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

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2
votes
1answer
56 views

Algebraic Manipulations with Indices

I am absolutely new to Mathematica, but I've heard it is a pretty powerful tool for symbolic calculations. My problem (stated generally): I have three dimensional array. I define a symbolic operator ...
3
votes
2answers
51 views

Using LeviCivitaTensor

I have 2 questions about using LeviCivitaTensor, based on the following session: The signs for the cross product seems to come out "opposite" of what I expected. Why is that? Did I miss anything? ...
4
votes
4answers
275 views

Spiral roots, how?

I found this picture on the net, as I can play in mathematica
-1
votes
1answer
39 views

Different output, simple question [closed]

I found a slightly different output than what was expected in a book. DefSumMod[10] G={0,1,2,3,4,5,6,7,8,9} CircleGraph[G,Add[1]] Why is the tracing directed ...
1
vote
1answer
48 views

Factor bivariate polynomial over the complex numbers

This is very much like Factoring polynomials to factors involving complex coefficients except that I'm concerned about bivariate polynomials, not univariate polynomials. Take for example the ...
0
votes
0answers
60 views

Computing Poincaré symbolic solution for an arbitrary integer order polynomial

In the 1880s, Poincaré created functions which give the solution to the nth order polynomial equation in finite form. These functions turned out to be "natural" generalizations of the elliptic ...
0
votes
1answer
44 views

How to prevent factorial from being evalauted?

Suppose I have: Do[Print[i/i!], {i, 1, 10}] I would like the output to be like: 1/1!, 2/2!, 3/3! , ...,10/10! However, when I use the code above the ...
0
votes
1answer
38 views

Computing $V(p_1, p_2)$ and determining whether $V(p_1) \subset V(p_2)$

Say I have two homogeneous polynomials $p_1, p_2 \in \mathbb{C}[x_0, \dots, x_n]$. In other words, they cut out co-dimension 1 varieties in $\mathbb{P}^n$. I would like to know how to compute two ...
0
votes
3answers
61 views

How do we solve an equation for a product?

I've been asked to verify my maths with mathematica - today is my first time using it. The maths is simplest if we make a substitution. I have a = bcd/fg and I ...
2
votes
0answers
131 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 ...
0
votes
1answer
28 views

Variable as Difference of 2 Variables

I would like to evaluate a function based on the absolute difference of two variables. An example: g=5*x-5*x*y-5*y diff=x-y D[g,x] D[g,y] D[g,diff] I cannot find ...
7
votes
3answers
189 views

Ovals of plane curves (and esoteric surfaces in space)

Consider the curve $y^2 - x^3 + x=0$ with $x, y$ real. This curve has two connected components (one bounded, one not), and the question is: how do you get Mathematica to tell you that (if you do: ...
5
votes
1answer
347 views

Very serious multiplication bug when subscripts are used

I have found a serious bug in Mathematica 10.0.1.0 on mac os x. See the attached screenshot. It is applying the square root to the Mpc. I am very shocked by this. Does anyone know how to avoid this ...
1
vote
0answers
65 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
votes
1answer
68 views

PolynomialReduce inconsistent results

I was playing around with gröbner basis and s-polynomials and I fell upon the PolynomialReduce, and I was wondering why it gives different results when I move around the polynomials in its second ...
1
vote
2answers
82 views

Solve gives a solution which is contradicted by an example

I have the problem as described in the title. Here is the code: ...
0
votes
1answer
60 views

Abstract algebra: define constants in a finite field

How can I to define a constant in $Z_{2}$? For example, I want to create a constant b that inherits the properties of an element from $Z_{2}$. For example ...
0
votes
1answer
79 views

Constructible numbers

Can Mathematica detect constructible numbers? I know it has MinimalPolynomial but for degrees higher than 4 it's not obvious whether a given polynomial yields a ...
-2
votes
1answer
99 views

Algebra problem [closed]

I have recently run into an algebra problem that goes as follows. Using the numbers 1-9 A + B + C + D = EF E + F + G + H = CJ B + G + J = ?D total = B? where ...
3
votes
1answer
66 views

How does GroupActionBase affect the order of elements in a group?

Related (math.SE): How does the base of a group determine the “sort” of the elements in the group The help page for GroupActionBase says: A base of a group ...
4
votes
1answer
388 views

Polynomial GCD over a ring (with composite characteristic)

I'd like to implement the "Franklin-Reiter Related Message Attack" (see section 4.3 of Boneh's paper). As part of the implementation, I require to compute the GCD of two polynomials over ...
1
vote
1answer
66 views

Commutative algebra by generators and quadratic relations

My apologies if this has been asked before. Please also be gentle, as this is my first question here. I am trying to define a commutative algebra by generators and relations in the following way. ...
1
vote
1answer
696 views

Taking the LCM of algebraic expressions

Is it possible in Mathematica to take the LCM of an algebraic expression? For example, I want to take the LCM of $9$, $9y$, ...
3
votes
1answer
302 views

Define operator algebra

My objective is to work out commutators like this $$[f(x,y)\partial_x^2+g(x,y)\partial_x+h(x,y),a(x,y)\partial_x^2+b(x,y)\partial_x+c(x,y)]$$ or ...
4
votes
1answer
329 views

Simplifying polynomials in non-commutative variables

I would like to be able to simplify a polynomial in two non commuting variables, the desired result being that in every term one variable occurs to the left of the other variable. An example would be ...
2
votes
1answer
663 views

How to define custom operators

I am currently running Mathematica 8 and I would like to know how to define custom operators. Let's say I define an operator called $\times$ where: $$a\times b = a+a\cdot b+b$$ I also want to know ...
0
votes
2answers
103 views

Rearranging a simple algebraic equation

Suppose I have a simple algebraic equation like: ChebyshevT[4, p] == 0 1 - 8 p^2 + 8 p^4 == 0 and I want to solve for the ...
1
vote
0answers
34 views

How can I convert a list to an expression? [duplicate]

For example, I have the following list: {x1,op1,x2,op2,x3,op3,...} And I would like to convert the list to the following expression: x1 op1 x2 op2 x3 op3 ...
28
votes
14answers
17k views

Alternatives to Mathematica

Inspired by the recent question Alternatives to LaTeX (currently 58 upvotes) on http://tex.stackexchange.com/: Are there any paid-for or open source alternatives to Mathematica which produce equal or ...
4
votes
2answers
889 views

Inverse of a polynomial in a polynomial ring

Let $N$ be a prime, and $q$ be a positive integer. Given a polynomial $f(x)$ in $R = \mathbb Z[x]/(x^N-1)$, I want to find another polynomial $f_q(x)$ in $R_q = \mathbb Z_q[x]/(x^N-1)$, such that ...
9
votes
2answers
162 views

Unexpected behaviour of SeriesCoefficient?

Following this question/answer I discovered and played with SeriesCoefficient. In particular, I tried ...