The art of manipulating an algebraic expression into the desired form.

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1
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1answer
43 views

I need to move X to right side without solving or simplifying anything else

I need to manipulate this equation where x is on the left side of the equation. I will be using this in excel and all other numbers will actually be referencing cells so I need x moved to the right ...
14
votes
1answer
267 views

Why is ReplaceAll behaving like this?

I'm learning to use the ReplaceAll function and I found the behavior of which is quite confusing. For Sqrt[f[x, y]] /. f[___] -> u Mathematica returns ...
8
votes
4answers
5k views

Factoring polynomials to factors involving complex coefficients

I've run into some problems using Factor on polynomials with complex coefficient factors. Reading the documentation it looks like it only factors over the ...
0
votes
1answer
27 views

Simplifying an expression given a known variable relation

I am wondering if there is a way to simplify an algebraic expression given a known variable equation using Mathematica. For instance, I wish to simplify an expression for the heat change in a process: ...
5
votes
1answer
129 views

Speed up MinimalPolynomial

My Mathematica code runs slowly MinimalPolynomial[Sqrt[2] + Sqrt[3]+ Sqrt[5]+ Sqrt[7]+ Sqrt[11]+ Sqrt[13], x] runs slowly, but the Maple version ...
1
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1answer
59 views

Collect powers of variables and integers separately?

Let expr contain a sum of powers of x with some coefficients ci. The exponents of ...
4
votes
2answers
100 views

Pull out scalars from NonCommutativeMultiply in commutator of SU2 spin algebra

I am trying to work on spin chains in Mathematica. That is, N spin-1/2 on a one-dimensional lattice with periodic boundary condition (N+1=1). I need therefore the SU2 spin algebra $S_z, S_+, S_-$ with ...
0
votes
1answer
74 views

How to find all roots of a complex number [duplicate]

Finding all roots, and I know there are four f them, of this (1 - i)^(1/4) Not only real, but imaginary as well
4
votes
5answers
214 views

Extracting Coefficients from a List of Sines

I want to extract the coefficients from the following list: list={16.2219 Sin[16.2219 t], 6.60924 Sin[6.60924 t], 13.927 Sin[ 13.927 t], 2.91309 Sin[2.91309 t]} ...
0
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1answer
56 views

Algebraic manipulation of closed loop state space system [closed]

I have the following equations $$ \begin{align} x(k+1) &= A x(k) + B \tilde{u}(k) \\ y(k) &= C x(k) + D \tilde{u}(k) \\ w(k+1) &= E w(k) + F \tilde{e}(k) \\ u(k) &= G w(k) + H ...
1
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1answer
96 views

Expressing a matrix in terms of four basis matrices

I have five matrices and I want to represent one in the basis of other four. So how do I find the value of coefficients? For example, if the matrices are I1, ...
1
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1answer
118 views

Mathematica spitting code back when using Resolve over a large range of interest

I've just started using Mathematica and have encountered my first issue. Below are two commands which only differ in the range of values I am asking Mathematica to check. The first works fine, but the ...
36
votes
6answers
5k views

Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)

Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$. When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], Mathematica gives the ...
0
votes
0answers
78 views

Rearranging 5 equations

I am trying to rearrange 5 equations in terms of 5 variables. I have the equations for y1, y2, ...
1
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0answers
47 views

Use of Mathematica to put equation into vector form

Is there a way to put the following equation of a line into vector form using Mathematica (or a Mathematical package)? $\displaystyle ...
7
votes
1answer
148 views

Extract common subexpressions from expressions [duplicate]

I am trying to evaluate multiple independent expressions with common parts. I would like Mathematica to somehow give me this common parts. It's probably not so clear, so let me give you an example. ...
3
votes
1answer
80 views

Pulling powers to the outside of expressions (inverting PowerExpand)

Is there something like an inverse of PowerExpand that pulls powers to the outside of expressions: $$ x^2 y^2 \leadsto (x y)^2 \\ x^2/y^2 \leadsto (x/y)^2 $$ I ...
1
vote
0answers
96 views
1
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1answer
84 views

Find the solution of A^2+AB+B^2 = f(a,b,c) [closed]

I wanted to ask the following question: I need to find the solutions (a particular one is enough!) A and B of the equation $A^2 + AB + B^2 = (a^2+ab+b^2)(c^2+cd+c^2)$ How can I do it? Thank ...
0
votes
0answers
76 views

Using one complicated equation to reduce another

(Relative noob here so don't assume much!) I need to use a vector equation (with $N-1$ entries) in the general form $y_j(x_{i,j},x_{i,j+1},x_{i,j-1})=0, i=1...3, j=1...N-1; x_{i,0}=x_{i,N}=0$, ...
1
vote
1answer
62 views

How to factorise a variable out of an indefinite sum?

(I should start by saying I'm a total beginner with Mathematica, so if the answer needs code I'll need it spelled out quite clearly, the learning curve for this is proving steep!) Basically what I am ...
3
votes
1answer
54 views

How to pick out terms in a linear equation with a positive coefficient?

