Questions tagged [algebra]
Abstract manipulation of symbols. Transforming an algebraic expression into the desired form.
0
votes
0answers
6 views
how to program a homomorphism function between polynomial rings [migrated]
Suppose a polynomial ring $\mathbb Q[X_1,...,X_n],$ a homomorphism is a function $f:\mathbb Q[X_1,...X_n]\rightarrow \mathbb Q[X_1,...X_n]$ such that $f(x+y)=f(x)+f(y), f(xy)=f(x)f(y)$ for any $x,y \...
1
vote
1answer
21 views
Trying to apply Jensen's inequality to a complicated symbolic expression
I have a somewhat complicated inequality expression like this:
...
0
votes
2answers
41 views
How to manipulate sequences of inequalities?
I am trying to write some symbolic inequality proofs in Mathematica. What would be a clean way to make the inference that a >= b and ...
1
vote
1answer
118 views
Symbolic non-commutative algebra
Consider 3 non-commutative elements $A,B,C$ and we have the relation $CB=\alpha BC$.
I want to compute things like : $(A\otimes BC ) ( B \otimes B) = AB \otimes \alpha B^2C$
Is there any package ...
1
vote
2answers
59 views
How to get Mathematica to simplify/refine a Polygamma expression of fractions
I got the following ugly ev[n] as the least complicated answer to a Fourier coefficient integral
Integrate[Cos[t]*Sin [(2 n + 1)*t]/Sin[t], {t, 0, Pi/2}
...
4
votes
1answer
130 views
How to implement split-complex numbers?
For those who do not know, the split-complex numbers are an analogue to the complex numbers where J is defined such that $J^2=1$ but $J\ne\pm1$, so they are all of the form $a+bJ$.
By using ...
0
votes
0answers
36 views
Find a matrix that are unitarily equal to the given matrix
I have four $5\times 5$ matrices, $P_i, Q_i$ ($i=1, 2$) as follows:
$P_1=\begin{pmatrix}
1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & -...
7
votes
4answers
146 views
Simplifying simple signed expression ( such as $-x(x-1) \to x(1-x)$ ) based on assumptions
Context
I would like to simplify expression involving, say, (x-1) or (x^2-1) when I know that |x|<1 so that the global ...
0
votes
3answers
85 views
Finding the integer terms of a binomial expansion [closed]
What functions can I use to find how many integer terms the following expression has?
$$\left (\sqrt[19]{19}+\sqrt[95]{95}\right )^{1995}$$
Edit 1
In the development of that binomial, at some point ...
1
vote
0answers
41 views
Function ellipticAdd to add points belonging to an elliptic curve $y^2 = x^3 + a\,x^2 + b\,x$ [duplicate]
In the EllipticLog WRI web page, there is a function called"ellipticMultiply defined as:
...
2
votes
1answer
76 views
Symmetrize a polynomial forgetting the commutativity property of multiplication
I need a script to authomatically symmetrize a given polynomial.
For example, if the input is
xy
the output should be
...
2
votes
2answers
208 views
Solving an equation with vector coefficients
I want to solve $(ct)^2 = d(t)\cdot d(t)$ for $t$, where $ d(t) = \frac{1}{2}at^2 + vt + r$
Where$ a, v$, and $r$ are all 3-dimensional vectors in Cartesian coordinates. How can I do this?
1
vote
0answers
62 views
Connectivity of semi-algebraic set
I am given the following semi-algebraic set:
$$
\{
x=
\begin{bmatrix}
x_1,x_2,x_3,x_4,x_5
\end{bmatrix}
^T\in\mathbb{R}^5|
-2 \leq (1 - x_2x_3)x_5 - 2x_4x_3x_1 \leq 1.5,\\
~ -1 \leq x_1 \leq 30,...
1
vote
0answers
61 views
Some Mathematica textbooks specialized for use in (nontrivial) algebra?
So, Mathematica was constructed as a computer algebra system, but most textbooks focus on programming, mathematical problems of secondary school type or numerically-technical specialization (matrix, ...
0
votes
1answer
44 views
Conditions on parameters in Reduce
i have a system of equations in which there are two parameters F, G. I choose F,G positive. the code is:
...
0
votes
0answers
64 views
How do I separate 2 variables to be independent from each other in the equation?
I have an equation namely
...
