Questions tagged [algebra]

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

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22 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
37 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
206 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
42 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
32 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
60 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
61 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 ...
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2answers
243 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
291 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
61 views

Extracting subexpressions

This is a recurrent topic: replacing subexpressions. See for instance: ...
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0answers
47 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
64 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
39 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
96 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
121 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
64 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 ...
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1answer
52 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
29 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 ...
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1answer
52 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
29 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.
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2answers
193 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
60 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
33 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
128 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
29 views

Proper AspectRation and PlotRange options with Graphics[]

I have code: ...
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6answers
101 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
125 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 ...
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1answer
52 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
64 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
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1answer
59 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
154 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 ...
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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 ...
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2answers
79 views

Replacing value by another value

My question is that in Mathematica notebook when I write replacing commands, it didn't replace. In[1]:= 2*x+y+1/.(x+y)->0 Out[1]:=1+2x+y or ...
2
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2answers
40 views

Count number of individual operations

Im interested in counting the number of operations required to evaluate a given formula. Let me give you an example. Lets say I have entered the expression $\dfrac{\operatorname{Sqrt}[\operatorname{...
2
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3answers
208 views

How do I solve this equation with Mathematica? [closed]

I've used Solve, Reduce, and NSolve, but I don't get anything $$ \frac{w^{3w-20}-w^{w}}{w^{...
2
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0answers
92 views

Hafnian of a matrix

Is there a Mathematica built-in function for the calculation of the Hafnian of a matrix? I am interested in the function as it appears naturally in the calculation of moments of a multivariate ...
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1answer
87 views

Algebra deduction?

I was trying to use Mathematica for some simple algebra deduction, but it didnt work. code: TrueQ@(Sqrt[(e0 u0)/(e1 u1)] == Sqrt[e0 u0]/Sqrt[e1 u1]) Any ideas ...
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1answer
40 views

Assuming x real, simplifying or refining Im[1/(x+i)] doesn't yield anything

I think it is straightforward from the title, Simplify[Im[1/(x+I)], x > 0] spits out, Im[1/(x+I)] while I would have ...
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0answers
47 views

Algebraic manipulation on removing common factor outside

d[i,j] and M[i,j] are elements of size arrays of size 2x2 After some manipulations I get this as Output ...
6
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1answer
51 views

Abelianness-forcing number Q

In the theory of finite abstract group, abelianness-forcing number $n$ is characterized as a positive integer with standard factorization $n=p_1^{k_1}p_2^{k_2}\cdots p_r^{k_r}$ with $k_i \le 2$ and $...
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2answers
50 views

Replace rules change dimension

This is absolutely driving me crazy, I don't know if this is a bug or what, but replace rule sometimes change dimension of my data. Say I have data: ...
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2answers
67 views

Apparent contradiction in double summation

I have two expressions which, if my maths is correct, should both be true. But Mathematica doesn't agree. I can take the expression E^(-n^3) out of the single ...
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1answer
68 views

Sum of powers of zero [duplicate]

I would like to calculate the following sum Sum[0^(k-a), {k, 0, Nin}] for a positive integer $a$. With considering $0^0=1$, my expected answer of the sum is $1$, ...
1
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1answer
34 views

How to change the form of the answer? [duplicate]

Reduce[x^2 + y^3 == z && x + 2 y == 3 z + 1 && x y z != 0, {x, y, z}] you get ...
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1answer
28 views

Trying to apply Jensen's inequality to a complicated symbolic expression

I have a somewhat complicated inequality expression like this: ...
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2answers
51 views

How to manipulate sequences of inequalities?

I am trying to write some symbolic inequality proofs in Mathematica. What would be a clean way to make the inference that a >= b and ...
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1answer
255 views

Symbolic non-commutative algebra

Consider 3 non-commutative elements $A,B,C$ and we have the relation $CB=\alpha BC$. I want to compute things like : $(A\otimes BC ) ( B \otimes B) = AB \otimes \alpha B^2C$ Is there any package ...
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2answers
76 views

How to get Mathematica to simplify/refine a Polygamma expression of fractions

I got the following ugly ev[n] as the least complicated answer to a Fourier coefficient integral Integrate[Cos[t]*Sin [(2 n + 1)*t]/Sin[t], {t, 0, Pi/2} ...
6
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2answers
177 views

How to implement split-complex numbers?

For those who do not know, the split-complex numbers are an analogue to the complex numbers where J is defined such that $J^2=1$ but $J\ne\pm1$, so they are all of the form $a+bJ$. By using ...