Questions tagged [ncalgebra]

Questions about the NCAlgebra, a package for manipulating noncommuting algebraic expressions.

Filter by
Sorted by
Tagged with
0
votes
1answer
51 views

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 (...
0
votes
1answer
99 views

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 ...
0
votes
1answer
42 views

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 $$ I=\left(\int f(x)g(x) dx\right) * h $$ ...
1
vote
0answers
31 views

rule generalization-NCA algebra [duplicate]

How can I generalize the rule ...
2
votes
2answers
73 views

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 ...
0
votes
1answer
113 views

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 ...
0
votes
2answers
56 views

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)?
1
vote
2answers
161 views

Collecting terms in NCAlgebra

Let's say we have GP[v],GM[v]: two noncommutative objects depending on the commutative variable v. ...
3
votes
1answer
95 views

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, ...
2
votes
0answers
94 views

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. ...
0
votes
0answers
57 views

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 ...
1
vote
1answer
52 views

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 ...
1
vote
3answers
139 views

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 ...
1
vote
1answer
63 views

Factorizing non commutative terms

Is it possible to factor a ** b ** c - a ** b ** d as a ** b ** (c - d) ? I am using ...
3
votes
0answers
83 views

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: ...
1
vote
2answers
82 views

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 $n>1$. ...
0
votes
1answer
93 views

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: ...
4
votes
1answer
118 views

NCAlgebra to Mathematica Standard form

Is there any way to convert the output of NCAlgebra to standard Mathematica form? For example ...
4
votes
1answer
112 views

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-...
3
votes
2answers
257 views

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. ...
0
votes
2answers
481 views

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 ...
0
votes
1answer
71 views

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 $$a[-i]a[-j]=a[-j]a[-i],$$ $$a[-i]b[-j]=b[-j]a[-i],$$ $$b[-i]b[-j]=b[-j]b[-i],$$ ...
2
votes
1answer
235 views

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 ...
0
votes
1answer
179 views

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 ...
10
votes
2answers
1k views

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 ...
4
votes
2answers
342 views

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 ...
2
votes
1answer
1k views

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 ...
2
votes
1answer
345 views

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 ...