Questions tagged [algebra]

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

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1answer
28 views

Perform Eliminate, Solve and Format at once in Mathematica

I have a series of equations where I use eliminate to get a new equation with desired variables. This equation is then solved for a specific variable and then the result is presented in a specific ...
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0answers
30 views

rule generalization-NCA algebra [duplicate]

How can I generalize the rule ...
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4answers
82 views

numerical values of coefficients

Consider the following output: x= (Sqrt[3/(2 (1 + Sqrt[11]/4))] b[0, π/3] - (1 + Sqrt[7/3]) b[(2 π)/3, (2 π)/3])/(4 Sqrt[2] 7^(1/4) Sqrt[1 + Sqrt[7]/4]) If i do <...
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1answer
67 views

Expression conversion to a sum of base-N

I have: 1/(2^(1/2) - 2^(1/3)) And would like to dissolve the denominator and convert it to sum of numbers in the form 2^q where q is Rational. Does Mathematica ...
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0answers
40 views

dot product of vectors with noncommutative elements

I came upon an interesting problem. Suppose you have three vectors $\psi=(a, b)$, $\phi=(c,d)$ such that their components do not commute: $ac\neq ca$, $bd \neq db$ etc. (in general the vectors may ...
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0answers
28 views

Obtain real roots [duplicate]

I'm evaluating polynomials that are solvables by radicals in their algebraic solutions but it allways return complex values. Apparently the main issue is with the radicals e.g. N[(-1)^(1/3)] returns 0....
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1answer
57 views

simplifying indefinite sums containing Kronecker Deltas

I want to simplify indefinite sums containing KroneckerDeltas, e.g: $\sum_{k,k1,q} \beta(q) \beta(k+k1+q) \delta(k1+q)= \sum_{k,q} \beta(k)\beta(q)$ where $k,k1,q \;\epsilon \; \mathrm{R}$ ...
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1answer
35 views

NonCommutativeMultiply syntax question

I define: ...
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1answer
40 views

NonCommutativeMultiply question- syntax question

if I define id as: id /: NonCommutativeMultiply[id, x_] := x id /: NonCommutativeMultiply[y_, id] := y then ...
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2answers
56 views

Solve for two variables but output second variable in terms of first variable

Here are some equations for illustration: Format[Solve[{4*r1^3 == r2^2*(3*h), t*r2^2*(h - d) == r2^2*(h + d)}, #] & /@ {{h, d}}, InputForm] Here is their ...
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1answer
53 views

normal ordering of Bose operators

Suppose I have lot of product terms of Bose operators, e.g: ...
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1answer
48 views

grouping common powers of Bose operators

I compute a product of Bose operators and turn it into normal ordering using Boson commutation relations, e.g: ...
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1answer
31 views

How to find the norm of an imaginary exponential expresion?

I need to find the norm of the following expression $$ |1+e^{-i2\pi w}+e^{-i4\pi w}|^2$$ With w real number. For doing this I coded: ...
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1answer
44 views

Define commutator of operators, to do computations

I'm actually new to Mathematica I have been using sympy and sometimes cadabra to do calculations for a while though, I was wondering if there is an easy way to compute arbitrary expressions simplified ...
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1answer
38 views

Algebraic simplification of elements in a matrix

The matrix is defined as: ...
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1answer
39 views
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1answer
51 views

Find values of n for which expression is integer

I have an expression for which I want ot find values of n that will make it an integer. Here is the expression: (n^(3/2) - n)^(1/3) or n^(1/2) - n^(1/3) I want to ...
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2answers
98 views

Generates first degree exponential equations

I try to generate a list of first degree exponential equations in the real ones and that the solution is in logarithm in base 10 as simplified as possible, for example x= log(7) , where log is in base ...
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1answer
48 views

Solve equations for multiple variables at same time

Here is an example equation: Solve[{a*x + b*y == c}, {a}] It gives me: a -> (c - b*y)/x To solve the same equation for <...
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2answers
222 views

