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

learn more… | top users | synonyms

1
vote
2answers
103 views

Update: Calculate Tensor products and traces with Mathematica

My goal is to algebraically simplify expressions involving tensor products and taking the trace. That is, I would like to compute $\operatorname{Tr}\left( \prod_i(id+a_i \otimes b_i) \right)$, using ...
2
votes
0answers
42 views

Identity Matrix in symbolic Tensor Product

I am trying to simplify symbolic tensor products. E.g. ...
0
votes
0answers
41 views

Find the height(h) of a Circular segment based on Radius and Length(c) [on hold]

I have found the formula for calculating the R of a circle, based on a circular segment, which is; R=h/2+c^2/(8h) Where, R is ...
2
votes
2answers
68 views

intermediate steps of simplification of algebraic expression without evaluation [closed]

I am using MMA do do some algebra and I need to do some simplification. For example, I have the following expression $$ x^2 \left( \frac{6 \left(2 c_1 x^6+c_2\right)}{x^4} \right)-x \left( 4 c_1 ...
1
vote
1answer
62 views

Solving equations with subscripted variables

A student of mine tried: Solve[1/R == 1/Subscript[R, 1] + 1/Subscript[R, 2], R] which did not work. We then tried: ...
8
votes
1answer
84 views

How to make `D` apply chain rule on user-defined symbols as it does on `Dot` and `NonCommutativeMultiply`

I have my own version of Dot called mydot, and it behaves quite similar to the built-in version in that it represents the ...
6
votes
1answer
132 views

What kind of Arnoldi method is used in Mathematica?

Can someone give me a bit more information about what mathematical method Mathematica is using, (preconditioner, filtering-restarting, deflation) in the Lanczos implementation when I input something ...
0
votes
0answers
68 views

What is the function in Mathematica that can be used to find the derivative of a constant value function with respect to an arbitrary matrix?

I have a function that consists of some matrices. This function results in a constant value. I need to take the partial derivative of this function with respect to one of the matrices it depends on. ...
1
vote
0answers
56 views

How to stop mathematica from exchanging my matrices this way ? [closed]

Mathematica is exchanging the matrices i have written in a way that makes my equation doesn't make sense as the dimensions do not match anymore. I want the order of my Matrices to stay the same.
1
vote
3answers
103 views

Coefficient and Addition Formula

If I type: Coefficient[Cos[x + b], Cos[x]] I get zero. But I would like Mathematica to apply: $$\cos(x+b)=\cos x\cos b-\sin x\sin b$$ Therefore the ...
1
vote
2answers
81 views

Solve an algebraic equation

I want to obtain some positive x and y which satisfy the equation 0.01x^2-0.01x^3-0.01x+0.01x^2+y=0 I have written: ...
0
votes
0answers
35 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 ...
0
votes
0answers
78 views

Ideals in Mathematica

I am having trouble finding the commands for ideals and basic manipulation of them, such as: (1) how to designate my field, (2) how to create a polynomial ring over this field in several variables, ...
2
votes
1answer
74 views

Not commuting operator calculation

I am working on some operator calculation; I do not want the commutation relation. so xy ≠ yx. I found the mathematica code from ...
8
votes
2answers
229 views

Boson commutation relations

I have tried to adapt this answer to my problem of calculating some bosonic commutation relations, but there are still some issues. The way I'm implementing the commutator is straightforward: ...
0
votes
0answers
36 views

Divide both sides of an equation by -2 [duplicate]

I have: n = Cross[{-1, 2, 2}, {2, 0, -2}]; p = {1, -1, 1}; plane = ({x, y, z} - p).n == 0 // Expand Which gives: 10 - 4 x + 2 y - 4 z == 0 I'd like to divide ...
3
votes
1answer
103 views

How to reduce an expression into user-defined variables?

In the following code, I define a set of matrices. Then, I define a function that calculates the commutation relation relation between these matrices ...
4
votes
3answers
230 views

How to find a quotient group?

Given a normal subgroup H of a (large, finite permutation) group G, knowing a set of generators for each of H and G, how to find a subgroup K of G that is isomorphic to G/H? (Using Mathematica.)
1
vote
0answers
40 views

Algebraic equation with 4 components [closed]

I need help solving: $x^{3}-x^{2}-3x-1=0$ I understand using a calculator to find the zeros is fairly easy, but I would like to learn how to solve this equation by hand. Thank you
5
votes
1answer
208 views

Distribute transpose on matrix multiplication

I need to do the following: Transpose[A.(B+C)]=Transpose[B].Transpose[A]+Transpose[C].Transpose[A] How should I do this in mathematica? So far mathematica does ...
1
vote
0answers
49 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
vote
0answers
50 views

How to test for a non--zero rational function? [duplicate]

I want to test if a rational function in one variable is identically zero. I was surprised that just writing f==0 doesn't do it. I wrote the following code: ...
3
votes
4answers
437 views

How to Find “n” for n-th Triangular Number

For example, the 7th triangular number is 28. How do I create something that will tell me that 28 is the 7th triangular number? This is what I have created. ...
2
votes
1answer
70 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 ...
4
votes
2answers
117 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? ...
-1
votes
1answer
41 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
71 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 ...
2
votes
1answer
144 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
49 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
41 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 ...
2
votes
0answers
165 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
29 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
205 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
364 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
70 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
88 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
84 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
76 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 ...
2
votes
1answer
98 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 ...
3
votes
1answer
74 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 ...
5
votes
1answer
488 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
79 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
971 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
398 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 ...
5
votes
1answer
472 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 ...
3
votes
1answer
1k 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 ...
1
vote
0answers
36 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 ...
5
votes
2answers
1k 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 ...
10
votes
2answers
182 views

Unexpected behaviour of SeriesCoefficient?

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