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Sage Reference Manual | |
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