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

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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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5answers
132 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
119 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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1answer
147 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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1answer
168 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
129 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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3answers
116 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
119 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
285 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
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 ...
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1answer
264 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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1answer
62 views

Working with Function Domain

Consider $f(x)=x^2+1$ and $g(x)=\sqrt{x-1}$. Note that $(f\circ g)(x)=x$ and this checks in Mathematica. ...
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1answer
95 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: ...
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2answers
56 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
100 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
76 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 ...
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1answer
193 views

How to get Coefficient List from an expression with various variables

consider following expression: ...
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2answers
99 views

How to get a rule for, e.g., (x + y) to apply to (-x - y), etc.?

For example, the substitution (x + y) -> s fails here: In[1]:= (-x - y) /. (x + y) -> s Out[1]= -x - y Of course, I ...
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1answer
68 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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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}} ...
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1answer
82 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. ...
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1answer
207 views

Forcing solutions to avoid Root[]

I'm solving a system of ordinary non-homogeneous differential equations (4 equations). The solutions will include some algebraic equations solutions as known from text books due to the use of an eigen ...
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1answer
108 views

Solving equations using algebra [duplicate]

Has anyone ever solved an equation for students using algebraic steps? For example, you start with the equation. 2x+3 = 5 Then you show subtracting 3 from both ...
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1answer
73 views

I need to move X to right side without solving or simplifying anything else

I need to manipulate this equation where x is on the left side of the equation. I will be using this in excel and all other numbers will actually be referencing cells so I need x moved to the right ...
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2answers
155 views

Simplifying an expression given a known variable relation

I am wondering if there is a way to simplify an algebraic expression given a known variable equation using Mathematica. For instance, I wish to simplify an expression for the heat change in a process: ...
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1answer
133 views

Collect powers of variables and integers separately?

Let expr contain a sum of powers of x with some coefficients ci. The exponents of ...
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1answer
55 views

PiecewiseExpand doesn't take all kind of assumptions

Running PiecewiseExpand[expr, assum] does not work with all kind of assumptions. For example, the following line will not split the expression with absolute values in the chambers, considering m1=m2. ...
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2answers
100 views

Grouping constants in expressions

Starting from the general expression: i A(a x + b y + c z + ...) + j B(a' x + b' y + c' z + ...) + k C(a'' x +b'' y + c'' z + ...) I'd like to rearrange it to ...
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1answer
97 views

How to transform the polynomial in this way?

I have two functions f and g and a polynomial ...
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1answer
312 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 ...
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1answer
43 views

Rearrange an expression according to known items

I have this expresion: $\qquad q_{aft}=-i\,f \left(a_2\right){}^{\dagger }+i\,f \left(a_2\right){}^{\dagger }-\left(a_1\right){}^{\dagger }-a_1$ Defining $\qquad q_{0_1}=a_1+(a_1)^\dagger$ and ...
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1answer
77 views

Deriving the Fourier Coefficients Formulas with a Manual Procedure

I already know that there are built-in functions to compute the Fourier coefficients but I want to derive their formulas manually. In fact, I want to obtain the final well-known formulas for the ...
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1answer
104 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 ...
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1answer
138 views

How to factorise a variable out of an indefinite sum?

(I should start by saying I'm a total beginner with Mathematica, so if the answer needs code I'll need it spelled out quite clearly, the learning curve for this is proving steep!) Basically what I am ...
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1answer
126 views

How accurate is Collect?

Background: I am trying to compute the Lyapunov exponent for the logistic map given by \begin{equation*} x_{n+1}=F(x_n)=ax_n(1-x_n) \end{equation*} The formula for the Lyapunov exponent for a given ...
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1answer
142 views

Problem about Solve

See this example : ...
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1answer
78 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, ...
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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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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 ...
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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 ...
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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 ...
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0answers
518 views

Solving Symbolically Equations with Vectors and Matrices

I want to solve equations with vector variables and vector/matrix parameters symbolically. As a basic example I would like to be able to solve something like $[I-aG]x=b$ where $a,b \in \mathbb{R}^l$ ...
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0answers
94 views

Use of Mathematica to put equation into vector form

Is there a way to put the following equation of a line into vector form using Mathematica (or a Mathematical package)? $\displaystyle ...
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0answers
117 views

Giving hints to Integrate

I working with the integral ...
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0answers
147 views

How to make noncommutative multiplication agree with commutative multiplication

I need a noncommutative multiplication that is Associative Distributive $A**0=0$, $A**1=A$ Agrees with the commutative multiplication ($A**(k B)=(k A)**B=k (A**B)$) I have found a code ...
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0answers
117 views

Define inverse for the custom operator

I want to define simple matrix algebra (inspired by the following posts: Block Matrix Algebra with Mathematica ; How to define custom operators ). I assume the funtion ...
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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 ...
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1answer
62 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} ...
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1answer
50 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: ...
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2answers
119 views

Collect is not giving me the result I expect

When I evaluate Collect[(a ((G m ω)/c^3)^(1/2) + b ((G m ω)/c^3)^(1/2)), c] I get this: ...