Questions tagged [algebraic-manipulation]

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

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How can I check if a function can be written as $a * \sin (b * x + c) + d$?

I want to write a function that takes another function, say $f(x)$ and a variable $x$ as input and return True it this function can be written in the form ...
29 views

Collect ignoring negative exponential

I have the expression 1 + Exp[-2 x] (-1 - 2 x (1 + x)) I used Expand to get the x's to multiply within the parentheses, this ...
106 views

Generating an efficient way to compute einsum?

Given an einsum like below, how could I generate an efficient computation graph for it? $$X_{ik} M_{ij}M_{kl} X_{jl}$$ The indices range from $1$ to $d$ and the goal is to minimize computation time ...
65 views

Generating summation formulas for factorized 4th moments

I'm interested in getting summation formulas for the following expression, in Einstein summation notation, with indices ranging from $1$ to $d$ $$c=X_{ik}M_{ijkl}X_{jl}$$ Here $M_{ijkl}$ is ...
34 views

Einstein summation? [duplicate]

Is there something to help me do Einstein summations in Mathematica? I found a couple of Mathematica packages to do this, but not sure how out of date they are. In Python-land you can do things like <...
81 views

Is it possible to make Decompose work with coefficients containing radicals?

It appears that Decompose works reliably only on polynomials with integer coefficients, although it seems to be not mentioned in the docs. Can I make it work (or ...
47 views

How to replace a sub-expression when it implicitly exists in an expression

In order to make my question clear, I would like to use a simple expression as an toy example. Suppose we have an expression, which is, f = a + 2*b + c Now I ...
36 views

Assuming x real, simplifying or refining Im[1/(x+i)] doesn't yield anything

I think it is straightforward from the title, Simplify[Im[1/(x+I)], x > 0] spits out, Im[1/(x+I)] while I would have ...
186 views

Eigenvectors in the limit $\mu\rightarrow 0$ are not the same as eigenvectors when setting $\mu=0$ from the beginning

I would like to find the eigenvectors of a matrix and see what the eigenvectors look like in the limit of $\mu\rightarrow 0$: ...
16 views

Expressing Numbers with Rational Denominators (Surd Form) [duplicate]

Is there a command which expresses given real numbers in surd form (when possible)? That is, a form where any rooted terms are placed in the numerator, and the denominator is rational. Here are some ...
505 views

Factoring the square of this polynomial?

I have a polynomial $$\frac{b^4}{a^4}-\frac{2 b^2}{a^2}+1$$ and I want to complete the square to get this kind of expression: $$\left(1-\frac{b^2}{a^2}\right)^2.$$ I had try: ...
48 views

Get Mathematica to factor constants out of definite integral [duplicate]

Say we have Integrate[a f[x],{x,-Infinity,Infinity}] And want Mathmatica to factor out a to get ...
105 views

Optimal way to extract “positive part” of a multivariate polynomial

I've got multivariate polynomials with numerical coefficients, like e. g. p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3 and ...
39 views

Drop-down menu to globally change definition of a function t[x]?

If have a function t[x_] which is used extensively in a long notebook, but which has a variety of definitions, and which is used in a variety of ways. I'm looking ...
41 views

Algebraic manipulation on removing common factor outside

d[i,j] and M[i,j] are elements of size arrays of size 2x2 After some manipulations I get this as Output ...
96 views

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How to distribute exponentiation over multiplication?

I would expect the following: FullSimplify[(a*b)^i, a > 0 && b > 0 && i > 0] to give me a^i * b^i as ...
25 views

Trying to apply Jensen's inequality to a complicated symbolic expression

I have a somewhat complicated inequality expression like this: ...
45 views

How to manipulate sequences of inequalities?

I am trying to write some symbolic inequality proofs in Mathematica. What would be a clean way to make the inference that a >= b and ...
36 views

How to PowerExpand a generic Product?

I have: PowerExpand[Log[Product[f[i], {i, 1, n}]]] // InputForm (* Output: Log[Product[f[i], {i, 1, n}]] *) However, I would expect to get the following as the ...
52 views

Factor not factoring quadratic polynomial [closed]

I'm using version 11.3 Expand[(Sqrt - t)^2] 2 - 2 Sqrt t + t^2, but ...
89 views

Monitoring PolynomialReduce/Alternatives for other CAS packages

I have a large generic polynomial That looks like $N = \sum_{i_1,i_2\cdots}c_{i_1,i_2,i_3,\cdots} {x_{1}}^{i_1}{x_{2}}^{i_2}\cdots$ This could have anywhere between 3000-9000 terms with a maximum ...
159 views

Solving for coefficients of a polynomial ansatz in a rational function

(This is now a solved problem by my own alternative methods, and using some more physical arguments to limit the complexity of the problem. However more generally, any answers and strategies would be ...
61 views

Splitting a general rational polynomial ansatz into powers

EDIT This question is completely wrong and useless. It is mathematically incorrect. I think something like Series is sufficient if you're trying to do something ...
38 views

Terms not cancelling properly [closed]

I have defined ...
97 views

Removing fractions without a particular variable

As a very minimal example, consider a sum of fractions such as: $A=\frac{a}{s_{123}bc}+\frac{d}{e}$ In practice, I have many hundreds of thousands of these fractions generated from a recursion ...
35 views

Evaluating Fourier coefficients when Exponential terms are present

I am trying an analytical solution for a 3D Laplace equaition, and just wanted to know if I could use the symbolic calculation capabilities of Mathematica to calculate the Fourier coefficients ...
113 views

Transform expression into a certain standard form for an ODE

I'm using Mathmatica 11.1 on Windows. Given an expression containing a differntial equation of the form $\qquad A\, x'(z) = C\, x''(z) - B\, x(z)$ Or ...
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Neglect terms of order $1/n$

I have expressions like the following $A+B/n+C/n^2+\cdots,Z/n^p$. I'd like to keep just the first two terms, i.e., $A+B/n,$ however it seems that using the command O[1/n^2] is not working. The ...
45 views

Collect term in a distributive way

Consider P = x (a2 b2 v^a2-1+a3 b3 v^a3-1+d1+d2-2 y)-(y-d1)(y-d2)-x I would like to collect terms in (x,y,z) in a distributive way, that is to get an expression ...
136 views

How to implement split-complex numbers?

For those who do not know, the split-complex numbers are an analogue to the complex numbers where J is defined such that $J^2=1$ but $J\ne\pm1$, so they are all of the form $a+bJ$. By using ...