Questions tagged [algebra]

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

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1answer
45 views

How to wrap any function/curver around a circle? [closed]

I have a function defined as $y=f(x)$ which i want to wrap around a circle, to get a transformed function $r=f(ϕ)$. It is important that the length of the wrapped curve stay's the same. For two ϕ ...
2
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1answer
57 views

How can I find all polynomials that fit an equation?

How can I ask Mathematica to find all polynomial $ f \! $s such that, for a constant $ k $: $$ f(x) \ f(y) = f(x) + f(y) + f(xy) + k $$ I've solved it on paper and want to check my results. I've ...
3
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1answer
51 views

How to find noncommutative product of two expression

I have the following function $$ B(n)=x \alpha ^n-y \alpha ^n q^n + \epsilon \left(x \alpha ^{n+1}-y \alpha ^{n+1} q^{n+1}\right). $$ Here, I want to find the product $B(n)^2$ or $B(n)*B(n+1)$ ...
5
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1answer
125 views

Implement abstract algebraic structure

I would like to implement algebraic structures in Mathematica such as groups, algebras, Lie-algebras, Hopf-algebras, ... In particular, after initialising such a structure, I would like to have ...
7
votes
1answer
108 views

Is AlgebraicRulesData magical?

I am trying to understand what AlgebraicRules is all about in the answer to this question. It apparently returns an ...
1
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2answers
64 views

Replacing value by another value

My question is that in Mathematica notebook when I write replacing commands, it didn't replace. In[1]:= 2*x+y+1/.(x+y)->0 Out[1]:=1+2x+y or ...
2
votes
2answers
32 views

Count number of individual operations

Im interested in counting the number of operations required to evaluate a given formula. Let me give you an example. Lets say I have entered the expression $\dfrac{\operatorname{Sqrt}[\operatorname{...
2
votes
3answers
204 views

How do I solve this equation with Mathematica? [closed]

I've used Solve, Reduce, and NSolve, but I don't get anything $$ \frac{w^{3w-20}-w^{w}}{w^{...
3
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0answers
71 views

Hafnian of a matrix

Is there a Mathematica built-in function for the calculation of the Hafnian of a matrix? I am interested in the function as it appears naturally in the calculation of moments of a multivariate ...
1
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1answer
84 views

Algebra deduction?

I was trying to use Mathematica for some simple algebra deduction, but it didnt work. code: TrueQ@(Sqrt[(e0 u0)/(e1 u1)] == Sqrt[e0 u0]/Sqrt[e1 u1]) Any ideas ...
1
vote
1answer
39 views

Assuming x real, simplifying or refining Im[1/(x+i)] doesn't yield anything

I think it is straightforward from the title, Simplify[Im[1/(x+I)], x > 0] spits out, Im[1/(x+I)] while I would have ...
0
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0answers
20 views

Expressing Numbers with Rational Denominators (Surd Form) [duplicate]

Is there a command which expresses given real numbers in surd form (when possible)? That is, a form where any rooted terms are placed in the numerator, and the denominator is rational. Here are some ...
0
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0answers
49 views

Grassman and Clifford algebras as quotients of the tensor algebra

I've been working with tensors in Mathematica; it's great to have something like TensorProduct built-in with linearity and everything. Maybe you can take advantage of these structures to work with ...
0
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0answers
43 views

Algebraic manipulation on removing common factor outside

d[i,j] and M[i,j] are elements of size arrays of size 2x2 After some manipulations I get this as Output ...
6
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1answer
49 views

Abelianness-forcing number Q

In the theory of finite abstract group, abelianness-forcing number $n$ is characterized as a positive integer with standard factorization $n=p_1^{k_1}p_2^{k_2}\cdots p_r^{k_r}$ with $k_i \le 2$ and $...
1
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2answers
46 views

Replace rules change dimension

This is absolutely driving me crazy, I don't know if this is a bug or what, but replace rule sometimes change dimension of my data. Say I have data: ...
0
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0answers
34 views

Ordering of Eigenvectors [duplicate]

I am interested in computing the derivatives of the eigenvalues of a certain $n\times n$ Hermitian matrix $M(t)$. I know I can do this easily since I know the exact expression for $\dot{M}$, and the ...
0
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2answers
66 views

Apparent contradiction in double summation

I have two expressions which, if my maths is correct, should both be true. But Mathematica doesn't agree. I can take the expression E^(-n^3) out of the single ...
0
votes
1answer
61 views

Sum of powers of zero [duplicate]

I would like to calculate the following sum Sum[0^(k-a), {k, 0, Nin}] for a positive integer $a$. With considering $0^0=1$, my expected answer of the sum is $1$, ...
1
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1answer
30 views

How to change the form of the answer? [duplicate]

Reduce[x^2 + y^3 == z && x + 2 y == 3 z + 1 && x y z != 0, {x, y, z}] you get ...
1
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1answer
25 views

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

I have a somewhat complicated inequality expression like this: ...
0
votes
2answers
47 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
186 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
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2answers
67 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
143 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
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0answers
40 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 & -...
8
votes
4answers
202 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
96 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
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0answers
46 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
89 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
251 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
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0answers
65 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
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0answers
67 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
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1answer
97 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
43 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
48 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: ...
7
votes
2answers
774 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
109 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
47 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
200 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
201 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
92 views

Summation returns unevaluated

Please help me do this summation as Mathematica returns the same expression: ...
3
votes
1answer
96 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 ...
1
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0answers
30 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
60 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
70 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
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0answers
48 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
38 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 &...