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

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93 views

How to make algebraic substitutions?

I would like to simplify complicated expressions by defining some variable that is a combination of other variables that appear in the expression, but without eliminating the original variables. As a ...
3
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2answers
79 views

Factor a specific sub-polynomial?

Consider the following example for a polynomial in several variables: ...
3
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3answers
258 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
118 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
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2answers
156 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
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3answers
438 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
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1answer
255 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 ...
3
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2answers
257 views

Eliminate several variables between five Conic_section equations

I want to eliminate x1, x2, y1, y2 between these 5 equations. I tried ...
3
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1answer
189 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 ...
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1answer
1k 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
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1answer
95 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
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4answers
126 views

How can I group constants/parameters using Mathematica?

I am trying to solve a problem which may seem quite simple, although I have been unable to find any solution in the documentation or discussion forums. I am not a mathematician, so please bare with ...
3
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1answer
123 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 ...
3
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1answer
66 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
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0answers
186 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
576 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
171 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
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3answers
294 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
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4answers
303 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
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2answers
440 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
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3answers
309 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
1answer
174 views

Factoring terms out of a polynomial

I don't do much algebra in Mathematica and was surprised to discover, while attempting to answer this question, that I had no idea how to factor out an expression from a polynomial. The question was, ...
2
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2answers
174 views

Trigonometry expansion of a product

The following command does what I want: ...
2
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1answer
117 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 ...
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2answers
183 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 ...
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1answer
296 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
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1answer
80 views

How to distribute PermutationProduct over the sum

Assuming I have two elements of the permutation group algebra $a_1$, $a_2$ such that $a_i=\sum_{p\in S_n}\alpha_pp$, I want to define a linear product $\odot$ that distributes over the sum and pulls ...
2
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1answer
362 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 ...
2
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3answers
123 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 ...
2
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1answer
252 views

Expressing a matrix in terms of four basis matrices

I have five matrices and I want to represent one in the basis of other four. So how do I find the value of coefficients? For example, if the matrices are I1, ...
2
votes
1answer
70 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 ...
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2answers
142 views

Simplification with assumptions

I'm trying to make Mathematica do some simplifications for me. I have the expression ((1 + s[1]) (-1 + s[2]) )/(-1 + s[1] s[2]) and want to simplify this with ...
2
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2answers
349 views

Pulling out common terms when simplifying complicated equations

I have a complicated expression where common terms are apparent but Simplify[] and FullSimplify[] don't appear able, even with plenty of assumptions added, to reduce down to a simpler form with common ...
2
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0answers
53 views

Changing variables in a series expansion

I want to compute the Taylor expansion of some pure function f[x_], but then perform a change of variables in the resulting expression. So, for example, the output ...
2
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1answer
102 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: ...
2
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0answers
71 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 ...
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1answer
111 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 ...
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4answers
106 views

How find constant term of quadratic with square already completed?

Suppose I have a quadratic polynomial in two variables x and y in which the squares with respect to ...
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1answer
153 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 ...
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1answer
128 views

Mathematica spitting code back when using Resolve over a large range of interest

I've just started using Mathematica and have encountered my first issue. Below are two commands which only differ in the range of values I am asking Mathematica to check. The first works fine, but the ...
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1answer
138 views

What is the inside? [closed]

What is the inside of the Mathematica command, solve, for a system of equations like the following? $$\eqalign{ (x +2\phantom{3} z)^2 + (y +\phantom{3} w)^2 &= 52\cr (x + 30z)^2 + (y + 3w)^2 ...
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3answers
102 views

Coefficient and Addition Formula

If I type: Coefficient[Cos[x + b], Cos[x]] I get zero. But I would like Mathematica to apply: $$\cos(x+b)=\cos x\cos b-\sin x\sin b$$ Therefore the ...
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1answer
106 views

If statement and elements of an imported data

I import a data file: SetDirectory["C:\\Users\\SE7EN\\Desktop\\mathematica\\test"]; dd = Import["data.dat", "Table"] Out[2] = {{1}, {2}, {3}, {4}, {5}, {6}, {7}} ...
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3answers
275 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 ...
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2answers
77 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 ...
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1answer
249 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 ...
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2answers
47 views

How to reorder and combine terms in a polynomial with multi-variables?

I have a polynomial with the coefficients of {a1, b1, b2} ...
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1answer
91 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 ...
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1answer
75 views

Simplification of algebraic expression

I found an entry of a matrix from two different methods using mathematica. Which are given as; g/(Sqrt[2] Sqrt[1 + g^2 - Sqrt[1 + g^2]]) and ...