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

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4
votes
1answer
117 views

Expand power of a polynomial

I'm very new to Mathematica, so excuse my innocence. I have the following expression: $$ \left( \sum_{n=0}^r \frac{(-1)^n}{n!} y^n \right)^f $$ I would like Mathematica to expand out the expression ...
0
votes
0answers
40 views

Rewriting of rational fractions [closed]

I want to write $\frac{ad+bc}{bd}$ as $\frac{a}{b}+\frac{c}{d}$. What should be the procedure in Mathematica?
0
votes
0answers
32 views

ApartSquareFree function

I have a doubt concerning the ApartSquareFree function in Mathematica. Roughly speaking, it is supposed to compute the partial fraction decomposition of a rational function $h/g$ with the denominators ...
0
votes
0answers
7 views

mathematical question on the block-diagonalization [migrated]

since my last question is thought by someone to be a physical question. Now I re-express it in a pure mathematical way here because there is nobody can give me an answer in physics.se. Suppose we ...
4
votes
1answer
84 views

Function inversion [closed]

I have an expression of this kind ...
2
votes
1answer
72 views

Replace pattern for exponentials

Ultimately, I want to replace every Exp[(const) w[i,j]] to T[i,j] and Exp[-(const) w[i,j]] to 1/T[i,j] in the following expression ...
2
votes
3answers
79 views

expressing a rising factorial as a polynomial

I have an equation in $x$ as follows: $f(x)=\prod\limits_{j=0}^{k}(j+x)=x(1+x)(2+x)\cdots(k+x)$ I want to express this as a polynomial in $x$, i.e., as $a_0x^0+a_1x^1+\cdots+a_kx^k$ I tried doing ...
3
votes
0answers
32 views
2
votes
0answers
44 views

How to remove parentheses from algebraic expression? [closed]

Suppose I have an expression like $x+x+y(x+y(x+y))$. I used Simplify command and get $y^3+x(2+y+y^2)$. How to remove parentheses to get every summand explicitly? ...
3
votes
1answer
52 views

Collecting the Log Problem

I have been having tremendous success with my students due to the following idea: ...
1
vote
1answer
62 views

Working with Function Domain

Consider $f(x)=x^2+1$ and $g(x)=\sqrt{x-1}$. Note that $(f\circ g)(x)=x$ and this checks in Mathematica. ...
1
vote
1answer
44 views

Rearrange an expression according to known items

I have this expresion: $\qquad q_{aft}=-i\,f \left(a_2\right){}^{\dagger }+i\,f \left(a_2\right){}^{\dagger }-\left(a_1\right){}^{\dagger }-a_1$ Defining $\qquad q_{0_1}=a_1+(a_1)^\dagger$ and ...
1
vote
1answer
77 views

Deriving the Fourier Coefficients Formulas with a Manual Procedure

I already know that there are built-in functions to compute the Fourier coefficients but I want to derive their formulas manually. In fact, I want to obtain the final well-known formulas for the ...
0
votes
1answer
39 views

Collection prefactors of arbitrary functions

I generated a very lengthy expression in Mathematica which can be written in the form $f(x,y,z)\log(x-y+z) + g(x,y,z)\log(x+y+z) + h(x,y)\log(x+y-z)$ etc. I would like to collect the functions ...
3
votes
0answers
84 views

How to force Series[] to compute expansions by considering non commutative multiplication?

I wish to compute the Taylor series expansion of the following iteration method $x_{k+1}=x_k-f'(x_k)^{-1}f(x_k)$ up to four terms of error ($e_k=x_k-\alpha$). When this is a scalar iteration, I very ...
6
votes
1answer
250 views
2
votes
1answer
57 views

Expanding rational functions with minimal denominator

I'm working with rational functions and I want to be able to put them in a specific form and then get a list of terms in which the numerators are monomials. Take for example ...
3
votes
1answer
57 views

How to gather terms into Elementary Symmetric Polynomials?

