Questions tagged [ncalgebra]
Questions about the NCAlgebra, a package for manipulating noncommuting algebraic expressions.
45 questions
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Creation & Annihilation Operators with Non-Commutative Algebra Mathematica 14.3
I want to work with (mostly expand/simplify) expressions involving some creation & annihilation operators.
Mathematica 14.3 now has the NonCommutativeAlgebra[] function which seems like it could ...
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How do I symbolically reduce traces of operators into a sum of squares?
Crossposted on Mathematics SE
How do I use Mathematica (and potentially the package NCAlgebra) to reduce traces of operators into sums of squares?
For example, I know that the expression $\mathrm{Tr}[...
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NCAlgebra computes basic commutators
I have a function comm[x_,y_]:=x**y-y**x //. ccr;
and some canonical commutation rules ccr = a**ad -> ad**a + 1;
given these, ...
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Simplification of quantum ladder operators (ideally using Using NCAlgebra)
I want to do math that involves a series of ladder operators. In the past I've tried to get it working with a 20 year old Mathematica package. But my feeling is that this is a very unused package and ...
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Modern way of simplifying non-commutative algebraic expressions in 2022
I have been asking about how to do modern quantum optics calculations in 2022, and one potential solution is to use a package that uses noncommutative algebra.
There are currently very old questions ...
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Modern way to do quantum optics calculations in 2024?
Quantum Optics can often require messy algebraic simplifications of noncommuting operators (usually ladder operators and commutators). I've asked here about how to do it before.
What are some modern ...
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1
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NCAlgebra 6.0.2 fails to compute the gradient of the trace of a simple quadratic product
NCAlgebra version 6.0.2 fails to compute the gradient of the trace of a quadratic product. Works fine in version ...
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Dealing with commutative, noncommutative variables and patterns with NC Algebra
I use NC ALgebra to deal with polynomials in non commutative variables ei and fj. The eis do not commute with themselves, the fjs do not commute with themselves, but the ei commute with the fjs. So e2 ...
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1
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ParallelTable and NC polynomial simplification
I use NC algebra to apply simplification rules on non commutative polynomials.
I would like to treat a huge number of polynomials, ~200, so I would like to run these computations in parallel.
However, ...
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0
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124
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NCAlgebra and Simplify, FullSimplify or TensorReduce
I want to simplify non-commutative expressions calculated using NCAlgebra with commuting coefficients, such as using identities for complex numbers, e.g. having
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2
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1
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153
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Factoring commutative coefficients to the left
Is it possible to make ncalgebra factorize commutative coefficients to the left?
For example, if I define a non-commutative object W and a commutative object ...
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How to install NCAlgebra to Mathematica Online
New Mathematica user, attempting to install NCAlgebra to Mathematica Online. Following instructions from https://github.com/NCAlgebra/NC/blob/master/README.md , I first tried:
...
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Derivative of quadratic form in NCAlgebra
I installed the NCAlgebra package in the hope that it contains enough rules for symbolic work with most branch-matrix expressions.
...
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NCAlgebra - Factoring common commutative coefficients
This is a rather simple question that I cannot quite figure out how to do.
Basically, I have the result of some matrix multiplication in which my resultant matrix has a mixture of commutative and non-...
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NCAlgebra conjugation
I'm trying to use NCAlgebra to simplify some expressions and I'm having trouble with simplifying conjugates. Let's say I have two variables $a, b$ and a third variable $c$ which I want to conjugate ...
