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From numerical variables to symbolic variables

asked 2019-05-24 19:10:20 +0200

sagenotdead gravatar image

updated 2019-05-24 21:02:07 +0200

I would like to define an Hamiltonian dynamics that I will integrate later using scipy.integrate. The Hamiltonian is computed with a symbolic expression and then I need to make substitution from the symbolic variables to the numerical variables.

var('q1 q2')
var('p1 p2')

zs = [q1,q2,p1,p2]

def dynq(t,z):
    H = p1*(q1^2+1/3*q2^2) + p2*(cos(q1)-2*sin(q2*q1)^2)
    jacHp = jacobian(H,tuple(ps))
    dqdt = list(jacHp[0])
    dqdt[0].subs({zs[i]:z[i] for i in range(0,2*N)})
    dqdt[1].subs({zs[i]:z[i] for i in range(0,2*N)})
    return dqdt

I call dynq(0.,[1.,0.5,4.,2.]) and the output is

[q1^2, -2*sin(q1*q2)^2 + cos(q1)]

so q1,q2,p1,p2 are still in the expression and are not replaced by the numerical values of the list $z$.

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answered 2019-05-24 20:49:39 +0200

tmonteil gravatar image

updated 2019-05-24 20:49:53 +0200

When you write:

dqdt[0].subs({qs[i]:z[i] for i in range(0,N)})

this returns another object, it does not change dqdt.

So, instead, you can write:

dqdt[0] = dqdt[0].subs({qs[i]:z[i] for i in range(0,N)})
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Asked: 2019-05-24 19:10:20 +0200

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Last updated: May 24 '19