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

learn more… | top users | synonyms

3
votes
0answers
150 views

Cyclic Noncommutative Multiplication

I work with traces of long matrix products and I want mathematica to employ the cyclicity when simplifying. I use this redefinition of the non-commutative multiplication: ...
1
vote
1answer
77 views

Differing behaviour of GeneratingFunction with different numbers of parameters

When given a single variable sequence, GeneratingFunction is automatically expressed in the most "direct form", for example, ...
5
votes
3answers
684 views

Square both sides of an equation?

Can I define an equation (for example, x+1 == y^2 + 2), and tell Mathematica to square both sides? If not, what is an equivalent way to achieve this?
2
votes
2answers
382 views

Eigensystem, Eigenvalue doesn't output nonreal eigenvalues

Basically I have a matrix and when I used either Eigenvalue or Eigensystem, it doesn't output nonreal eigenvalues, instead it ...
4
votes
5answers
865 views

How to group certain symbolic expressions?

For example, I have the following expression : A( 2 x1 + B(y1 + y2) + 2 x2 ) How do I make the output look like this (grouping ...
6
votes
3answers
157 views

Is there any way to collect only variables with a specific power?

Suppose I've got this: In[13]:= Expand[(a + b) (b + c) (c + a)] Out[13]= a^2 b + a b^2 + a^2 c + 2 a b c + b^2 c + a c^2 + b c^2 And I want to collect only ...
2
votes
0answers
68 views

How to expand terms within an integral? [duplicate]

Possible Duplicate: Why aren’t these additions of integrals and summations equal? I am trying to expand all the terms in a sum in order to apply assignment rules later, but can't figure out ...
3
votes
1answer
382 views

Showing the terms in a partial sum?

I am trying to get s[n_]:=Sum[1/2^k,{k,1,n}] to show me the actual terms involved in the $n$th partial sum and not just the sum itself. I've tried ...
9
votes
4answers
463 views

How to implement dual numbers in Mathematica?

I wonder how can I implement dual numbers in Mathematica, so that all functions work well with them (as with complex numbers). Particularly, for each function $f$, ...
5
votes
2answers
182 views

How to protect pattern or subexpression when distributing / expanding expression?

I've got an expression like expr = (1-x)(a+b) that I would like to distribute / expand while keeping factors of (1-x) intact, ...
8
votes
3answers
495 views

How can I convert x^2 to x*x?

When I try the following code: a b^2 c /. b c -> e Mathematica gives me: a b^2 c but what I want is: ...
17
votes
4answers
520 views

How do I introduce a new variable in a trigonometric equation?

I have the trigonometric equation \begin{equation*} \sin^8 x + 2\cos^8 x -\dfrac{1}{2}\cos^2 2x + 4\sin^2 x= 0. \end{equation*} By putting $t = \cos 2x$, I have \begin{equation*} \dfrac{3}{16} t^4+ ...
4
votes
1answer
418 views

Move variable to one side of the equation

Say if I have a formula like so: a1*a2*a3^(a4 + 1)*(1 - E^(a5*a6/a3^a4/a2)) == 0 How do I move a3 to the right? I've tried to follow other examples here on stack ...
4
votes
1answer
646 views

Reduce an equation by putting a new variable

I have the following equation given: $$ (26-x)\cdot\sqrt{5x-1} -(13x+14)\cdot\sqrt{5-2x} + 12\sqrt{(5x-1)\cdot(5-2x) }= 18x+32. $$ In order to solve it, I want to substitute $t = \sqrt{5x - ...
3
votes
3answers
441 views

Limiting form of a polynomial expression

When simplifying an expression by hand, a trick that is often used is to remove terms that are lower powers of the independent variable, for instance, as $x \rightarrow \infty$, $x^2 + x$ becomes ...
8
votes
3answers
1k views

How can I rationalize the denominator of an expression?

Mathematica doesn't rationalize the denominator automatically, and I haven't found anything in the documentation about it. But I found an old post on MathGroup, which proposes a solution using ...
4
votes
1answer
175 views

Finding mappings between expressions

Suppose we have an expression of the form: $j=\frac{A\left(t\right)}{B\left(t\right)}=\frac{C\left(s\right)}{D\left(s\right)}$ That is, $j$ can be expressed either as a function of $t$, or as a ...
2
votes
3answers
263 views

Is it possible to use Composition for polynomial composition?

