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

learn more… | top users | synonyms

4
votes
1answer
204 views

How to check if a given expression is an “explicit algebraic number”?

The documentation for PossibleZeroQ says: With the setting Method...
5
votes
2answers
157 views

How to check an algebraic number for membership in a list

I need to check an algebraic number for membership in a list of algebraic numbers. The numbers can be expressed in different forms (combinations of radicals, Root ...
7
votes
1answer
337 views

Writing an expression as sum of squares of expressions

Suppose we have a symmetric homogeneous polynomial expression $P$ in $X=(x_1,\cdots, x_n)$. I want to check whether there are functions $g(X)$ so that $P$ is of the form $\sum _{1\le i<j\le n} ...
1
vote
3answers
184 views

How to collect/reduce with respect to multiple variables?

I have this code: a == b + c + d - e Is it possible to collect or reduce this expression into this: c + d == a + e - b ...
9
votes
2answers
349 views

InverseSeries of multiple variables and multiple equations

CONTEXT Let us consider a bit of the Universe in which we draw spheres (see a high resolution image here). Astronomers have shown that the density within these spheres could be predicted quite ...
3
votes
3answers
243 views

How to extract phase angle from sinusoid

I'm doing some electric circuit calcualtions and I'm trying to get the phasor representation of some arbitrary function of Sin or Cos. Could be complex like: ...
11
votes
1answer
154 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. ...
7
votes
0answers
95 views

Apart may use Padé method: what's that?

How does Apart work? The page tutorial/SomeNotesOnInternalImplementation#7441 says, "Apart ...
3
votes
0answers
255 views

Solving recursion relations using Mathematica

I want to solve the recursion relation given in equation 2.7(a/b) on page $6$ of this paper. (..the initial seed is $F_1 = G_1 = 1$ and the functions $\alpha$ and $\beta$ are defined on page $5$ in ...
5
votes
1answer
114 views

How to apply tags to expression terms?

I often see on this site and at the mathgroup the repeated questions on how to rearrange expression that Mathematica "likes" to keep in one form, but the user prefers in another. Consider this trivial ...
3
votes
1answer
249 views

Non commutative multiply- expand expression

I began to use Mathematica a few days. My problem is: How to expand expression like $(a+b)*(a+b)$, where this multiplication is non commutative? Mathematica can do this?
5
votes
7answers
654 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] ...
9
votes
1answer
207 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 ...
2
votes
1answer
184 views

Is there any way to force Mathematica to collect a symbol in a polynomial?

Let's say that I have a polynomial like this: a + b + c Is there any way that I can get Mathematica to transform it to: ...
2
votes
2answers
806 views

Defining a non-commutative operator algebra in Mathematica

I am trying to develop a function(s) to do some commutator algebra to compute the enveloping algebra and ideals of a Lie algebra. For example if I have $SU(2)$ algebra generated by $L_i$ ($i=1,2,3$), ...
4
votes
2answers
123 views

Unexpected side effect of removing the Orderless attribute from Times

First I make Times orderless: ClearAttributes[Times, Orderless]; Then I evaluate ...
0
votes
1answer
161 views

Showing steps Mathematica uses for Resolve[ForAll[…]] [duplicate]

I have a quite complicated function of 2 variables: ...
6
votes
6answers
755 views

How to simplify a complicated Sum in terms of power Sums?

For example, I have: $a=\sum _{r=1}^n x_r \left(\left(\sum _{i=1}^n x_i-x_r\right){}^2-\sum _{i=1}^n x_i^2\right)$ ...
21
votes
7answers
803 views

How do I get my equation to have the form $(x-a)^2 + (y-b)^2 + (z-c)^2-d = 0$?

I want Mathematica to express the equation $$-11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2=0$$ in the form $$(x - 1)^2 + (y - 2)^2 + (z - 3)^2 - 25=0$$ How do I tell Mathematica to do that?
3
votes
2answers
231 views

Eliminate several variables between five Conic_section equations

I want to eliminate x1, x2, y1, y2 between these 5 equations. I tried ...
0
votes
0answers
125 views

Need conditions for DSolve

If I have differential equation of fourth order with four solutions $\alpha _1,\alpha _2,-\alpha _1,-\alpha _2 $ where we have appearing the solutions in the form $e^{\text{$i\alpha $}_1 ...
3
votes
3answers
170 views

How can I expand a inequality with Abs

I want Abs[x] + Abs[y] <= 1 to be convert to ...
1
vote
1answer
165 views

How to transform equation

Is there any possible way to write this equation of 4th order as a system of two diff equations of second order with two new variables and to do that automatically? statespace command is transforming ...
0
votes
1answer
542 views

Decoupling system of differential equations

Here I have one task and it is preparation for small exam. I solved it by hand for first case 1), but I need to check it in $Mathematica$ and to try to implement it for both cases 1) and 2) ...
0
votes
1answer
233 views

Hyperbolic numbers and their polar form

How can I implement Hyperbolic numbers in Mathematica? How could I express their polar form? How could I calculate their power?
1
vote
1answer
200 views

Efficient method for factor expressions with square roots

Inspired from this, I tried factor following expressions, Mathematica takes a long time, I couldn't even wait for it to finish. Maple calculating it takes about 5 sec. Can you recommend an efficient ...
12
votes
1answer
405 views

Most efficient way to determine conclusively whether an algebraic number is zero

Let x be an algebraic number of unspecified degree, expressed using arithmetic, rational powers, and algebraic integers (edit: ...
1
vote
1answer
142 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
votes
4answers
1k views

How to get exact roots of this polynomial?

The equation $$ 64x^7 -112x^5 -8x^4 +56x^3 +8x^2 -7x - 1 = 0 $$ has seven solutions $x = 1$, $x = -\dfrac{1}{2}$ and $x = \cos \dfrac{2n\pi}{11}$, where $n$ runs from $1$ to $5$. With ...
5
votes
1answer
180 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 ...
8
votes
1answer
633 views

How do I expand a sum?

I have a problem with Mathematica's symbolic manipulations. As an example, consider the following expression: $$\sum _{i=1}^n -2 x_i \left(-a x_i-b+y_i\right)=0$$ How do I get Mathematica to expand ...
10
votes
3answers
980 views

How can I convert a complex number a+b I to the exponent form A Exp(I phi)?

When I have an expression such as: (1/4 + I/4) ((1 - 2 I) x + Sqrt[3] y) it is hard to get an intuition of the number. So I want to convert it to the complex ...
3
votes
1answer
319 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
144 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
76 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
629 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
377 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
651 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
147 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
67 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
326 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 ...
7
votes
4answers
445 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
159 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
494 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
512 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
373 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
592 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
368 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
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 ...