Given x ⊕ x =5,x ⊕ (y ⊕ z) = (x ⊕ y)+z-5 what is 2009 ⊕ 1949

There is an operation "⊕" that satisfies $x ⊕ x =5$ $x ⊕ (y ⊕ z) = (x ⊕ y)+z-5$ what is 2009 ⊕ 1949? I think it is feasible to solve with Mathematica, but my code doesn't give a useful ...
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2answers
49 views

Solve the system using elimination What are a, b, and c in the quadratic equation, ax^2+bx+c=y given the [closed]

Solve the system using elimination What are a, b, and c in the quadratic equation, ax^2+bx+c=y given the points: (2,17), (-2,9), and (1,6), please solve the question using steps e.g. (step 1, step 2)?
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1answer
34 views

Changing initial conditions in a recursive polynomial family definition. Then, finding the generation function for this family

I'm following a paper trying to find a way to repeat the done computations using Mathematica. I'm beginner using Mathematica and I already read that: I could define functions by recursion; I could ...
3
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1answer
65 views

Counting terms in recursive operation

Suppose $X$ is an algebra and $T :X\to X$ is linear function. Let $L:X\to X$ be a function satisfying the following property $$L(a \cdot b)= T(a)\cdot b + a \cdot T(b)+b\cdot T(a)+T(b)\cdot a\tag{*}$$...
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1answer
66 views

How to neglect the terms containing second and higher powers of parameter in a function

I want to neglect the terms containing second and higher powers of a from some equations. Since the equations are lengthy expressions, I was using Mathematica to ...
3
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2answers
250 views

How to write a positive function as sum of positive terms only

A multivariate polynomial function can be written in a certain form (x^m (1-x)^n y^k + ... ) if the function is Positive in the whole domain and contains a finite ...
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4answers
308 views

How to generate all combination of multiplication of multiple variables (raised to some powers)

I want to generate all the possible combinations (commutative) of a few variables but also raised to some fixed powers. Lets take the following example: I have three variables ...
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1answer
62 views

Extracting subexpressions

This is a recurrent topic: replacing subexpressions. See for instance: ...
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0answers
50 views

Eliminate doesn't work

I tried to define r by the polynomials a,b,c only. The result which I want is r=4/3 a. But this eliminate doesn't work! It is continue running without stop and without any output. Eliminate[{a == x[1] ...
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2answers
69 views

Use method “ExactAlgebraics” of PossibleZeroQ for Series zero test

I am trying to compute a series expansion around infinity with very large numerical, but entirely algebraic coefficients, and I keep running into zero test errors, which look exactly like the ones ...
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0answers
41 views

Define quaternions by properties instead of coordinates

I'd like to manipulate an expression of quaternions and only use the following properties ...
2
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1answer
111 views

Solving a system of polynomial equations - can I be sure that the number of solutions, and the solutions are correct?

I need to solve a system of two polynomials with integer coefficients in two variables, $\{Q_1(w,z)=0,\,Q_2(w,z)=0\}$, and want to compute all real solutions. I'm able to run ...
3
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3answers
140 views

Find solution for specific similarity transformation

I have a situation where I need to find a similarity transformation of a specific form. I have some Hermitian matrix $X$, and I need to find a matrix $T$ that satisfies $X = T J T^\dagger$ where, $$ J ...
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1answer
65 views

Counting real roots of bivariate polynomial

For a proof, I'm working with a polynomial $p(x,m)$ and I need to show that: For any $m\in (0,6)$, $p_m(x)\equiv p(x,m)$ has a unique real root in $(0,1/2)$. I find that this is true by using Reduce ...
4
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1answer
58 views

Series function not expanding an expression

I have the following code: FDE[d_, η_] := η^(d + 1)/Gamma[d + 2] + π^2/(6*Gamma[d])*η^(d - 1); Series[FDE[d/t, 1/η]/FDE[d/t - 1, 1/η], {η, 0, 3}] The series ...
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1answer
30 views

Checking equivalence of two expression [closed]

whenever I tried to check this I got "False" for ln[2] and I do not know how to overcome this situation. Actually these two expressions are the elements of a matrix and I can not check either both are ...
1
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1answer
53 views

Is it possible to expand a polynomial written as a product with symbolic range?

