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

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2
votes
1answer
69 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 ...
1
vote
2answers
44 views

expressing a rising factorial as a polynomial

I have an equation in $x$ as follows: $f(x)=\prod_{j=0}^{k}(j+x)=x.(1+x).(2+x)\cdots.(k+x)$ 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 the ...
3
votes
0answers
31 views
2
votes
0answers
43 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
51 views

Collecting the Log Problem

I have been having tremendous success with my students due to the following idea: ...
1
vote
1answer
61 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
42 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
75 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
78 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
1
vote
1answer
48 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
55 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 ...
2
votes
1answer
66 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
56 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
42 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
123 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
118 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
226 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
183 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
113 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
75 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
43 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
114 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 ...
5
votes
3answers
162 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
155 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
89 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
107 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
38 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
55 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
289 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
85 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
135 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
199 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: ...
5
votes
1answer
231 views

Distribute transpose on matrix multiplication

I need to do the following: Transpose[A.(B+C)]=Transpose[B].Transpose[A]+Transpose[C].Transpose[A] How should I do this in mathematica? So far mathematica does ...
8
votes
2answers
142 views

How to sort arguments of Times in nonstandard order?

Is there an elegant way to sort the arguments of Times in e.g. TraditionalForm so that factors go to the front and state ...
1
vote
1answer
102 views

Min function for functions f1, f2, [closed]

There are several "min" functions in Mathematica. In the "Numerical" category, there is a "Min" function that works on a numerical list. Then there's MinValue for finding the minimum of a whole ...
3
votes
2answers
90 views

Factor a specific sub-polynomial?

Consider the following example for a polynomial in several variables: ...
2
votes
1answer
136 views

How to convert a rational parametric plane curve into implicit form?

This problem is generated from another Green's theorem related question of mine. And here is a forward of the same problem in math.stackexchange. The original equation of the plane curve is not in ...