Tagged Questions

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

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How to get Quantity to collect like terms?

In Mathematica numerical terms collect when their variables are equal. .2 "SERC" + .7 "SERC" (* 0.9 "SERC" *) However, numerical ...
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generating random algebraic matrix using elementary operations

I generate several algebraic matrices of 12x12 where each element is a combination no repeat of the variables x, y, z and operations +, -, *, /, power, establishment (square root), any of them or any ...
128 views

How to plot a lattice (2D or 3D) given a basis

I want a graphical picture of a lattice with basis such as $\{(1,1), (\sqrt{2}, -\sqrt{2})\}$. Does Mathematica already have a pre-made function that finds all linear combinations over $\mathbb{Z}$ ...
104 views

Symbolic calculation on roots of polynomial

Given a polynomial like $x^3 + a_2 x^2 + a_1 x + a_0$ with roots $r_i$, I would like to symbolically compute the coefficients of a polynomial whose roots are $r_i^3 + r_i + 1$. How can I do this in ...
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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 ...
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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 ...
63 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 ...
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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: ...
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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 non-...
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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.
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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 ...
90 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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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 ...
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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, (...
128 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 https://reference.wolfram.com/language/ref/NonCommutativeMultiply....
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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: ...
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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 ...
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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 ...
400 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.)
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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
241 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 ...
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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 ...
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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: <...
481 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. ...
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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 ...
154 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? ...
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 ...
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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 ...
157 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 ...
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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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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 ...
173 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 ...
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 ...
210 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: <...
367 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 ...
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 ...
99 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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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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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 ...
133 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 ...