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Questions tagged [algebra]

Abstract manipulation of symbols. Transforming an algebraic expression into the desired form.

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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 \...
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1answer
21 views

Trying to apply Jensen's inequality to a complicated symbolic expression

I have a somewhat complicated inequality expression like this: ...
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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
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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 ...
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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
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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 ...
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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 & -...
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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 ...
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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 ...
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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
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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?
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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,...
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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, ...
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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: ...
3
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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
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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: ...
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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
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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
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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
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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
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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
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1answer
91 views

Summation returns unevaluated

Please help me do this summation as Mathematica returns the same expression: ...
3
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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 ...
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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
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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 ...
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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
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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 & ...
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0answers
34 views

Combinatorica and MultiplicationTable in Mathematica 11

I try to use <<Combinatorica` or call IntervalSlider; Needs["Combinatorica`"] or call ...
2
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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
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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 &...
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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
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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 ...
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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 <...
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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
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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
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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
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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 ...
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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
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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
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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 ...