Mathematica Stack Exchange
Mathematica Stack Exchange

Questions tagged [algebra]

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

282 questions
13
votes
2 answers

How to specify algebraic relations between objects?

so I'm wanting to screw around a bit with Geometric Algebra in Mathematica. To start, I want to create some basis objects: $e_1,~ e_2,~e_3$ and then specify the relations between them which are $$ e_i e_j =-e_je_i ~~~\mathrm{For}~~ i \ne…
Mason
  • 560
  • 2
  • 10
9
votes
4 answers

Subtracting equations from each other?

I have two equations eqhy -2 x + f[x, y[x]] - x^2 y[x]^3 == hy[y[x]] eqfhx -2 E^(4 y[x]) + f[x, y[x]] - x^2 y[x]^3 == hx[x] I would like to subtract these equations from one another, like this solu12 = eqhy - eqfhx which currently yields -(-2…
jay
  • 235
  • 1
  • 6
5
votes
1 answer

How to define custom operators

I am currently running Mathematica 8 and I would like to know how to define custom operators. Let's say I define an operator called $\times$ where: $$a\times b = a+a\cdot b+b$$ I also want to know if it is commutative, associative, its inverse,…
simplesedition
  • 191
  • 1
  • 2
5
votes
1 answer

How to get the extension degree

The real number field cannot express $\sqrt{2}$, so we extend $2$ times to get $Q(\sqrt{2})=a+b\sqrt(2)$. But it cannot express $\sqrt{3}$ still. So we are going to extend it $2$ more times to get…
yode
  • 26,686
  • 4
  • 62
  • 167
5
votes
2 answers

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, x3, and x4. (The general problem could of course use any number of variables.) Some (constant) terms do not depend on any variables. Some of the terms depend…
David G. Stork
  • 41,180
  • 3
  • 34
  • 96
5
votes
3 answers

How can I implement anti-commuting (Grassmann) numbers (variables)?

I am looking for a way to define anti-commuting numbers (variables) in Mathematica. Let say we have a set of four variables like ${x_1,x_2,x_3,x_4}$ from which I need to get all possible permutations, then multiply them so they appear as a sum as…
Hawi
  • 173
  • 9
4
votes
3 answers

Odd behavior of GroebnerBasis

I have a parametric equation like following: expr = {1/(4 (1 + t^2)^3) - (15 t^2)/(4 (1 + t^2)^3) + (15 t^4)/(4 (1 + t^2)^3) - t^6/(4 (1 + t^2)^3) + 3/(4 (1 + t^2)) - (3 t^2)/(4 (1 + t^2)), -((3 t)/(2 (1 + t^2)^3)) + (5…
yode
  • 26,686
  • 4
  • 62
  • 167
4
votes
1 answer

How to cancel out denominator without expanding the numerator

I am trying to do algebra the way we do by hand. For example, test1=(x - b^2 + 3/(x-a)) + ((x+b)^2/((x-a)*(x+a))+z+(x+x)^3/(x-a)) test2=(x-a)*(x+a) test3=test2*test1 output is: (x-a)*(x+a)*(x - b^2 + 3/(x-a)) +…
Aschoolar
  • 883
  • 5
  • 14
3
votes
1 answer

Removing denominator and rearranging by powers of $t$

Suppose the following function $f(t)$ $$f(t)=x^2+y^2+2m(u-y)-u^2,$$ where $$m=\frac{(t-2)(1-t^{2}+\sqrt{1-t^{2}})}{t(1+\sqrt{1-t^{2}})(1-t-\sqrt{1-t^{2}})},$$ and $$u=\frac{t}{1+\sqrt{1-t^{2}}}.$$ Is there any set of methods in Mathematica…
justik
  • 133
  • 3
3
votes
1 answer

I am a beginner and How to read the Result of Reduce

I am a beginner and cannot read the result given by the reduce command kindly help. I used: Reduce[(8 x^3 - x^3 (1 + x^2)^(3/2))/(8 x^3 + (1 + x^2)^(3/2) (-5 + 4 x^3))>0] My result : -Sqrt[3] < x < 0 ||Root[25 + 75 #1^2 - 40 #1^3 + 75 #1^4 -…
Atique Khan
  • 333
  • 1
  • 6
3
votes
0 answers

Command to find whether ideal is binomial in Mathematica?

Consider the ideal $$I=\left\{p_2 \left(p_3^2-p_4^2\right) \left(p_5 p_6+p_7\right),-\left(p_2 p_3-p_1 p_4\right) \left(p_5 p_6+p_7\right),-\left(p_3+p_4\right) \right\}.$$ Corollary 1.3 gives a technique to use elimination ideal repeatedly to test…
hhh
  • 2,603
  • 2
  • 19
  • 30
2
votes
2 answers

Graded commutativity

As we all know, Mathematica has extensive built-in support for computations in free commutative algebras, AKA polynomials algebras. It's also not that hard to make computations in exterior algebras with a fixed set of generators. One possibility is…
Najib Idrissi
  • 576
  • 3
  • 11
2
votes
3 answers

How to find constant term of binomial

There is supposed to be a command or set of commands to find the constant term of a binomial expression like $$ \left(-2x^4 + \dfrac{-5}{x}\right)^{25} $$ (-2*x^4 - 5/x)^25 but I can manage to find it. Help would be greatly appreciated.
Orm
  • 137
  • 3
2
votes
1 answer

SeriesCoefficient returns unevaluated

SeriesCoefficient[x^m, {x, 0, p}] This gives back the same thing. I tried Assumptions, FullSimplify etc. I keep getting back the same thing. The answer is clearly KroneckerDelta[p,m]
Quasar Supernova
  • 1,678
  • 8
  • 13
2
votes
0 answers

How can I test that an expression is a member of a field extension of $Q$

Are there functions in Mathematica that I can use to define a field extension of $Q$? I want to be able to check if an element $a \in Q(\sqrt2)$. So far I've tried to bypass this with with expressions like MinimalPolynomial[a, x, Extension ->…
Andrea Licata
  • 21
  • 2
1
2 3