3
votes
1answer
39 views
Removing denominator and rearranging by powers of $t$
Suppose the following function $f(t)$
$$f(t)=x^2+y^2+2m(u-y)-u^2,$$
where
$$m=\frac{(t-2)(1-t^{2}+\sqrt{1-t^{2}})}{t(1+\sqrt{1-t^{2}})(1-t-\sqrt{1-t^{2}})},$$
and
$$u=\frac{t}{1+\sqrt{1-t^{2}}}.$$...
3
votes
1answer
45 views
I am a beginner and How to read the Result of Reduce [duplicate]
I am a beginner and cannot read the result given by the reduce command kindly help.
I used:
...
6
votes
2answers
403 views
Removing higher order terms
I have a very long expression in terms of the three functions u1, u2, u3. I am writing below only a small number of terms. I would like to define a rule that keeps terms of order three or less of any ...
5
votes
1answer
98 views
How to stop GroebnerBasis from automatically normalizing?
I need to compute the Groebner basis modulus a set of prime without normalizing the Groebner basis output. Is this possible?
Example:
...
1
vote
0answers
45 views
Defining an abstract multiplication over finite indices
I would like to define a map (a "multiplication" denoted $\otimes$) over the finite set of symbols $G=\{a,b,c,d,e,f,g,h\}$. I would like to define several rules like
$$a \otimes b= \{b \} $$
$$a \...
3
votes
4answers
186 views
How to separate integers and radicals from a term?
If I have a variable such as
r = 1 + Sqrt[2] + Sqrt[13]
how can I separate that into two separate variables with the rational and irrational parts? i.e.
...
3
votes
1answer
142 views
Efficient implementation of the divided difference
Question. I am looking for more efficients ways to compute Newton's divided difference, i.e. the operator
$$\partial : f(x,y) \mapsto \frac{f(x,y)-f(y,x)}{x-y} \ , $$
for the case where $f$ is a ...
1
vote
1answer
91 views
Summation returns unevaluated
Please help me do this summation as Mathematica returns the same expression:
...
3
votes
1answer
93 views
Factoring expression with rational powers
To any great Mathematica-matician. Why Mathematica can’t factor this
Factor[-1+x^(2/3)]
I know that Factor mainly targets ...
0
votes
0answers
24 views
Use a solution of an equation as a variable [duplicate]
Suppose that I want to take a solution of an equation, for example
a=Solve[x+3==0,x]
and use it as a number, for example to evaluate another expression such as:
<...
1
vote
0answers
28 views
Computational discrepancy for plugging in equivalent forms into an expression
When the following 9th root of unity is raised to the 6th power a 3rd root of unity is returned.
(Power[-(1/2) + (I Sqrt[3])/2, (3)^-1])^6 // N
-0.5 - 0.866025 I
...
0
votes
1answer
56 views
Relabeling/matching variables of big data (in MultiplicationTable)
Let A and B be two sets of tables (from multiplication tables of a group, 24 by 24 as rows by columns),
how can we effectively (and possibly also efficiently) find a way to map between them, if two ...
2
votes
1answer
67 views
Relabeling and matching variables (in MultiplicationTable)
Suppose we have a set of data given here as the multiplication table of 8 elements labeled {1,2,3,4,9,10,11,12}:
$$
\begin{array}{cccccccc}
1 & 2 & 3 & 4 & 9 & 10 & 11 & ...
0
votes
0answers
34 views
Combinatorica and MultiplicationTable in Mathematica 11
I try to use
<<Combinatorica`
or call
IntervalSlider; Needs["Combinatorica`"]
or call
...
2
votes
0answers
35 views
Search the full group $G$ based on the partial list of its matrix representations
Suppose I have a list of matrices that may represent the partial list of the full group $G$. And here are the given set of 7 matrix elements.
$$e =\begin{pmatrix}
1 & 0 \\
0 & 1
\end{...
1
vote
0answers
32 views
Solving some constraints on a subgroup of a Lie group [closed]
Let $M$ be a rank-3 matrix, I am interested in searching all the group elements $g \in$ SU(3) Lie group, such that,
$$
g^T M g =M.
$$
Example 1. Let
$$
M[1]=
\left(
\begin{array}{ccc}
0 & 1 &...
1
vote
1answer
61 views
Picking out terms according to proportionality in expressions
I am trying to figure out how to pick terms proportional to $x$ (or any other expression).
