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Defining 4jm Wigner symbols

asked 2020-09-30 15:15:10 -0500

pmd gravatar image

Hi everyone,

I am a neophyte and I can't understand my error in spite of the many tutorials I have watched. I want to define the 4jm Wigner symbols, which should basically be defined as:

var('m') 
wigner_4j(j1,j2,j3,j4,j,m1,m2,m3,m4) = sum(wigner_3j(j1,j2,j,m1,m2,m)*wigner_3j(j,j3,j4,-m,m3,m4),m,-j,j)

I get plenty of errors that I can't fix. It is weird to me because the overall logic seemed good, as it works for instance when I define in a similar manner:

var('n')
b(p,q) = sum(binomial(p,n)*binomial(q,n),n,0,min(p,q))

Thanks for your help!

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Welcome to Ask Sage! Thank you for your question!

slelievre gravatar imageslelievre ( 2020-09-30 16:24:16 -0500 )edit

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answered 2020-09-30 16:00:54 -0500

rburing gravatar image

With this syntax you are trying to create a callable symbolic expression. It doesn't work because the symbolic sum that you are using requires a symbolic expression (depending on the symbolic summation index m here) as the first argument, and wigner_3j in Sage does not accept symbolic arguments, only numeric arguments (more precisely, only integers or half-integers). This explains the errors. (By contrast, Sage does support symbolic binomial coefficients and sums, and hence callable symbolic expressions involving them.)

In this case you have no need for symbolics at all; you can just define a plain Python function, using the plain (non-symbolic) sum:

wigner_4j = lambda j1,j2,j3,j4,j,m1,m2,m3,m4: sum(wigner_3j(j1,j2,j,m1,m2,m)*wigner_3j(j,j3,j4,-m,m3,m4) for m in range(-j,j+1))

Or, without lambda:

def wigner_4j(j1,j2,j3,j4,j,m1,m2,m3,m4):
    return sum(wigner_3j(j1,j2,j,m1,m2,m)*wigner_3j(j,j3,j4,-m,m3,m4) for m in range(-j,j+1))
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Perfect, thanks for your help!

pmd gravatar imagepmd ( 2020-10-01 06:56:23 -0500 )edit

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Asked: 2020-09-30 15:04:35 -0500

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Last updated: Sep 30