I want to do this: $P = (x^3+x)$ $Q = (x^2+1)$ $P \circ Q = P \circ (x^2+1) = (x^2+1)^3+(x^2+1) = x^6+3x^4+4x^2+2$ I used Composition for testing if that could ...
7
votes
1answer
280 views

RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
8
votes
4answers
552 views

“Evaluating” polynomials of functions (Symbols)

I want to implement the following type evaluation symbolically $$(f^2g + fg + g)(x) \to f(x)^2 g(x) + f(x) g(x) + g(x)$$ In general, on left hand side there is a polynomial in an arbitrary number of ...
6
votes
3answers
550 views

What function can I use to evaluate $(x+y)^2$ to $x^2 + 2xy + y^2$?

What function can I use to evaluate $(x+y)^2$ to $x^2 + 2xy + y^2$? I want to evaluate It and I've tried to use the most obvious way: simply typing and evaluating $(x+y)^2$, But it gives me only ...
3
votes
2answers
202 views

What does MinimalPolynomial do?

suppose $x^5-x-1=0$, $y^7-y-1=0$ and $z=x+y$. I want to find a minimal polynomial expression of $z$, such that $p(z)=0$, and the code can be written like this: ...
3
votes
2answers
3k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
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 ...
4
votes
2answers
700 views

expanding a polynomial and collecting coefficients

I'm trying to expand the following polynomial ...
7
votes
4answers
2k views

Checking if two trigonometric expressions are equal

Say I have two trigonometric expressions which are a bit complicated. Is there a quick way to check if they reduce to the same thing (that they are equal) using Mathematica? I was solving this: $y'' ...
7
votes
4answers
421 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 ...
2
votes
2answers
508 views

How do I make Mathematica understand roots of unity?

Try the following: z = Exp[2 \[Pi] I / 5] Z = { { z, 1 }, { 0, 1/z } } Simplify[MatrixPower[Z, 5]] //MatrixForm Of course, this should return a 2 x 2 identity ...
2
votes
4answers
232 views

I need to move all the variables(x,y,z) to one side of an equality for the equation of a plane

I have 5(x-1)-(y+1)-(z+1)==0. If I use FullSimplify on it it returns 5x==7+x+y. This is not ...
7
votes
2answers
469 views

Manipulating an equation into standard quadratic form?

Say I have an equation of the form $$u s + \frac{1}{v} + \frac{1}{p s + q} = 0$$ (or any form that can be written as a standard quadratic, really, the above form is just an example; they'll all be ...
9
votes
2answers
453 views

Shaping/simplifying equations in a certain way

A problem I am occasionally facing is to simplify an equation not to it's shortest form but to a form that is simple by other means. Often, this is grouping the term according to certain functions, ...
15
votes
2answers
573 views

How to define a non-standard algebra in Mathematica?

I want to define an algebra, where there are three elements: 0, 1 and $\infty$ and two operations, addition and multiplication defined, both commutative: $$\begin{align*} 0+0&=0\\ 0+1&=1\\ ...
12
votes
4answers
2k views

Is it possible to have Mathematica move all terms to one side of an equation?

I have an inequality expression that I would like to express in terms of the relation of the parameters to zero. More simply, I want to have mathematica move all the terms to one side of the ...
10
votes
2answers
2k views

Why doesn't Mathematica expand Cos[x]^3 Sin[x]^2?

I found some examples of Mathematica's commands usage in an old manual but the program gives me different result than expected ...
32
votes
6answers
4k 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 ...
13
votes
6answers
2k views

Replacing composite variables by a single variable

To replace a single variable by another variable, one can simply use the the replace all (/.) operator (e.g., ...
9
votes
2answers
808 views

Expand modulus squared

Is it possible to make a function in Mathematica that expands expressions of the form $$|z + w|^2 = |z|^2 + 2\text{Re} \overline{z}w + |w|^2?$$ Preferably it should also be able to handle things ...
12
votes
7answers
2k 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 ...
12
votes
4answers
741 views

Is there a way to Collect[] for more than one symbol?

Oftentimes you find yourself looking for polynomials in multiple variables. Consider the following expression: a(x - y)^3 + b(x - y) + c(x - y) + d as you can ...