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

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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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49 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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55 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
251 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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75 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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111 views

Giving hints to Integrate

I working with the integral ...
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87 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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104 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
61 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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33 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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42 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
112 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: ...
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134 views

How to find all roots of a complex number [duplicate]

Finding all roots, and I know there are four f them, of this (1 - i)^(1/4) Not only real, but imaginary as well
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258 views

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

I have a quite complicated function of 2 variables: ...
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1answer
287 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?
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913 views

How to neglect higher power terms in a polynomial expression

I have a polynomial expression of order n (say n=20). F(x)=1+x+x^2+x^3++...x^20. I want to approximate the polynomial for order 3 only. So I need to make the ...
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1answer
64 views

Using Collect with equations

Is it possible to somehow use the expression that Mathematica has collected once the Collect command has been used? What I mean is, I have an expression like this ...
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1answer
99 views

how to permute bit strings and manipulate their elements

I want to write a function(has 2 paremeter, n=range,k=number of 1 digits) which finds all probable combinatorics of arbitrary bit strings and evaluate sum of tensor ...
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1answer
918 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) ...
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1answer
64 views

Algebraic manipulation of closed loop state space system [closed]

I have the following equations $$ \begin{align} x(k+1) &= A x(k) + B \tilde{u}(k) \\ y(k) &= C x(k) + D \tilde{u}(k) \\ w(k+1) &= E w(k) + F \tilde{e}(k) \\ u(k) &= G w(k) + H ...
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2answers
160 views

Expand expression into quotient of negative power series

I have a function T(z) and want to expand it to the following form: At the end I want to have a list of equations, which can calculate a0, a1, a2, b0, b1 and b2 with different values of h1, h2, ...
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1answer
182 views

Impose an specific Trigonometric expansion with TrigExpand

Is there a way to impose in mathematica an specific trigonometric expansion with TrigExpand? I have various double-angle expressions for cosine and sine in my ...
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1answer
134 views

Replacement rules in combination with pure functions to make a change of variables

I have defined my function in this way w = f[r,Θ] ; After some calculations i obtained my results with respect to the previous function. For instance: ...
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1answer
87 views

Manipulating formal vectors

I want to work with a formal vector space spanned by integer triplets: $$ V=\text{span}\{(a,b,c):a,b,c\in\mathbb N^3\}, $$ such that Mathematica can do additions for me. For example,if I input ...
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119 views

Why do I get a different answer from the use of TrigExpand?

This is an old post but I get two different answers from Mathematica 9.0.1.0 ...
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114 views

Rearranging 5 equations

I am trying to rearrange 5 equations in terms of 5 variables. I have the equations for y1, y2, ...
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92 views

Using one complicated equation to reduce another

(Relative noob here so don't assume much!) I need to use a vector equation (with $N-1$ entries) in the general form $y_j(x_{i,j},x_{i,j+1},x_{i,j-1})=0, i=1...3, j=1...N-1; x_{i,0}=x_{i,N}=0$, ...
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55 views

Ordering oscillators with negative powers: Infinite loops

I have been working with ordering of oscillators for example $[a,a^\dagger]=1$ and I have a fairly stable code. I have needed to use inverse oscillators for example expressions like $a^m ...
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34 views

Solving an algebraic equation with one or more constraints? [duplicate]

Just as a simple example, say I wanted to solve Sin[x] == a for x with the constraints -1<=a<=1 and 0 < x < Pi. Is there any way to do this?
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96 views

Unexpected result from InverseFunction

Given the following two equivalent inverse functions, why does one simplify (using inverse functions that are acceptable to me) and the other doesn't? Is there an assumption or setting I can give ...
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1answer
455 views

Solving Det[matrix] == 0 with an 8 x 8 matrix [closed]

I want to solve the equation Det[matrix] == 0 which came from the consistency of solutions of a set of 8 equations. This matrix has two constants λ and μ and two variables $P$ and $q$. I want to get ...