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

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3
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45 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 ...
0
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0answers
5 views

Higher order single value decomposition [migrated]

Can anyone give a clear explanation with example of HOSVD. All the references are theoretical stuff.I would like to have a simple example.
0
votes
1answer
44 views

Two Variable First Order Approximation [duplicate]

I found that using Series and Normal command, I am able to approximate the first order of x or y, but If I also get rid of x*y (cross term), Series command does not work any more. Let's define some ...
-1
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1answer
61 views

how to get a constant value by mathematica?

I'm anew user of mathematica ,, forgive me A.B - B.A = 2Ιf C and c = {{0, 0, 0}, {0, 0, -Ι}, {0, Ι, 0}}; I is imaginary number, f is a constant and equal (1/2) How to get the value of f by ...
0
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0answers
51 views

Normal ordering in Mathematica

I want to create a function which normally orders a string of field operators. Consider the following: $$\langle0\vert\hat{a}(k_n) \cdots ...
0
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1answer
37 views

Expansion on sums of NonCommutativeMultiply

Following the MMa's documentations, the ExpandNCM[] function expands a**(b+c) without efforts (although I don't have very good ...
1
vote
1answer
92 views

New data type, interval, and overloading operators (+,-,*,/) [duplicate]

How can I create a new data type, interval, with different behavior than the built-in one. I want to write [a, b] and perform operator overloading, as in C ++? (I ...
1
vote
2answers
113 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
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0answers
53 views

Identity Matrix in symbolic Tensor Product [closed]

I am trying to simplify symbolic tensor products. E.g. ...
2
votes
2answers
71 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
81 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
97 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 ...
1
vote
0answers
60 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
112 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
88 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: ...
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votes
0answers
43 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
79 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
105 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
286 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
37 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
111 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
327 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
41 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
231 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
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0answers
51 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
468 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
72 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
132 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? ...
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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
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1answer
74 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
151 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
50 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
170 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
207 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
366 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
93 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
82 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
124 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
76 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
524 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
82 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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vote
1answer
994 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 $9$, $9y$, ...
4
votes
1answer
433 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
532 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 ...