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Questions tagged [algebra]

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

25 questions with no upvoted or accepted answers
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62 views

Command to find whether ideal is binomial in Mathematica?

Consider the ideal $$I=\left\{p_2 \left(p_3^2-p_4^2\right) \left(p_5 p_6+p_7\right),-\left(p_2 p_3-p_1 p_4\right) \left(p_5 p_6+p_7\right),-\left(p_3+p_4\right) \right\}.$$ Corollary 1.3 gives a ...
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{...
2
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0answers
101 views

Operations on ideals of polynomial rings

There is GroebnerBasis to compute a Gröbner basis of an ideal in a polynomial ring, but I am looking for a package to perform operations on ideals $I,J\subseteq\Bbb ...
2
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0answers
211 views

What are the steps using boolean algebra for transforming one equation into another?

I have a special case where I have two equations, which I have solved in a better and quicker way, but I need to solve with Boolean algebra. Using the laws of Boolean algebra, I have to prove that ...
1
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0answers
63 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
63 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, ...
1
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0answers
46 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 \...
1
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0answers
29 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 ...
1
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0answers
74 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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0answers
162 views

collecting terms with different order

I am using homotopy perturbation method to solve nonlinear ODE. The first step is to introduce P parameter and collect different order of P. The code is like this: ...
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0answers
703 views

Algebra with Sums In Mathematica

I'm trying to perform basic algebra with summations and I haven't been able to find any information on whether it is possible in Mathematica. For instance, I took this rule about multiplying sums ...
1
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0answers
44 views

Find rectangle boundries with any angle

I have a rectangle that has an angle and i need to find its boundaries in an equality form ( less than, greater than). so i guess the best way to start is to tell you what i know CENTER: (...
1
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0answers
73 views

Sum of zeros in finite Galois field

In the following code: << FiniteFields` GF[2][{0}] + GF[2][{0}] == GF[2][{0}] GF[2][{0}] + GF[2][{0}] + GF[2][{0}] == GF[2][{0}] Why does the second line ...
1
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0answers
87 views

RSolve with simple initial condition

Suppose we have the following equation: $$ g_ma_m=r_ma_{m-1} $$ with initial condition $a_L=d$ and $L$ might be negative. The following command ...
0
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1answer
59 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 ...
0
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0answers
42 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
41 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 ...
0
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0answers
38 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 & -...
0
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0answers
47 views

Combinatorica and MultiplicationTable in Mathematica 11

I try to use <<Combinatorica` or call IntervalSlider; Needs["Combinatorica`"] or call ...
0
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0answers
54 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 ...
0
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0answers
24 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 ...
0
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0answers
358 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 ...
0
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0answers
255 views

Manipulations with complex numbers, phasors

I am trying to implement phasor arithmetic, but cannot get it to work well. The key is that the arguments to the phasor function are Reals, but I cannot get Mathematica to deal with that efficiently. ...
0
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0answers
86 views

Multivariate remainder of polynomial in respect to a set of polynomials

I would like to have a really fast routine that computes the so called Normal Form of a multivariate polynomial f in respect to a set of other multivariate ...