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

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1
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1answer
153 views

How do I expand a sum (again)? [duplicate]

Possible Duplicate: How do I expand a sum? How do I expand an equation in the given form: $\sum _{i=1}^n -2 x_i \left(-a x_i-b+y_i\right)=0$ into this form: $-\sum _{i=1}^n x_i y_i +a ...
5
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1answer
193 views

Numbered symbols

I work with an exterior algebra over $R^n$. I have the basis $\{1,\omega_i\}_{i=1}^n$ in this algebra, and my differential operator is defined as $$d\omega_k=\sum_{i>j>0,i+j=k} (i-j)w_i\wedge ...
3
votes
1answer
371 views

How can I express an algebraic expression as a product?

I have a simply expression that I can see that I can express as a product. ...
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: ...
5
votes
3answers
666 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?
4
votes
5answers
798 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 ...
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 ...
6
votes
3answers
155 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
372 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 ...
8
votes
4answers
461 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
179 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: ...
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 ...
17
votes
4answers
518 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
627 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 - ...
4
votes
1answer
406 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 ...
2
votes
3answers
260 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 ...
3
votes
3answers
424 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 ...
4
votes
1answer
172 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 ...
6
votes
3answers
543 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 ...
7
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1answer
274 views

RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
8
votes
4answers
528 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 ...
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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) : ...
2
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2answers
199 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: ...
4
votes
2answers
679 views

expanding a polynomial and collecting coefficients

I'm trying to expand the following polynomial ...
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., ...
11
votes
4answers
700 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 ...
2
votes
2answers
497 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
225 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
459 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
442 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
560 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\\ ...
9
votes
2answers
789 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 ...