Basically I have a really large output which looks like a long linear equation $AAA-BAA-CAA+DAA+...-ZZZ$ And I only am concerned about those terms that have a positive coefficient (i.e. a plus in ...
1
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1answer
44 views

PiecewiseExpand doesn't take all kind of assumptions

Running PiecewiseExpand[expr, assum] does not work with all kind of assumptions. For example, the following line will not split the expression with absolute values in the chambers, considering m1=m2. ...
2
votes
3answers
205 views

How to obtain non-trivial solution of equal ratios

How can I obtain a non-trivial solution of the following: $$\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}$$ The answer is $a=b=c=1$.
7
votes
4answers
450 views

Distances between points in periodic cube

How can one implement more efficiently/elegantly/memory savvily the following function which returns a matrix of all Euclidian distances between points in 3D within a cube of width ...
12
votes
1answer
249 views

ToNumberField won't recognize Root as an explicit algebraic number

In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an explicit algebraic number. ...
0
votes
0answers
53 views

Ordering oscillators with negative powers: Infinite loops

I have been working with ordering of oscillators for example $[a,a^\dagger]=1$ and I have a fairly stable code. I have needed to use inverse oscillators for example expressions like $a^m ...
4
votes
1answer
127 views

Infinite expression encountered when simplifying ArcTan sums although the result is finite

If I attempt to simplify the sum ArcTan[1/x] + ArcTan[x] with ArcTan[ Simplify[ TrigExpand[ Tan[ ArcTan[1/x] + ArcTan[x]]]]] ...
1
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0answers
77 views

Transform Root objects into Trigonometric expressions

Consider the Root objects roots = Table[Root[-1 + 27 #1^2 - 162 #1^4 + 243 #1^6 &, i],{i,1,6}] These can be expressed in terms trigonometric functions as ...
1
vote
1answer
117 views

Factoring terms out of a polynomial

I don't do much algebra in Mathematica and was surprised to discover, while attempting to answer this question, that I had no idea how to factor out an expression from a polynomial. The question was, ...
2
votes
2answers
116 views

Choosing a branch of the square root when performing a series expansion

I have the following problem. Consider expression f=Sqrt[(x-2y)^2] There is an obvious ambiguity in the definition of f ...
7
votes
8answers
1k views

Defining a function that completes the square given a quadratic polynomial expression

How can I write a function that would complete the square in a quadratic polynomial expression such that, for example, CompleteTheSquare[5 x^2 + 27 x - 5, x] ...
1
vote
1answer
69 views
1
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1answer
62 views

If statement and elements of an imported data

I import a data file: SetDirectory["C:\\Users\\SE7EN\\Desktop\\mathematica\\test"]; dd = Import["data.dat", "Table"] Out[2] = {{1}, {2}, {3}, {4}, {5}, {6}, {7}} ...
4
votes
1answer
124 views

Generate expressions equivalent to rooted trees

I would like to know how to generate all rooted trees on $n$ vertices using Mathematica? More precisely, I am interested in generating algebraic expressions equivalent to rooted trees and constructed ...
1
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1answer
104 views

What is the inside?

What is the inside of the Mathematica command, solve, for a system of equations like the following? $$\eqalign{ (x +2\phantom{3} z)^2 + (y +\phantom{3} w)^2 &= 52\cr (x + 30z)^2 + (y + 3w)^2 ...
-2
votes
1answer
97 views

Algebra problem [closed]

I have recently run into an algebra problem that goes as follows. Using the numbers 1-9 A + B + C + D = EF E + F + G + H = CJ B + G + J = ?D total = B? where ...
2
votes
1answer
55 views

How to distribute PermutationProduct over the sum

Assuming I have two elements of the permutation group algebra $a_1$, $a_2$ such that $a_i=\sum_{p\in S_n}\alpha_pp$, I want to define a linear product $\odot$ that distributes over the sum and pulls ...
0
votes
2answers
86 views

Expand expression into quotient of negative power series

I have a function T(z) and want to expand it to the following form: At the end I want to have a list of equations, which can calculate a0, a1, a2, b0, b1 and b2 with different values of h1, h2, ...
6
votes
1answer
237 views

Maple like collect command in Mathematica

In Maple I often simplify expressions for functions of same argument using the collect command: > collect(a*f(x)+f(y)+x*f(x), f, factor) (a+x)*f(x)+f(y) where ...
0
votes
1answer
108 views

Impose an specific Trigonometric expansion with TrigExpand

Is there a way to impose in mathematica an specific trigonometric expansion with TrigExpand? I have various double-angle expressions for cosine and sine in my ...
0
votes
1answer
114 views

Replacement rules in combination with pure functions to make a change of variables

I have defined my function in this way w = f[r,Θ] ; After some calculations i obtained my results with respect to the previous function. For instance: ...
0
votes
1answer
77 views

Manipulating formal vectors

I want to work with a formal vector space spanned by integer triplets: $$ V=\text{span}\{(a,b,c):a,b,c\in\mathbb N^3\}, $$ such that Mathematica can do additions for me. For example,if I input ...
1
vote
0answers
51 views

How to make noncommutative multiplication agree with commutative multiplication

I need a noncommutative multiplication that is Associative Distributive $A**0=0$, $A**1=A$ Agrees with the commutative multiplication ($A**(k B)=(k A)**B=k (A**B)$) I have found a code ...
0
votes
1answer
90 views

Force multiplication by a single factor [closed]

I have an expression that Mathematica decides to return in the general form: y = f ( a/f + b/Sqrt[f + 2] + c*f^2/Sqrt[f + 2]) (actually my expression is much ...
13
votes
1answer
479 views

Block Matrix Algebra with Mathematica

I have come up with some BlockMatrix Algebra for Mathematica to make notations easier. I have the following: ...
1
vote
0answers
80 views

Define inverse for the custom operator

I want to define simple matrix algebra (inspired by the following posts: Block Matrix Algebra with Mathematica ; How to define custom operators ). I assume the funtion ...
6
votes
1answer
126 views

Is there a version of Together that doesn't cancel common factors?

I'm running code that produces a long combination of rational functions with free constants that need to be tuned such that the combination vanishes. My current method is to put the combination over ...
12
votes
7answers
3k views

How do I replace a variable in a polynomial?

How do I substitue z^2->x in the following polynomial z^4+z^2+4? z^4+z^2+4 /. z^2->x ...