I would like to gather the terms of this polynomial (and much higher order ones): $$q = 1-3 c+c^2+p[1]-2 c p[1]+p[2]-2 c p[2]+p[1] p[2]-c p[1] p[2]+p[3]-2 c p[3]+p[1] p[3]-c p[1] p[3]+p[2] p[3]-c ...
3
votes
1answer
75 views

Factor a polynomial Root into Roots of smallest possible degree

Suppose I have a polynomial Root representing an algebraic number. I want to represent it (if possible) as a product of several polynomial ...
0
votes
1answer
48 views

Simple grouping equations [closed]

I'm new in the Mathematica world. A very basic question. I have been using the command Eliminate on a set of equations as follow: ...
0
votes
1answer
57 views

Eliminate variable on multiple equations [closed]

I'm pretty new with Mathematica. I have to perform a really simple operation, but I'm really struggling with that. I have a set of 4 equations, for example (they can also be more complex): $ AA = 2 ...
4
votes
1answer
89 views

Pertubation series of given equations

I would like to define a function that does the following. If I have an equation, for example: $$f(x)+[1-f^2(x)]+f^{\prime\prime}(x)+f(x)\ f^\prime(x)=0$$ and I am given a value for $f$ to expand ...
0
votes
1answer
44 views

Dividing out any constant factor from expression [closed]

How do I divide out any constants from an expression? Let's say: $2A+4B+2C+6 \rightarrow A+2B+C+3$ What's the right command for this? I have been using ...
6
votes
4answers
124 views

Forcing Mathematica to Output $1/\sqrt2$ as $\sqrt2/2$

I am trying to force Mathematica to output $\frac{1}{\sqrt2}$ as $\frac{\sqrt2}{2}$. I tried: {1, Sqrt[2]}*Sqrt[2] Which outputs: ...
8
votes
1answer
192 views

How does Mathematica calculate $\sin(\pi/5)$?

Consider: Sin[Pi/5] which returns: $$\sqrt{\frac58-\frac{\sqrt5}{8}}$$ Does anyone know how to figure out the trigonometric identities used by Mathematica to ...
5
votes
4answers
120 views

Solving an equation with rational expressions (step by step) [duplicate]

Consider the following equation with rational expressions: $$\frac{5}{x+4}=4+\frac{3}{x-2}$$ We will look at the plot. We will use the Solve command to check our answer. ...
7
votes
5answers
236 views

How can I group constants/parameters using Mathematica?

I am trying to solve a problem which may seem quite simple, although I have been unable to find any solution in the documentation or discussion forums. I am not a mathematician, so please bare with ...
3
votes
2answers
101 views

How to make algebraic substitutions?

I would like to simplify complicated expressions by defining some variable that is a combination of other variables that appear in the expression, but without eliminating the original variables. As a ...
5
votes
1answer
189 views

How to write polynomial expression as commutator form?

I want to write some polynomial expressions as commutator form. For example : $$ \frac{\text{BA}}{2}-\frac{\text{AB}}{2} = -\frac{1}{2}[A,B] $$ or $$ ...
0
votes
3answers
41 views

How to transform a noncommutative product to a different expression?

I have a (long) sum of the following ** (noncommutative) products: gg**qs**rh (each variable always consists of two letters like in the artificial example ...
1
vote
3answers
116 views

Coefficient and Addition Formula

If I type: Coefficient[Cos[x + b], Cos[x]] I get zero. But I would like Mathematica to apply: $$\cos(x+b)=\cos x\cos b-\sin x\sin b$$ Therefore the ...
0
votes
0answers
79 views

Speed up the Eliminate

I have problem of eliminating some variables from a set of equations, which contain logarithmic function, in order to obtain a differential equation. These are the parameter and functions in ...
0
votes
0answers
45 views

