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2019-03-05 14:13:50 -0600 asked a question Checking that symbolic expression is zero

How do I show that a simple algebraic expression like e.g.

(-1/16*sqrt(6)*sqrt(3)*sqrt(2) + 1/16*I*sqrt(6)*sqrt(2) - 1/8*I*sqrt(3) + 3/8).full_simplify

is zero?

2017-06-24 05:10:32 -0600 commented answer Elements in the lattice $A_n$

Sorry this uses the wrong norm. Actually the norm of the OP is not a norm.

2017-06-24 05:10:32 -0600 commented answer Series expansion for theta function of even lattice

Thanks a lot. I figured this in the meanwhile and wrote my own answer which i guess needed moderating. I definitely think the documentation should be updated. Or an example like $A_2$ should be given.

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2017-06-22 08:33:56 -0600 asked a question Series expansion for theta function of even lattice

I am new to sage and trying to figure out how to calculate the series expansion of the theta function for an even lattice $L$, i.e. $$\Theta_L(q)=\sum_{x\in L} q^{\langle x,x\rangle/2}$$

I tried the following code for the $A_2$ lattice, but I doesn't really do what its supposed to do

Q=QuadraticForm(QQ,2,[2,-1,2]); Q
Q.theta_series(20)

I found the following code on https://oeis.org/A004016 (OEIS), which gives the correct result:

ModularForms( Gamma1(3), 1, prec=81).0
2017-06-22 08:33:47 -0600 answered a question Elements in the lattice $A_n$

I would suggest something like this

k=2
Q=QuadraticForm(ZZ,2,[1,-1,1]);Q
m=Q.short_vector_list_up_to_length(k^2+1)
m[k^2]

which is $A_2$ for some $k$ which gives the result in the basis $e_1=(1,-1,0), e_2=(0,1,-1)$.

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