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

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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 ...
5
votes
2answers
144 views

Pull out scalars from NonCommutativeMultiply in commutator of SU2 spin algebra

I am trying to work on spin chains in Mathematica. That is, N spin-1/2 on a one-dimensional lattice with periodic boundary condition (N+1=1). I need therefore the SU2 spin algebra $S_z, S_+, S_-$ with ...
5
votes
2answers
163 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 ...
5
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1answer
210 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 ...
5
votes
1answer
139 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 ...
4
votes
4answers
262 views

How to compute MIN$(A(x), B(x))$

I have two polynomials: $\;A(x) = \sum a_i\;x^i$, $\quad B(x) = \sum b_i\;x^i$. Given $A(x)$, $B(x)$, I want to compute $\;C(x) = $MIN$(A(x), B(x)) = c_i\;x^i$ where $c_i = $MIN$(a_i, b_i)$. How can ...
4
votes
2answers
341 views

How can I simplify $\log(512)$ to $9\log(2)$?

Can you explain me about the result of Integrate. ...
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5answers
225 views

Extracting Coefficients from a List of Sines

I want to extract the coefficients from the following list: list={16.2219 Sin[16.2219 t], 6.60924 Sin[6.60924 t], 13.927 Sin[ 13.927 t], 2.91309 Sin[2.91309 t]} ...
4
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2answers
144 views

Unexpected side effect of removing the Orderless attribute from Times

First I make Times orderless: ClearAttributes[Times, Orderless]; Then I evaluate ...
4
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2answers
362 views

Force a negative square root to be interpreted as an I

I have expressions like $$\sqrt{-\sqrt{1+x^2}} $$ how can I force mathematica to systematically rewrite this as $$i(1+x^2)^{1/4} \quad ? $$
4
votes
2answers
162 views

HornerForm of polynomials in terms of E^(i x)

I want to know how to get the HornerForm of the following expression in terms of E^(I x): ...
4
votes
1answer
703 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
2answers
896 views

expanding a polynomial and collecting coefficients

I'm trying to expand the following polynomial ...
4
votes
1answer
151 views

Infinite expression encountered when simplifying ArcTan sums although the result is finite

If I attempt to simplify the sum ArcTan[1/x] + ArcTan[x] with ArcTan[ Simplify[ TrigExpand[ Tan[ ArcTan[1/x] + ArcTan[x]]]]] ...
4
votes
1answer
241 views

Plot a cone in spherical co-ordinates

As we all know in spherical coordinates a function phi = π/3 gives us a cone. The cone makes an angle of π/3 with the imagined ...
4
votes
1answer
135 views

Generate expressions equivalent to rooted trees

I would like to know how to generate all rooted trees on $n$ vertices using Mathematica? More precisely, I am interested in generating algebraic expressions equivalent to rooted trees and constructed ...
4
votes
1answer
475 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
829 views

What do the hashtags represent in the result of Solve, and how should I use them? [duplicate]

There is a function that I'm trying to get the inverse of. My function is a simple polynomial: Tn[T_] := 4/9 T^3/Tc^2 + 5/9 T Now I tried to find ...
4
votes
1answer
265 views

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

The documentation for PossibleZeroQ says: With the setting Method...
4
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2answers
2k 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
1answer
176 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 ...
4
votes
0answers
86 views

Transform an expression to remove the singularity

I have the expression Sin[c x]/c. Clearly it is undefined at $c=0$, but that is merely a removable singularity, since $$\frac{\sin(cx)}c=x\frac{\sin(cx)}{cx}= ...
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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) : ...
3
votes
3answers
581 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 ...
3
votes
2answers
210 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
3answers
211 views

Speed up Eliminate

I have a set of trig equations, c1,c2,c3 are constants, I excepted the result is c1 c2 c3 r^2 + (c1^2 + c2^2 + c3^2 - 1) r + c1 c2 c3 == 0 but following code ...
3
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3answers
213 views

How can I expand a inequality with Abs

I want Abs[x] + Abs[y] <= 1 to be convert to ...
3
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1answer
85 views

Pulling powers to the outside of expressions (inverting PowerExpand)

Is there something like an inverse of PowerExpand that pulls powers to the outside of expressions: $$ x^2 y^2 \leadsto (x y)^2 \\ x^2/y^2 \leadsto (x/y)^2 $$ I ...
3
votes
2answers
144 views

Exploiting a relation among constants

Say I have two arbitrary real constants $p,q$ that satisfy $p^2+q^2=1$. Is there any way to easily declare this relation in Mathematica? Edit More specifically I have this (among others) expression: ...
3
votes
3answers
332 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: ...
3
votes
1answer
554 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?
3
votes
2answers
242 views

Eliminate several variables between five Conic_section equations

I want to eliminate x1, x2, y1, y2 between these 5 equations. I tried ...
3
votes
1answer
472 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 ...
3
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1answer
254 views
3
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1answer
167 views

Implementing new algebra for list-like objects

I would like to implement an algebra (addition, multiplication, etc.) for what is called "truncated power series" (TPSA) (Differential Algebraic description of beam dynamics). . These 'objects' (sets ...
3
votes
1answer
567 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
1answer
58 views

How to pick out terms in a linear equation with a positive coefficient?

Basically I have a really large output which looks like a long linear equation $AAA-BAA-CAA+DAA+...-ZZZ$ And I only am concerned about those terms that have a positive coefficient (i.e. a plus in ...
3
votes
1answer
75 views

How to order lexicographically the monomers of a parametrized polynomial?

I want to order lexicographically the monomials in a "parametrized polynomial", i.e. polynomials whose "symbolic bits" may be either "variables" or "parameters". For example: ...
3
votes
0answers
133 views

Do a gauge transformation for a Chern-Simons theory?

Suppose we have the following Lagrangian density: $$ L=\epsilon^{\mu\nu\rho}\big(\sum_a A^a_{\mu}(x) \partial_\nu A^a_{\rho}(x)-\sum_{a,b,c}\frac{1}{3} f^{bca} A^a_{\mu}(x) A^b_{\nu}(x) ...
3
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0answers
354 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 ...
3
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0answers
159 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: ...
2
votes
3answers
277 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 ...
2
votes
2answers
589 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
261 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 ...
2
votes
2answers
397 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 ...
2
votes
3answers
220 views

How to obtain non-trivial solution of equal ratios

How can I obtain a non-trivial solution of the following: $$\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}$$ The answer is $a=b=c=1$.
2
votes
2answers
157 views

Trigonometry expansion of a product

The following command does what I want: ...
2
votes
2answers
124 views

Choosing a branch of the square root when performing a series expansion

I have the following problem. Consider expression f=Sqrt[(x-2y)^2] There is an obvious ambiguity in the definition of f ...
2
votes
1answer
239 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
3answers
110 views

How to make $a1**a2** \cdots **an=0$ for a given $n$?

In order to optimize my computation and save memory, I'd like to modify NonCommutativeMultiply so that for a given $n$ one has $a1**a2** \cdots **an=0$ for any $a1, a2, \ldots, an$. To make it ...