 | 1 | initial version |
I have an expression in term of an independent variable $q$. Now, I would like to assume that $q$ is an arbitrary $14$-th root of unity (i.e. $q^{14}=1$).
It is not allow to evaluate in any primitive root of unity, say $\eta$, since the coefficients of my expression are in the $7$-th cyclotomic field (i.e. the field is generated by $\xi=e^{2\pi i/7}$), so $\eta$ is in the field.
I also tried with "assume(q^14==1)", but it didn't work.
How can I do?
| | 2 | No.2 Revision |
I have an expression in term of an independent variable $q$. Now, I would like to assume that $q$ is an arbitrary $14$-th root of unity (i.e. $q^{14}=1$).
It is not allow to evaluate in any primitive root of unity, say $\eta$, since the coefficients of my expression are in the $7$-th cyclotomic field (i.e. the field is generated by $\xi=e^{2\pi i/7}$), so $\eta$ is in the field.
I also tried with "assume(q^14==1)", but it didn't work.
How can I do?
Added after Bruno's comment: Here is an example. I have the expression
exp=q^16*xi^5 + (q^325-12*q^235)*xi^2.
where q is an independent variable and xi is the 7th-root of unity with least argument. In other words, I have an expression in terms of an independent variable q with coefficients in the 7-th cyclotomic field
K.<xi> = CyclotomicField(7)
Now, I want to assume that $q^{14}=1$, thus the resultant expression should be
q^2*xi^5 + (q^3-12*q^11)*xi^2
since $16\equiv 2\pmod {14}$, $325 \equiv 3\pmod {14}$ and $235\equiv 11\pmod {14}$.
How can I do that? Note that it is not sufficient to evaluate the expression in $q=$some primitive $14$-th root of unity, since $q$ can be $+1$ or $-1$.
Please, think that the expression have thousands of terms, so I cannot do it by hand as above.
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