I have the following problem:
I want to pick out $(1+2y) x$ from a polynomial of the form $(1+2y)x + e^xx +...
2
votes
1answer
94 views
Simple tensor manipulations in mathematica
I want to perform simple calculations involving kronecker deltas without specifying the dimension of the space I am in.
For example, I would like to automatically calculate (note the implied Einstein ...
0
votes
0answers
45 views
Implement commutativity and associativity for custom operation
Just to give context: I want to implement quantum mechanical ladder operators and for this I want Mathematica to realize when it can just commute my ladder operators with numbers or variables because ...
2
votes
1answer
48 views
Function definition interrupts pattern matching?
I'm trying to redefine NonCommutativeMultiply (NCM) to behave like an anticommuting operator, based on the question here. This involves calling Unprotect on NCM and adding a definition that leaves <...
0
votes
1answer
50 views
Solving a system of inequalities
I'm trying to solve a system of inequalities with $6$ variables using Reduce but it's taking a long time (at least 30 mins) and has not yet finished.
...
2
votes
1answer
38 views
SeriesCoefficient returns unevaluated
SeriesCoefficient[x^m, {x, 0, p}]
This gives back the same thing. I tried Assumptions, FullSimplify etc. I keep getting back the same thing. The answer is ...
1
vote
1answer
47 views
Complex algebra
I give Mathematica these commands:
$Assumptions = Element[x, Reals] && Element[y, Reals]
\[Theta] = ArcTan[x, y]
z = Exp[I \[Theta]]
Conjugate[z]
I get
<...
4
votes
1answer
233 views
Symbolic calculation with generators and relations
Is it possible to do the following in Mathematica:
Define an algebra $A$ via generators and relations and multiply some tensors in $A\otimes A$ (and of course simplify the relations via the relations)...
6
votes
2answers
178 views
Turn single fraction into multiple fraction expression
I would like to find a way to take an algebraic fraction, where there is only a single numerator and denominator, and to turn it into multiple fractions multiplied by each other. I would like to ...
0
votes
0answers
23 views
Finding trivial solutions, of the type 0 = 0, of an equation involving su(N) structure constants
so I have a bunch of equations $f_{abc} = f_{egd}m_{ae}m_{bg}m_{cd}$ (sum over repeated indices), where $f_{abc}$ are the structure constants of $su(N)$, for some $N$, and $m_{ab}$ are elements of ...
2
votes
1answer
161 views
Linear operator algebra: How to distinguish scalars and operators?
In the book "A Physicist' s Guide to Mathematica" Patrick Tam introduces symbolic rules for an algebra of linear operators. Mathematically the rules are as follows, where upper (lower) case letters ...
1
vote
0answers
71 views
How can I test that an expression is a member of a field extension of $Q$
Are there functions in Mathematica that I can use to define a field extension of $Q$? I want to be able to check if an element $a \in Q(\sqrt2)$.
So far I've tried to bypass this with with ...
-1
votes
2answers
65 views
Algebra-Quadratics and Logarithms [closed]
If the two roots of the quadratic equation $x^2 - 6x + 1 = 0$ are $\log a$ and $\log b$. What is the value of $\log(a, a b^2) + log(b, a^2 b)$?
1
vote
1answer
68 views
Hochschild complex differential
For a finite-dimensional $\mathbb{C}$-algebra $A$ with basis $\{e_1,...,e_n\}$ (structure of algebra encoded by structural constants $\{c_{ij}^k\}_{i,j,k=1}^n$ such that $e_ie_j = \sum_{k=1}^n c_{ij}^...
3
votes
3answers
591 views
How can I implement anti-commuting (Grassmann) numbers (variables)?
I am looking for a way to define anti-commuting numbers (variables) in Mathematica. Let say we have a set of four variables like ${x_1,x_2,x_3,x_4}$ from which I need to get all possible permutations, ...
0
votes
0answers
291 views
Normalize a complex matrix
I have a complex matrix say,
M={{a+bi,c,c,d},{0,a-di,c,d},{d,c,a-di,0},{d,c,c,a+bi}};
Normalize[M]
I attempted to normalize this symbolic matrix with Mathematica ...
3
votes
2answers
149 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.
...
3
votes
1answer
61 views
Algebra, Local variables and the Module function
Algebra is so much fun but I'm struggling to understand how MMA executes local variables within Module. Reading the Module ...