Multivariate remainder of polynomial in respect to a set of polynomials

I would like to have a really fast routine that computes the so called Normal Form of a multivariate polynomial f in respect to a set of other multivariate ...
2
votes
0answers
60 views

Changing variables in a series expansion

I want to compute the Taylor expansion of some pure function f[x_], but then perform a change of variables in the resulting expression. So, for example, the output ...
1
vote
1answer
119 views

Polynomial decomposition algorithm with a hint

If $p,f,g$ are polynomials of degree 2 or higher and $p(x)=f(g(x))$ we have a polynomial decomposition of $p$. When Mathematica (as noted below this was actually on Wolfram Alpha) says ``decomposition ...
6
votes
3answers
163 views

Expanding out multiplied terms

Is there any command in Mathematica to expand terms like $x^2\, y^3$ to $x\,x\,y\,y\,y$? I tried PowerExpansion, but it works for expressions like $(x\,y)^2$ which ...
5
votes
2answers
125 views

Can one prevent operators like `Factor` or `Apart` from changing full form of some algebraic expressions?

In this question I will talk about a toy example, it should be clear what do I actually mean in general. Also, not only Factor but also ...
1
vote
1answer
68 views

Adding algebraic functions to NDSolve

I want to define an integral function which depends on a system of ODE and is also used to NDSolve the ODEs. ...
3
votes
1answer
167 views

Separate variables in equation

I need to know is there a way to separate the desired variables in the equation at one side of the equality. For instance, the following equation ...
0
votes
1answer
59 views

problem with Collect when using indexed variables [closed]

I'm not getting the expected output when I use Collect with indexed variables. ...
1
vote
1answer
95 views

Using the Norm Function

I am trying to take the norm of a general vector and show that for vectors, v,w, that Norm[v cross w]^2==Norm[v]^2*Norm[w]^2-(v dot w)^2 In Mathematica, here are my steps: ...
4
votes
1answer
115 views

How to collect terms with z-derivative?

my equations are very long (several pages). Here I will provide simple example: ...
1
vote
0answers
35 views

Changing the order of a factor [duplicate]

I've done: p[x_] := x^2 + x + 1; roots = Solve[p[x] == 0, x] // ComplexExpand; roots = roots /. x -> y; Times @@ (x - y /. roots) Which produces this output: ...
1
vote
1answer
39 views

How can I rewrite this expression in terms of V_o/V_s?

$$\frac{V_o-\frac{A \left(R_{\text{int}} ...
1
vote
2answers
56 views

How to reorder and combine terms in a polynomial with multi-variables?

I have a polynomial with the coefficients of {a1, b1, b2} ...
1
vote
0answers
66 views

“Reduce” works fine for a non-linear system with 9 equations, but cannot solve it if 10 equations. Any ways to improve the code?

I am trying to solve a class of problems, which are basically about a solution to a system of non-linear equations subject to the constraint that some subset of solutions must be non-decreasing. I ...
-11
votes
3answers
294 views

A tricky algebraic simplification [closed]

EDIT from the OP: The problem was that I was using a very old version of Mathematica on a friend's computer without realizing it. FullSimplify[] handles it perfectly even on v9. This code produces ...
1
vote
2answers
87 views

Writing a polynomial quotient with a specific denominator

I have a polynomial quotient $$\frac{1-z+z^4}{(1-z)^2}$$ that I want to write in the form $$\frac{g(z)}{(1 - z) (1 - z^4) (1 - z^5) (1 - z^6) (1 - z^7)}.$$ However, every time I try some combination ...
5
votes
1answer
137 views

List of unknowns in a differential equation

I often find myself wanting to see what variables/constants are undefined in a large set of differential equations, is there a function that will do this for me? As an example, for the following ODE ...
16
votes
1answer
201 views

Undocumented fourth parameter of Collect; how long has it been there?

While tinkering with How to get a list of monomials of a polynomial without coefficients? on a whim I tried a fourth argument in Collect and found: ...