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

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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 ...
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41 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 ...
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36 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 ...
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3answers
59 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 ...
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0answers
118 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 ...
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26 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 ...
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3answers
186 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: ...
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337 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 ...
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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 ...
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1answer
59 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 ...
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2answers
79 views

Solve gives a solution which is contradicted by an example

I have the problem as described in the title. Here is the code: ...
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1answer
56 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 ...
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69 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 ...
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97 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 ...
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1answer
63 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 ...
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1answer
349 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 ...
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1answer
64 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. ...
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1answer
595 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 $9$, $9y$, ...
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1answer
270 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
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1answer
267 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 ...
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1answer
525 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 ...
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2answers
100 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 ...
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0answers
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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 ...
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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 ...
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2answers
751 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 ...
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152 views

Unexpected behaviour of SeriesCoefficient?

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