# Questions tagged [algebra]

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

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### 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 ...
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 <...
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 ...
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)?
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 ...
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 $$L(a \cdot b)= T(a)\cdot b + a \cdot T(b)+b\cdot T(a)+T(b)\cdot a\tag{*}$$...
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 ...
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 ...
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 ...
61 views

### Extracting subexpressions

This is a recurrent topic: replacing subexpressions. See for instance: ...
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 ...
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 ...
39 views

### Define quaternions by properties instead of coordinates

I'd like to manipulate an expression of quaternions and only use the following properties ...
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 ...
121 views

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### 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 ...
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 ...
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 ...