Zoho,
On Mon, Jan 07, 2008 at 10:13:34AM -0800, Zoho wrote:
>
> Hello:
>
> I am brand new to python/sympy scripting and I have a project I have
> written in Maxima but would like to port it to sympy (as it is far
> more readable than the specific Maxima language) but I am not sure if
> sympy yet has the funcialanity that I require.
>
> What I would like to do is create an array with symbolic coefficients
> and then use the array coeffiecents to create expressions. The
> coeffiecents are solved for later. To give you and idea of what I mean
> here is a small snippet of the Maxima code:
>
> /* A Maxima program to solve
> psi'' + lambda *sin(psi) = 0 , psi'(0)=psi'(1)=0,
> int(sin(psi(s),s=0..1) = 0.
> where psi = b*cos(n*pi*s) + b^3*cos^3(n*pi*s) + ...
> lambda=1+k*b^2+k*b^4 + ... */
>
> /* Setup the expressions for psi, lambda, x, y and solve for
> the parameters */
> setup(terms):=block([],
> kill(k,a,b,d),
> n:terms,
> ratweight (b,1,c,1),
> ratwtlvl: 2*(2*n+1),
> /* Calculate expansion for psi and lambda */
> C[0]:c,
> Cpp[0]:-c,
> k[0]:1,
> for i thru n do (
> C[i]:sum(a[i,j]*c^(2*j+1),j,1,i),
>
> Cpp[i]:sum(a[i,j]*(-(2*j+1)^2*c^(2*j+1)+(2*j+1)*(2*j)*c^(2*j-1)),j,
> 1,i) ),
> psi:sum(b^(2*i+1)*C[i], i,0,n),
> lam:sum(b^(2*i)*k[i], i,0,n),
>
> ....
>
> in the Maxima code you do not need to declare the array before. Here
> 'a' is an array and the expressions 'psi' and 'lam' are later solved
> for the coefficients.
>
> So is there a way to do this using sympy?
Is this what you need?
========================================
#!/usr/bin/env python
from sympy import *
pprint_try_use_unicode()
c = Symbol('c')
b = Symbol('b')
def irange(a,b):
"""inclusive range -- range(a,b+1)"""
return range(a,b+1)
def setup_terms(n):
a = {}
C = [None]*(n+1)
C[0] = c
for i in irange(1,n):
for j in irange(1,i):
a[i,j] = Symbol('a_%i%i' % (i,j))
C[i] = sum(a[i,j] * c**(2*j+1) for j in irange(1,i))
psi = sum(b**(2*i+1) * C[i] for i in irange(0,n))
return psi
if __name__ == '__main__':
psi = setup_terms(3)
print 'PSI:'
pprint(psi)
========================================
On my host the output is:
[EMAIL PROTECTED]:~/src/sympy/sympy$ ./psi.py
PSI:
5 ⎛ 3 5⎞ 7 ⎛ 3 5 7⎞ 3 3
b*c + b *⎝a₂₁*c + a₂₂*c ⎠ + b *⎝a₃₁*c + a₃₂*c + a₃₃*c ⎠ + a₁₁*b *c
> post scriptum: Thank you for writing such great software!
Thanks for your interest to SymPy too!
--
Всего хорошего, Кирилл.
http://landau.phys.spbu.ru/~kirr/aiv/
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