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

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1answer
122 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
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2answers
126 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 ...
6
votes
3answers
166 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 ...
-11
votes
3answers
301 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
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1answer
69 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. ...
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2answers
121 views

Rearranging a simple algebraic equation

Suppose I have a simple algebraic equation like: ChebyshevT[4, p] == 0 1 - 8 p^2 + 8 p^4 == 0 and I want to solve for the ...
3
votes
1answer
177 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
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1answer
62 views

problem with Collect when using indexed variables [closed]

I'm not getting the expected output when I use Collect with indexed variables. ...
1
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1answer
105 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: ...
6
votes
3answers
360 views

How to do algebra on unevaluated integrals?

I am working with functions calculated from a set of general basis functions. ...
4
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1answer
128 views

How to collect terms with z-derivative?

my equations are very long (several pages). Here I will provide simple example: ...
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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: ...
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1answer
39 views

How can I rewrite this expression in terms of V_o/V_s?

$$\frac{V_o-\frac{A \left(R_{\text{int}} \left(V_s-V_1\right)\right)}{R_{\text{int}}+R_s}}{R_o}+\frac{V_o}{R_L}+\frac{V_o-V_1}{R_1}=\frac{V_1-V_s}{R_{\text{int}}+R_s}+\frac{V_1-V_o}{R_1}+\frac{V_1}{...
1
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2answers
60 views
1
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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 ...
9
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1answer
155 views

Apart may use Padé method: what's that?

How does Apart work? The page tutorial/SomeNotesOnInternalImplementation#7441 says, "Apart ...
1
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2answers
87 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 ...
0
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1answer
158 views

Rearranging 5 equations

I am trying to rearrange 5 equations in terms of 5 variables. I have the equations for y1, y2, ...
16
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1answer
203 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: ...
2
votes
1answer
157 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 ...
3
votes
1answer
280 views

Multivariate resultant in Mathematica?

Is there any command in Mathematica 7 which can compute the (McCaulay) resultant of a parametric system of multivariate polynomial equations? In fact, it would be great if there is also a way to ...
11
votes
5answers
2k 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 ...
8
votes
1answer
237 views

Speed up MinimalPolynomial

My Mathematica code runs slowly MinimalPolynomial[Sqrt[2] + Sqrt[3]+ Sqrt[5]+ Sqrt[7]+ Sqrt[11]+ Sqrt[13], x] runs slowly, but the Maple version ...
5
votes
1answer
137 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 ...
1
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1answer
84 views

How to reduce trigonometric expressions under special conditions

For the following problems I used "FullSimplify" and "TrigReduce" but I manage to reduce more by hand. ...
13
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1answer
336 views

ToNumberField won't recognize Root as an explicit algebraic number

Bug fixed in 10.0.0 In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an ...
8
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2answers
145 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 ...
14
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4answers
3k 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 ...
5
votes
1answer
240 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 ...
5
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1answer
81 views

Is there a way to Collect[] for more than one symbol in Mathematica 10.0?

This question has already been asked three years ago (Is there a way to Collect[] for more than one symbol?) but I'm not allowed to comment since I'm new at Mathematica StackExchange. The first ...
1
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1answer
105 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
98 views

Factor a specific sub-polynomial?

Consider the following example for a polynomial in several variables: ...
13
votes
4answers
707 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 $f$, $f(\varepsilon)=f^\prime(0)\...
0
votes
1answer
64 views

How can I manipulate a long expression to order it by factors/derivatives of a particular function?

I have a Mathematica notebook that generates a linear expression involving derivatives of a given variable. Expanded (and simplified for our purposes), it looks something like this: \begin{equation} ...
14
votes
3answers
3k views

How can I convert a complex number into an exponent form

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 ...
13
votes
2answers
512 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 ...
1
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1answer
170 views

Handling minus signs in mathematica

I am doing symbolic manipulations in Mathematica where expressions like $(-1)^{1/3}\left(-\log z \right)^{2/3}+\log z^{2/3}$ We see that clearly this expression is zero. But Mathematica does not ...
1
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1answer
52 views

2D plot using Manipulate command [closed]

Can anyone tell me what the problem is with the following code: y[x_ a_] := Sin[x (1 + a x)] Manipulate[Plot[y[x a], {x, 0, 6}], {a, 0, 2}] However, the ...
4
votes
1answer
150 views

Collect without grouping terms

The built-in function Collect, when applied to more than one variable, will group expressions by the first variable, as here: ...
0
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1answer
51 views

Grouping by multiple coefficients

Good day! I have an output equation that has a very large amount of coeff. b(x,y), like so: ...
5
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1answer
73 views

Ordering in noncommutative multiply

I have an expression like s ** p1 ** p1 ** p2 - s ** p1 ** p2 ** p1 Which should be zero because the commutator between p1 ...
2
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1answer
126 views

Moving certain variables to one side of the equation [duplicate]

I am having trouble moving certain variables from one side of the equation to the other. For example, if i want to solve for x1: ...
13
votes
2answers
294 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}= x\...
1
vote
1answer
102 views

How do I find the constant term of a multivariate polynomial, when (x^0)(y^0)?

So let's say f[x_,y_]:=(2x+2y+1)^2, when I type Coefficient[f[x,y],x y] I recieve 8. But what can I input to recieve 1, when (x^...
12
votes
9answers
2k 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] ...
18
votes
1answer
352 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 <...
1
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0answers
58 views

Abstract Vectors [duplicate]

Is there a way to deal with abstract vectors in the following sense: Say I have a function f[y]. Now I want to evaluate ...
2
votes
1answer
73 views

Algebraic Manipulations with Indices

I am absolutely new to Mathematica, but I've heard it is a pretty powerful tool for symbolic calculations. My problem (stated generally): I have three dimensional array. I define a symbolic operator ...
0
votes
3answers
63 views

Simplifying Terms in a Matrix

Given the following 3 matrices: M1=1/3*{{1,1,1},{1,α,α^2},{1,α^2,α]}} Z1={{Z+Zg,Zg,Zg},{Zg,Z+Zg,Zg},{Zg,Zg,Z+Zg}} M2={{1,1,1},{1,α^2,α},{1,α,α^2}} where alpha ...
5
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1answer
147 views

Working with quantum mechanics spins

I've written the following code for simple quantum mechanics operators on spin states: It seems to work, but the output could be better - how do I let Mathematics know that $0**\ 0==0$, and can I ...