1 / 12

SymPy A Symbolic Mathematics package in and for Python

SymPy A Symbolic Mathematics package in and for Python. Getting Started. x,y = symbols('x y') a = 2*x ＋ y a + y expand(a**3) factor(x**3+3*x**2+3*x+1) simplify(x**2-y**2-(x+y)*(x-y)). Substitution. expr = cos(x) + 1 expr.subs(x,y) expr.subs(x,0) expr = x**y expr = expr.subs(y,x**y)

heath
Download Presentation

SymPy A Symbolic Mathematics package in and for Python

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SymPy A Symbolic Mathematics package in and for Python

  2. Getting Started • x,y = symbols('x y') • a = 2*x＋y • a + y • expand(a**3) • factor(x**3+3*x**2+3*x+1) • simplify(x**2-y**2-(x+y)*(x-y))

  3. Substitution expr = cos(x) + 1 expr.subs(x,y) expr.subs(x,0) expr = x**y expr = expr.subs(y,x**y) (repeat a few times)

  4. Trigs trigx = sin(2*x) + cos(2*x) expand_trig(exprx) trigsimp(cos(x)**2 + sin(x)**2) Also for hyperbolic functions: trigsimp(cosh(x)**2=sinh(x)**2)

  5. sympify and evalf simpify('x**2+2*x+4') expr = sqrt(8) expr.evalf() pi.evalf(100)

  6. simplification What is simplification? simplify((x**3 + x**2 -x -1)/(x**2 +2*x +1)) simplify((x**4 – 1)/(x - 1)) simplify((x**4 – 1)/(x**2 – 1)) expand((x+2*y)**3) cancel((x**4 - 1)/(x – 1)) cancel((x**2 + 2* x + 1)/(x**2 - 1))

  7. Watch out for powers: xp,yp = symbols('x y',positive=True) a,b = symbols('a b', real=True) powsimp(x**a*y**a) powsimp(xp**a*yp**a)

  8. Exponentials and logarithms ln(x) expand_log(log(x*y)) expand_log(log(x/y)) expand_log(log(x**2)) expand_log(log(x**n)) expand_log(log(x**a)) logcombine undoes expand_log (if possible)

  9. Calculus diff(expr,var,var,var,....) integrate(expr,var) or integrate(expr,(var,low,high)) Can repeat variables (or limit tuples) as with diff. For infinity, use oo limit(expr,var,value)

  10. Equations Equations represented by Eq, but any expression can implicitly be Eq to 0 solve(exprs,vars) Note: not guaranteed (cfr Hilbert's 10th problem) For a polynomial, use roots roots(x**3 – 6*x**2 + 9*x,x)

  11. Matrices Matrix([[1, 2],[3,4],[5,6]]) # rowwise Matrix([1,2,3]) # is a column vector Matrices are mutable (unlike other sympy objects) Transpose: M.T eye(n) (n x n id matrix) zeros(n,m) #n rows, m columns ones(n,m) diag(a,b,c,,,) #diagonal matrix, the args can also be matrices..

  12. Matrix methods: M.det() M.rref → reduced row echelon form, list of indices of pivot columns M.nullspace M.eigenvals (returns a dictionary of algebraic multiplicity pairs) M.diagonalize → (P,D) such that D is diagonal, and M = P D P**(-1)

More Related