37 lines
1.4 KiB
Python
37 lines
1.4 KiB
Python
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import sympy.physics.mechanics as _me
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import sympy as _sm
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import math as m
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import numpy as _np
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q1, q2 = _me.dynamicsymbols('q1 q2')
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x, y, z = _me.dynamicsymbols('x y z')
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e = q1+q2
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a = (e).subs({q1:x**2+y**2, q2:x-y})
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e2 = _sm.cos(x)
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e3 = _sm.cos(x*y)
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a = (e2).series(x, 0, 2).removeO()
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b = (e3).series(x, 0, 2).removeO().series(y, 0, 2).removeO()
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e = ((x+y)**2).expand()
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a = (e).subs({q1:x**2+y**2,q2:x-y}).subs({x:1,y:z})
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bm = _sm.Matrix([i.subs({x:1,y:z}) for i in _sm.Matrix([e,2*e]).reshape(2, 1)]).reshape((_sm.Matrix([e,2*e]).reshape(2, 1)).shape[0], (_sm.Matrix([e,2*e]).reshape(2, 1)).shape[1])
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e = q1+q2
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a = (e).subs({q1:x**2+y**2,q2:x-y}).subs({x:2,y:z**2})
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j, k, l = _sm.symbols('j k l', real=True)
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p1 = _sm.Poly(_sm.Matrix([j,k,l]).reshape(1, 3), x)
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p2 = _sm.Poly(j*x+k, x)
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root1 = [i.evalf() for i in _sm.solve(p1, x)]
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root2 = [i.evalf() for i in _sm.solve(_sm.Poly(_sm.Matrix([1,2,3]).reshape(3, 1), x),x)]
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m = _sm.Matrix([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]).reshape(4, 4)
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am = (m).T+m
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bm = _sm.Matrix([i.evalf() for i in (m).eigenvals().keys()])
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c1 = _sm.diag(1,1,1,1)
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c2 = _sm.Matrix([2 if i==j else 0 for i in range(3) for j in range(4)]).reshape(3, 4)
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dm = (m+c1)**(-1)
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e = (m+c1).det()+(_sm.Matrix([1,0,0,1]).reshape(2, 2)).trace()
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f = (m)[1,2]
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a = (m).cols
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bm = (m).col(0)
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cm = _sm.Matrix([(m).T.row(0),(m).T.row(1),(m).T.row(2),(m).T.row(3),(m).T.row(2)])
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dm = (m).row(0)
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em = _sm.Matrix([(m).row(0),(m).row(1),(m).row(2),(m).row(3),(m).row(2)])
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