I have an expression of a polynomial here $$\prod_{k=1}^n{x+2(-1)^k\cos{\frac{k\pi}{2n+1}}}.$$ I'd like to expand the product, but the function Expand just give me the same expression. I wonder if ...
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2answers
38 views

How do I get the maximum the maximum degree of a polynomial? [duplicate]

For example applied to y^2*x^3 + z^2+1 it should give 5 due to the y^2*x^3component.
3
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2answers
214 views

Defining a*b=-b*a

I am fairly new to using Mathematica and was wondering if it's possible to define something along the lines of: $a*b=-b*a$ a sort of antisymmetry or skew symmetry if you will. I would like to do ...
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3answers
62 views

How to make `Manipulate[]` to show me the result of expression evaluation live (question updated!)?

I have code that works the way I need: ...
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1answer
34 views

Why the Plot[] is plotting the result of expression evaluation always on y axis of coordinate plane?

I have a code: Plot[-3*x + 2, {x, -10, 10}, AspectRatio -> Automatic, PlotRange -> {{-20, 20}, {-20, 20}}] output: and it does not matter what will be ...
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2answers
137 views

Using Manipulate[] to manipulate Plot[] min and max values

I have code: Plot[y = -3*x + 2, {x, -10, 10}, AspectRatio -> Automatic, PlotRange -> {{-20, 20}, {-20, 20}}] output: Now I want to use ...
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1answer
30 views

Proper AspectRation and PlotRange options with Graphics[]

I have code: ...
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6answers
151 views

Plotting horizontal and vertical lines

If I run: Plot[y = 10, {x, -3, 5}] output: If I run: Plot[x = 10, {y, -3, 5}] I am getting exactly same output as in ...
3
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1answer
137 views

How to determine irreducibility over the algebraic numbers in Mathematica? [closed]

How can the irreducibility over the algebraic numbers be determined in Mathematica for a given univariate or multivariate polynomial with algebraic coefficients? In particular: How should the field ...
0
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1answer
53 views

Algebraic Simplification only multiplication in one step

I want to simplify an algebraic expression in Mathematica. In[1] 1/a(2ba+ca+ba) Out[1] 3b+c but i want to multiply 1/a only. ...
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1answer
71 views

How to wrap any function/curver around a circle? [closed]

I have a function defined as $y=f(x)$ which i want to wrap around a circle, to get a transformed function $r=f(ϕ)$. It is important that the length of the wrapped curve stay's the same. For two ϕ ...
2
votes
1answer
60 views

How can I find all polynomials that fit an equation?

How can I ask Mathematica to find all polynomial $ f \! $s such that, for a constant $ k $: $$ f(x) \ f(y) = f(x) + f(y) + f(xy) + k $$ I've solved it on paper and want to check my results. I've ...
3
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1answer
55 views

How to find noncommutative product of two expression

I have the following function $$ B(n)=x \alpha ^n-y \alpha ^n q^n + \epsilon \left(x \alpha ^{n+1}-y \alpha ^{n+1} q^{n+1}\right). $$ Here, I want to find the product $B(n)^2$ or $B(n)*B(n+1)$ ...
5
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1answer
173 views

Implement abstract algebraic structure

I would like to implement algebraic structures in Mathematica such as groups, algebras, Lie-algebras, Hopf-algebras, ... In particular, after initialising such a structure, I would like to have ...
7
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1answer
119 views

Is AlgebraicRulesData magical?

I am trying to understand what AlgebraicRules is all about in the answer to this question. It apparently returns an ...