Questions tagged [algebra]

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

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Mathematica package for computing Macdonald polynomials

I want to implement computation of Macdonald polynomials in mathematica. A similar question was raised in another question 5 years ago (Macdonald-Koornwinder polynomials?), but received no clear ...
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66 views

Who found also, that algebraic equations of degree 5 can be solved analytically much more than in literature? [closed]

We should go on with Euler's determining equations for algebraic degree 5. Has anyone some experience with this?
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1answer
100 views

How to apply this function? [closed]

I have defined functions f[x], g[x]. How can I let them act on variable x (I want to put the ...
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0answers
51 views

Inverse/Division in finite field?

Think of multiplictavie group of finite field F[p,n], where p is a prime number and n is a positive integer. The whole elements of F[p,n] can be represented as p^n-p^(n-1) positive integers in the ...
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2answers
71 views

How can I multiply two 2-dim. matrices? [closed]

If I have the given below matrix d1[7,7], how can I multiply d1 by d1 to get the square matrix d2=d1.d1 ? ...
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60 views

Simplify simple symbolic expression with KroneckerDelta

In short, my question is about finding a method for performing an automatic substitution f[a]/.{a->b}, where b depends on the ...
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1answer
77 views

No solution to the equation even though it has one

I was trying out Mathematica with a simple equation. I tried this one out, but it outputted nothing and when I went on WolframAlpha to test it, there was a result (c = 3 btw). Please let me know if ...
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1answer
52 views

generate quadratic functions to evaluate membership of points

How can I make a printable list with different quadratic functions and with points that belong or not to them so that a young person can check whether or not the point belongs to the parabola? my code ...
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1answer
101 views

Simplifying quantum operators (ladder operators with multiple modes)

Similar to this question, I am interested in working with an implementation of quantum ladder operators. I've been trying to use this "Quantum Mathematica Package" to solve some lengthy ...
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Using Curl and Grad in cylindrical coordinates gives different result than in Cartesian

I am doing a quite elementary calculation to verify $$ \vec \nabla\cdot V = \vec\nabla \times \vec A $$ Where $V$ is just some scalar function in $\rho$, $\phi$ and $z$ and $A$ is defined as $$ ...
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1answer
37 views

Substitution of sequences to derive recursive mean

I would have the following derivation to calculate the recursive moving average and I'd like to follow it as closely as possible in Mathematica. For the sequence where $y(i)$ is considered as an ...
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3answers
126 views

How to solve these type : If $a + b + c + d = 63$ then find the Maximum of $(a b+ b c+ c d)$

If a + b + c + d == 63 then find the Maximum of a b + b c + c d. I tried using If, ...
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2answers
61 views

Group terms in a large expression based on their minimum variable dependencies

Suppose I have a very large expression, myEq[x1,x2,x3,x4] in four variables, x1, x2, ...
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1answer
53 views

How to simplify for a ratio of two variables

Say I have an equation like $$2 z \ln[\frac{a v_{2}^{2}}{b_{2}}]+(v_{1}-2v_{2}) - z \ln[\frac{a v_{1}^{2}}{b_{1}}]\geq0$$ ...
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3answers
214 views

How to solve these algebraic identities?

I need help in finding/solving these types of algebraic equations using Mathematica. here is the problem/code. I tried using 'With' command but no use. Thanks in advance. ...
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1answer
45 views

Solving from previous results

I require in this program to use only all the value of “p” form “solution 1” in “solution 2”. Instead of copy and paste each value of “p” individually in solution 2, I am trying to write a function to ...
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2answers
53 views

How to generate multiplication tables up to nxn?

I'm doing a simple multiplication table and I have this that I'm having a hard time with. I imagine that there must be a shorter way to do it, what I can't get is that it paints black the first column ...
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1answer
97 views

Simplifying cross product expressions

Suppose I want to calculate: Cross[A1 + B1, A2 - B2] + Cross[A1 - B1, A2 + B2] which is equal to 2 A1xA2 - 2 B1xB2 Using ...
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1answer
105 views

Check if polynomial is in factored form, without factoring

I have a large list list of integer polynomials, all of which are the output of Factor. So my list looks something like this: <...
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1answer
48 views

Sorting terms in a huge equation by grouping specific products

I have a boundary condition for a problem, which contains around 100 terms! I have no trouble getting Mathematica to compute it, but the terms are sorted in a seemingly random order and I would like ...
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2answers
66 views

Can I implement a constant in such a way that every function of it gets redirected?

Basically, I want to implement split-complex numbers and tessarines. They can be easily implemented as 2x2 matrices with complex elements. But I want them to work in general expressions. So I want a ...
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1answer
30 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
31 views

rule generalization-NCA algebra [duplicate]

How can I generalize the rule ...
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4answers
87 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
75 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
48 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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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
68 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
37 views

NonCommutativeMultiply syntax question

I define: ...
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1answer
42 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
65 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
68 views

normal ordering of Bose operators

Suppose I have lot of product terms of Bose operators, e.g: ...
2
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1answer
53 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
45 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
82 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
39 views

Algebraic simplification of elements in a matrix

The matrix is defined as: ...
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1answer
44 views
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1answer
61 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
101 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
67 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
229 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
55 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
39 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
68 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
74 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
257 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
353 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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2answers
92 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
81 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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