The key difference from Lagrangian mechanics is that the Hamiltonian approach groups variables into pairs of coordinates called the phase space coordinates:This leads to having two times more unknown functions than in the Lagrangian. However, it also leads to a system of partial differential equations with only first order derivatives, which is nicer. Notably, it can be more clearly seen in phase space.
- generalized coordinates, generally positions or angles
- their corresponding conjugate momenta, generally velocities, or angular velocities
One, single. Actual word: μόνος.
Lowercase looks like a lowercase letter N for some reason.
Two lower case variants... both used in mathematical notation, and for some reason, in LaTeX
\varphi is the one that actually looks like the default standard modern lowercase phi, while \phi is the weird one. I love life.There is a Turing machine that halts for every member of the language with the answer yes, but does not necessarily halt for non-members.
As per classification of finite fields those must be of prime power order.
Video "Finite fields made easy by Randell Heyman (2015)" at youtu.be/z9bTzjy4SCg?t=159 shows how for order . Basically, for order , we take:For a worked out example, see: GF(4).
- each element is a polynomial in , , the polynomial ring over the finite field with degree smaller than . We've just seen how to construct for prime above, so we're good there.
- addition works element-wise modulo on
- multiplication is done modulo an irreducible polynomial of order
Get nucleotide at a given position of a FASTA file by 
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01This is how you transform the Lagrangian into the Hamiltonian.
Set of eigenvalues of a linear operator.
This is generally good, especially compared to how crappy Evince, the default Ubuntu one, has been around 2014-2020.
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