Questions tagged [algebra]

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

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5
votes
2answers
60 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, ...
0
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1answer
44 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
210 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. ...
0
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1answer
41 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 ...
0
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2answers
50 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 ...
2
votes
1answer
96 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 ...
5
votes
1answer
102 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: <...
0
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1answer
47 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 ...
0
votes
2answers
65 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 ...
0
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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 <...
2
votes
1answer
72 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
47 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 ...
0
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0answers
30 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....
0
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1answer
67 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 $k,k1,q \;\epsilon \; \mathrm{R}$ ...
1
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1answer
37 views

NonCommutativeMultiply syntax question

I define: ...
2
votes
1answer
42 views

NonCommutativeMultiply question- syntax question

if I define id as: id /: NonCommutativeMultiply[id, x_] := x id /: NonCommutativeMultiply[y_, id] := y then ...
2
votes
2answers
64 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 ...
1
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1answer
60 views

normal ordering of Bose operators

Suppose I have lot of product terms of Bose operators, e.g: ...
2
votes
1answer
51 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: ...
1
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1answer
40 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: ...
0
votes
1answer
66 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 ...
0
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1answer
39 views

Algebraic simplification of elements in a matrix

The matrix is defined as: ...
0
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1answer
41 views
2
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1answer
59 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 ...
1
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2answers
100 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 ...
0
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1answer
60 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 <...
8
votes
2answers
227 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 ...
0
votes
2answers
51 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
votes
1answer
67 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 $$L(a \cdot b)= T(a)\cdot b + a \cdot T(b)+b\cdot T(a)+T(b)\cdot a\tag{*}$$...
0
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1answer
70 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
votes
2answers
256 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 ...
5
votes
4answers
338 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 ...
1
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2answers
89 views

Extracting subexpressions

This is a recurrent topic: replacing subexpressions. See for instance: ...
0
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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] ...
2
votes
2answers
78 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 ...
2
votes
0answers
46 views

Define quaternions by properties instead of coordinates

I'd like to manipulate an expression of quaternions and only use the following properties ...
2
votes
1answer
162 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
votes
3answers
181 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 ...
1
vote
1answer
77 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
votes
1answer
82 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 ...
1
vote
1answer
32 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
vote
1answer
54 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 ...
1
vote
2answers
73 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
votes
2answers
280 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 ...
1
vote
3answers
64 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: ...
0
votes
1answer
36 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 ...
4
votes
2answers
164 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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