Questions tagged [ncalgebra]
Questions about the NCAlgebra, a package for manipulating noncommuting algebraic expressions.
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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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1
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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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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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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 ...
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NCReplaceRepeated destroys noncommutativity; is this a bug?
I am pretty new to patterns in Mathematica. Here is the example I want to consider:
...
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3
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1
answer
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Is the NCAlgebra package broken?
Just for fun I downloaded and installed the NCAlgebra package.
However upon running the NCTEST suite I got the following right off the bat:
SUMMARY OF TESTS
22 files tested.
1822 tests completed in ...
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Collecting coefficients of non-commutative products from an expression
I am trying to manipulate a Hamiltonian with non-commutative operators, $a_j,a_j^\dagger$. After some algebra using NCAlgebra package in Mathematica, I have an expression like, $$H = C_1 (b**a) + C_2 (...
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NCAlgebra: is it wrong or do I not understand commuting?
Let me try and do a simple non commutative expansion in NCAlgebra:
SetNonCommutative[xpt, rp, xq, s]
ExpandNonCommutativeMultiply[xpt*rp*rp*xpt*xq*xpt*rp*s*xq]
I ...
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56
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Replacement of functions bound by sums and integrals in NCAlgebra
I want to use the NCAlgebra package to do some simplification on non commutative expressions involving integrals. For example, one such expression would be
$$ I=\left(\int f(x)g(x) dx\right) * h $$
...
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Let NCAlgebra know that Tr[] commutes
I have an expression where there are terms like
a ** (b*Tr[a ** b])
and I want to simplify it to something like
...
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606
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Define commutator of operators, to do computations
I'm actually new to Mathematica I have been using sympy and sometimes cadabra to do calculations for a while though, I was wondering if there is an easy way to compute arbitrary expressions simplified ...
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Solve the system using elimination What are a, b, and c in the quadratic equation, ax^2+bx+c=y given the [closed]
Solve the system using elimination What are a, b, and c in the quadratic equation, ax^2+bx+c=y given the points: (2,17), (-2,9), and (1,6), please solve the question using steps e.g. (step 1, step 2)?
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Collecting terms in NCAlgebra
Let's say we have GP[v],GM[v]: two noncommutative objects depending on the commutative variable v.
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NCSolve - solve for a variable
I use the latest NCAlgebra package (5.0) for non-commutative algebra.
<< NC`
<< NCAlgebra`
NCSolve[a**x==b,x]
How do I solve for the variable x, ...
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how to find derivative of an equation of matrices with element-wise multiplication or division
For an equation like this:
$$ M= \left(\begin{array}{c} A\:x-B \otimes y\end{array}\right) \oslash C $$
where $\otimes$ is an element-wise multiplication and $\oslash$ is an element-wise division.
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Define a variable to satisfy $x^3 = -x$, then sum to find exponential
I'm wondering if it is possible to tell Mathematica that my non-commuting variable satisfies $x^3 = -x$ such that it can compute $\sum_{n=0}^\infty \frac{(Ax)^n}{n!} = e^{Ax} = \cos A+ x \sin A$ with ...
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How to set a symbolic function as non-commutative in NCAlgebra
Is there a way you can set a symbolic function to be non-commutative in NCAlgebra?
For example
SetCommutative[f[t]] returns ...
- 345
2
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3
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258
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Simplify expression with non-commutative products
I am using NCAlgebra but I am open to any solution. I would like to simplify some expressions with many terms (a few dozens) using:
the fact that each term is a ...
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Factorizing non commutative terms
Is it possible to factor
a ** b ** c - a ** b ** d
as
a ** b ** (c - d)
?
I am using ...
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3
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NCAlgebra: how to set distributivity?
Is the non-commutative product in NCAlgebra also not distributive? From the documentation it seems it should be. But here is an expression, that it does not seem to be able to simplify:
...
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In NCAlgebra, how can we make d**d**d=0 if d**d=0 is given?
I wrote the following code to eliminate $d^n$ from the equation for $n>1$.
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NCAlgebra square of commuting variable
I use the NCAlgebra Package.
Now when I enter the square(so standard product) of a noncommuting variable Mathematica returns the variable with NonCommutativeMultiply:
...
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NCAlgebra to Mathematica Standard form
Is there any way to convert the output of NCAlgebra to standard Mathematica form?
For example
...
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Distribute NonCommutativeMultiply over Times
Is there a method to transform
(a1 * a2) ** (b1 * b2)
into
(a1 ** b1) * (a2 ** b2)
I am trying to transform non-...
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Non-commutative Algebra $LM=t^2 ML$, using NCAlgebra/Mathematica
I am currently using the NCAlgebra package, and am working with the algebra where $LM=t^2 ML$, where t is commutative.
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Operator satisfies Leibniz rule
Suppose I have some symbols $a[-i]$ and $b[-j]$, where $i,j=1,\cdots,7$. The relation between them are $$a[-i]a[-j]=a[-j]a[-i],$$ $$a[-i]b[-j]=b[-j]a[-i],$$
$$b[-i]b[-j]=b[-j]b[-i],$$ I want to ...
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Expand a differentiation-like product
Suppose I have some symbols $\tau$, $a[-i]$ and $b[-j]$, where $i,j=1,\cdots,7$. The relation between them are
$$a[-i]a[-j]=a[-j]a[-i],$$
$$a[-i]b[-j]=b[-j]a[-i],$$
$$b[-i]b[-j]=b[-j]b[-i],$$
...
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Why If does not work instead of /; when searching condition in a list
I am trying to define a commutator. The way I am working this out is the following. I have a list with integers. I want to put the biggest on the right commuting them. For example, if I have a list ...
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Collect is not collecting properly with non-commutative algebra
I'm using the NCAlgebra package to do some error analysis of operator split methods. I am trying to reproduce the simple examples in Mathematica, but I'm coming ...
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2
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Non-commutative algebra (NCAlgebra): How to properly SetCommutingOperators
I am starting to work with non-commutative algebra in Mathematica and had a look at the NCAlgebra package. I installed it and can use its functions. However, what I am struggling with is the ...
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Is this a bug in NCAlgebra library?
In course of my work with NCAlgebra package for Mathematica, http://math.ucsd.edu/~ncalg/ , I encountered unexpected behavior of replacements. I am using ...
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1
answer
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How to simplify symbolic matrix multiplication using the associativity of scalar multiplication?
My input is (2A).(3B). Is there a way to get 6A.B? All I could get back from Mathematica was ...
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Differential operator involving permutations
I would like to construct an operator in Mathematica of the following form,
$$D_i=\partial_i +\sum_{i \neq j}^n\frac{1}{x_i-x_j}p_{ij}, \quad i=1,...,n$$
where $p_{ij}$ is a (symmetric) permutation ...
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