Questions tagged [algebra]
Abstract manipulation of symbols. Transforming an algebraic expression into the desired form.
206
questions
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
votes
1answer
44 views
How to simplify for a ratio of two variables
Say I have an equation like
$$2 z \ln[\frac{a v_{2}^{2}}{b_{2}}]+(v_{1}-2v_{2}) - z \ln[\frac{a v_{1}^{2}}{b_{1}}]\geq0$$
...
3
votes
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
votes
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
votes
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
votes
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
votes
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 ...
1
vote
0answers
31 views
1
vote
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 ...
1
vote
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
votes
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
votes
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
vote
1answer
37 views
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
vote
1answer
60 views
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
vote
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
votes
1answer
39 views
0
votes
1answer
41 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
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
vote
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
votes
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)?
1
vote
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
votes
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
vote
2answers
89 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
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 ...
