Questions tagged [algebra]
Abstract manipulation of symbols. Transforming an algebraic expression into the desired form.
155
questions
-1
votes
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
votes
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
votes
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
votes
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
vote
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
votes
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
vote
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
votes
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
votes
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
votes
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
votes
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
vote
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
votes
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
votes
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
vote
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
vote
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
vote
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
votes
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}$$
Edit 1
In the development of that binomial, at some point ...
1
vote
0answers
46 views
Function ellipticAdd to add points belonging to an elliptic curve $y^2 = x^3 + a\,x^2 + b\,x$ [duplicate]
In the EllipticLog WRI web page, there is a function called"ellipticMultiply defined as:
...
2
votes
1answer
89 views
Symmetrize a polynomial forgetting the commutativity property of multiplication
I need a script to authomatically symmetrize a given polynomial.
For example, if the input is
xy
the output should be
...
2
votes
2answers
251 views
Solving an equation with vector coefficients
I want to solve $(ct)^2 = d(t)\cdot d(t)$ for $t$, where $ d(t) = \frac{1}{2}at^2 + vt + r$
Where$ a, v$, and $r$ are all 3-dimensional vectors in Cartesian coordinates. How can I do this?
1
vote
0answers
65 views
Connectivity of semi-algebraic set
I am given the following semi-algebraic set:
$$
\{
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
vote
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
votes
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:
...
0
votes
0answers
84 views
How do I separate 2 variables to be independent from each other in the equation?
I have an equation namely
...
3
votes
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
vote
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} \ , $$
for the case where $f$ is a ...
1
vote
1answer
92 views
Summation returns unevaluated
Please help me do this summation as Mathematica returns the same expression:
...
3
votes
1answer
96 views
Factoring expression with rational powers
To any great Mathematica-matician. Why Mathematica can’t factor this
Factor[-1+x^(2/3)]
I know that Factor mainly targets ...
1
vote
0answers
30 views
Computational discrepancy for plugging in equivalent forms into an expression
When the following 9th root of unity is raised to the 6th power a 3rd root of unity is returned.
(Power[-(1/2) + (I Sqrt[3])/2, (3)^-1])^6 // N
-0.5 - 0.866025 I
...
0
votes
1answer
60 views
Relabeling/matching variables of big data (in MultiplicationTable)
Let A and B be two sets of tables (from multiplication tables of a group, 24 by 24 as rows by columns),
how can we effectively (and possibly also efficiently) find a way to map between them, if two ...
2
votes
1answer
70 views
Relabeling and matching variables (in MultiplicationTable)
Suppose we have a set of data given here as the multiplication table of 8 elements labeled {1,2,3,4,9,10,11,12}:
$$
\begin{array}{cccccccc}
1 & 2 & 3 & 4 & 9 & 10 & 11 & ...
0
votes
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 &...
