Questions tagged [algebra]
Abstract manipulation of symbols. Transforming an algebraic expression into the desired form.
197
questions
0
votes
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 ...
1
vote
0answers
30 views
1
vote
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 <...
2
votes
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 ...
1
vote
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 ...
0
votes
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....
0
votes
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 $k,k1,q \;\epsilon \; \mathrm{R}$
...
1
vote
1answer
35 views
2
votes
1answer
40 views
NonCommutativeMultiply question- syntax question
if I define id as:
id /: NonCommutativeMultiply[id, x_] := x
id /: NonCommutativeMultiply[y_, id] := y
then ...
2
votes
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 ...
1
vote
1answer
53 views
2
votes
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:
...
1
vote
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:
...
0
votes
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 ...
0
votes
1answer
38 views
0
votes
1answer
39 views
How to substitute value of one variable from an equation in another to get the desired result?
I have this equation
...
2
votes
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 ...
1
vote
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 ...
0
votes
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 <...
8
votes
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 ...
0
votes
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)?
1
vote
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
votes
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
$$L(a \cdot b)= T(a)\cdot b + a \cdot T(b)+b\cdot T(a)+T(b)\cdot a\tag{*}$$...
0
votes
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
votes
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 ...
5
votes
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 ...
1
vote
1answer
62 views
Extracting subexpressions
This is a recurrent topic: replacing subexpressions. See for instance:
...
0
votes
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
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 ...
2
votes
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
votes
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
votes
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,
$$ J ...
1
vote
1answer
65 views
Counting real roots of bivariate polynomial
For a proof, I'm working with a polynomial $p(x,m)$ and I need to show that: For any $m\in (0,6)$, $p_m(x)\equiv p(x,m)$ has a unique real root in $(0,1/2)$. I find that this is true by using Reduce ...
4
votes
1answer
58 views
Series function not expanding an expression
I have the following code:
FDE[d_, η_] := η^(d + 1)/Gamma[d + 2] + π^2/(6*Gamma[d])*η^(d - 1);
Series[FDE[d/t, 1/η]/FDE[d/t - 1, 1/η], {η, 0, 3}]
The series ...
1
vote
1answer
30 views
Checking equivalence of two expression [closed]
whenever I tried to check this I got "False" for ln[2] and I do not know how to overcome this situation. Actually these two expressions are the elements of a matrix and I can not check either both are ...
1
vote
1answer
53 views
Is it possible to expand a polynomial written as a product with symbolic range?
I have an expression of a polynomial here
$$\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 ...
1
vote
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
votes
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 ...
1
vote
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:
...
0
votes
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 ...
4
votes
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 ...
0
votes
1answer
30 views
0
votes
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
votes
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
votes
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. ...
-1
votes
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 $$
I've solved it on paper and want to check my results. I've ...
3
votes
1answer
55 views
How to find noncommutative product of two expression
I have the following function
$$
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
votes
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
votes
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 ...
