Questions tagged [algebra]
Abstract manipulation of symbols. Transforming an algebraic expression into the desired form.
169
questions
2
votes
1answer
86 views
Solving a system of polynomial equations - can I be sure that the number of solutions, and the solutions are correct?
I need to solve a system of two polynomials with integer coefficients in two variables, $\{Q_1(w,z)=0,\,Q_2(w,z)=0\}$, and want to compute all real solutions. I'm able to run ...
3
votes
3answers
90 views
Find solution for specific similarity transformation
I have a situation where I need to find a similarity transformation of a specific form. I have some Hermitian matrix $X$, and I need to find a matrix $T$ that satisfies $X = T J T^\dagger$ where,
$$ J ...
0
votes
1answer
54 views
Counting real roots of bivariate polynomial
For a proof, I'm working with a polynomial $p(x,m)$ and I need to show that: For any $m\in (0,6)$, $p_m(x)\equiv p(x,m)$ has a unique real root in $(0,1/2)$. I find that this is true by using Reduce ...
4
votes
1answer
45 views
Series function not expanding an expression
I have the following code:
FDE[d_, η_] := η^(d + 1)/Gamma[d + 2] + π^2/(6*Gamma[d])*η^(d - 1);
Series[FDE[d/t, 1/η]/FDE[d/t - 1, 1/η], {η, 0, 3}]
The series ...
1
vote
1answer
29 views
Checking equivalence of two expression [closed]
whenever I tried to check this I got "False" for ln[2] and I do not know how to overcome this situation. Actually these two expressions are the elements of a matrix and I can not check either both are ...
1
vote
1answer
51 views
Is it possible to expand a polynomial written as a product with symbolic range?
I have an expression of a polynomial here
$$\prod_{k=1}^n{x+2(-1)^k\cos{\frac{k\pi}{2n+1}}}.$$
I'd like to expand the product, but the function Expand just give me the same expression. I wonder if ...
1
vote
2answers
25 views
How do I get the maximum the maximum degree of a polynomial? [duplicate]
For example applied to y^2*x^3 + z^2+1 it should give 5 due to the y^2*x^3component.
3
votes
2answers
180 views
Defining a*b=-b*a
I am fairly new to using Mathematica and was wondering if it's possible to define something along the lines of:
$a*b=-b*a$
a sort of antisymmetry or skew symmetry if you will. I would like to do ...
1
vote
3answers
53 views
How to make `Manipulate[]` to show me the result of expression evaluation live (question updated!)?
I have code that works the way I need:
...
0
votes
1answer
31 views
Why the Plot[] is plotting the result of expression evaluation always on y axis of coordinate plane?
I have a code:
Plot[-3*x + 2, {x, -10, 10}, AspectRatio -> Automatic,
PlotRange -> {{-20, 20}, {-20, 20}}]
output:
and it does not matter what will be ...
4
votes
2answers
121 views
Using Manipulate[] to manipulate Plot[] min and max values
I have code:
Plot[y = -3*x + 2, {x, -10, 10}, AspectRatio -> Automatic,
PlotRange -> {{-20, 20}, {-20, 20}}]
output:
Now I want to use ...
0
votes
1answer
27 views
0
votes
6answers
80 views
Plotting horizontal and vertical lines
If I run:
Plot[y = 10, {x, -3, 5}]
output:
If I run:
Plot[x = 10, {y, -3, 5}]
I am getting exactly same output as in ...
3
votes
1answer
120 views
How to determine irreducibility over the algebraic numbers in Mathematica? [closed]
How can the irreducibility over the algebraic numbers be determined in Mathematica for a given univariate or multivariate polynomial with algebraic coefficients?
In particular: How should the field ...
0
votes
1answer
51 views
Algebraic Simplification only multiplication in one step
I want to simplify an algebraic expression in Mathematica.
In[1] 1/a(2ba+ca+ba)
Out[1] 3b+c
but i want to multiply 1/a only. ...
-1
votes
1answer
59 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
59 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 $$
I've solved it on paper and want to check my results. I've ...
3
votes
1answer
55 views
How to find noncommutative product of two expression
I have the following function
$$
B(n)=x \alpha ^n-y \alpha ^n q^n
+ \epsilon \left(x \alpha ^{n+1}-y \alpha ^{n+1} q^{n+1}\right). $$
Here, I want to find the product $B(n)^2$ or $B(n)*B(n+1)$ ...
5
votes
1answer
140 views
Implement abstract algebraic structure
I would like to implement algebraic structures in Mathematica such as groups, algebras, Lie-algebras, Hopf-algebras, ... In particular, after initialising such a structure, I would like to have
...
7
votes
1answer
111 views
Is AlgebraicRulesData magical?
I am trying to understand what AlgebraicRules is all about in the answer to this question. It apparently returns an ...
1
vote
2answers
70 views
Replacing value by another value
My question is that in Mathematica notebook when I write replacing commands, it didn't replace.
In[1]:= 2*x+y+1/.(x+y)->0
Out[1]:=1+2x+y
or
...
2
votes
2answers
35 views
Count number of individual operations
Im interested in counting the number of operations required to evaluate a given formula. Let me give you an example.
Lets say I have entered the expression $\dfrac{\operatorname{Sqrt}[\operatorname{...
2
votes
3answers
207 views
How do I solve this equation with Mathematica? [closed]
I've used Solve, Reduce, and NSolve, but I don't get anything
$$
\frac{w^{3w-20}-w^{w}}{w^{...
2
votes
0answers
78 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
87 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
40 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
51 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
46 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
51 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
47 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
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
63 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
34 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
27 views
Trying to apply Jensen's inequality to a complicated symbolic expression
I have a somewhat complicated inequality expression like this:
...
0
votes
2answers
49 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
240 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
71 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
155 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
42 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
214 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
99 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
48 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
93 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
256 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
67 views
Connectivity of semi-algebraic set
I am given the following semi-algebraic set:
$$
\{
x=
\begin{bmatrix}
x_1,x_2,x_3,x_4,x_5
\end{bmatrix}
^T\in\mathbb{R}^5|
-2 \leq (1 - x_2x_3)x_5 - 2x_4x_3x_1 \leq 1.5,\\
~ -1 \leq x_1 \leq 30,...
1
vote
0answers
68 views
Some Mathematica textbooks specialized for use in (nontrivial) algebra?
So, Mathematica was constructed as a computer algebra system, but most textbooks focus on programming, mathematical problems of secondary school type or numerically-technical specialization (matrix, ...
0
votes
1answer
145 views
Conditions on parameters in Reduce
i have a system of equations in which there are two parameters F, G. I choose F,G positive. the code is:
...
0
votes
0answers
89 views
How do I separate 2 variables to be independent from each other in the equation?
I have an equation namely
...
3
votes
1answer
44 views
Removing denominator and rearranging by powers of $t$
Suppose the following function $f(t)$
$$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}}}.$$...
