Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [algebraic-manipulation]

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

3
votes
2answers
98 views

Replace $ z z^* $ by $ |z|^2 $

I have a long expression involving different complex numbers. I want to force Mathematica to replace z Conjugate[z] by Abs[z]^2 ...
1
vote
1answer
39 views

Extracting parts of symbolic expressions

I've searched around and found things that could help me only in cases that are simpler than the one I had in mind. I would like to extract polynomials from expressions that schematically look like $$...
0
votes
0answers
29 views

Manipulating Equations: Substracting two equations

I was wondering why I fail to substract two equations using thread, while it works properly, as described here for additions. Example: Let a system of equations be given: ...
1
vote
1answer
35 views

Output of Apart as a list?

I have a rational funtion of one variable that I know will always have a simple partial fraction decomposition of the form $$\sum_{n=1}^N\frac{\alpha_n}{z- \beta_n},$$ but I do not know the values ...
0
votes
3answers
79 views

Finding the integer terms of a binomial expansion [closed]

What functions can I use to find how many integer terms the following expression has? $$\left (\sqrt[19]{19}+\sqrt[95]{95}\right )^{1995}$$ Edit 1 In the development of that binomial, at some point ...
1
vote
3answers
43 views

Eliminating radicals from denominator or numerator of an expression

I need to find the limit when r2 tends to r1 of the following expression: ...
0
votes
0answers
15 views

Pauli matrix dot momentum in _feyncalc_

So I want to perform a dot product of a Pauli matrix (vector form) and momentum (also a vector) in feyncalc. How would I do that?. And next question is: Can feyncalc show gamma matrices in terms of ...
3
votes
1answer
90 views

rational parameterization of a plane curve

Say one has a plane curve defined by a polynomial equation $$P(x,y)=0$$ and one knows that the curve has genus 0. Is there an implementation in Mathematica of a (proper) rational parameterization, i.e....
2
votes
1answer
45 views

FindInstance for all real values satisfying a condition

I seek at least one instance of positive fractions $p,q,r$ where $p,q,r \in \mathbb{Q}^+$, for which $$\frac12 (a - 2 b + c)^2 \ge pa^2 + qb^2 + rc^2\quad \forall\ a,b,c \in \mathbb{R}.$$ I used this ...
1
vote
1answer
34 views

Proofs and exponents to the N power

I'm still a beginner at Mathematica and I'd like to understand how to use it for proofs. Here is a simple one on exponent properties (a*b)^n == a^n*b^n I tried ...
10
votes
2answers
780 views

Mathematica can't simplify some logarithmic expressions

When I simplify some logarithmic expressions in Mathematica, it just returns the expression ...
3
votes
2answers
108 views

Rewrite $ x\sqrt{1-y^2/x^2} = \text{sgn}(x)\sqrt{x^2-y^2} $

I'm trying to coax Mathematica into rewriting $ x\sqrt{1-y^2/x^2} = \text{sgn}(x)\sqrt{x^2-y^2} $ for $ x $ and $ y $ real. I have tried all combinations of ...
2
votes
1answer
39 views

Separating positive and negative terms in an algebraic expression

I want to isolate positive and negative terms in this algebraic expression, for example. I have looked at the FullForm and tried many functions like ...
2
votes
1answer
69 views

Symmetrize a polynomial forgetting the commutativity property of multiplication

I need a script to authomatically symmetrize a given polynomial. For example, if the input is xy the output should be ...
1
vote
2answers
81 views

Relation between variables

I have the following two equations: ...
0
votes
2answers
40 views

Manipulation system of equation

I apologize for the banality of my question... Suppose we have two equations: b=a*x+l; y=3x+2 How can I have b as a function of y?
1
vote
1answer
130 views

Tag Times in Null is Protected [closed]

I've some problems with the error mentioned in the title. Unfortunately, my code is full of subscripts so I'll show it in a photo. In this code the central aspect is to assign a scalar value to an ...
1
vote
1answer
38 views

Strange thing about simplification between product and productory [closed]

Good morning, I have this strange problem. I have to divide a product of 5 variables by 4 of the 5 variables : $C x_1 * x_2* x_3 *x_4 / (x_1 * x_2* x_3 *x_4)$. Now if I do this I don't obtain only $C$...
2
votes
3answers
89 views

Noncommutative Expand into power series

I am new to Mathematica and am trying to apply it to quantum mechanics problems. The practice project I am dealing with now is considering quantum harmonic oscillator and ladder operator algebra ...
5
votes
3answers
291 views

Selecting parts of algebraic expressions?

(a1 q1^2 + b1 p1^2 + c1 q1 + d1 p1 + e1) E^(a2 q1^2 + b2 p1^2 + c2 q1 + d2 p1 + e2) Is there a command to select factor polynomial ...
0
votes
0answers
42 views

Defining commutations rules over arbitrary matrix

I'm working with spin connections with Dirac gamma matrix commutator (I know, mathematica has specific ways to work with it), and I need to define the following rules; $[\gamma_{0},\gamma_{i}]= 2 \...
2
votes
2answers
54 views

Maximizing number of positive elements in formatted output

The following code $Assumptions = {0 < x < 1, 0 < y < 1, z > 1}; myexpr = Expand[(1 - x) (1 - y) (z - 1)]; TraditionalForm[Simplify[myexpr]] ...
1
vote
0answers
17 views

ClearAttributes in ParallelDo

The following code ClearAttributes[Times, Orderless]; temp = b*a; Do[ Print[temp];, {i, 1} ] will print b*a However, the ...
0
votes
2answers
43 views

Solving for a variable [closed]

I have 2 equations that I want to equate to each other and solve for a certain variable in one of the equations. (1/a)-(b*e^-2a)/a= -(e^-2a*V0)/a I want to ...
4
votes
0answers
112 views

Non-determinstic kernel crash when manipulating large expressions in Mathematica 11.3

I have a encountered a very weird behavior of Mathematica 11.3 when collecting and factoring large expressions. To be more precise, such operations often lead to an abrupt kernel crash, but the ...
1
vote
1answer
62 views

Simplifying algebraic expressions with fractions in exponential

When letting Mathematica simplify (a^(-5) b (a^2 c^3)^3)/((a b^2 )^(-2) c^7) it returns the 'correct' answer a^3 b^5 c^2 ...
1
vote
0answers
69 views

How to find “nice” partial fraction decompositions

This is similar to one of my previous questions How to factorize polynomials into "shortest possible" pieces -- unfortunately I do not have any rigorous formulations of what I want to ...
0
votes
0answers
52 views

Simultaneous solving of three equations with nested, complicated expressions

I have the following variables s1, s2, and r1 defined as ...
5
votes
1answer
93 views

Indefinite order of differential operator

In the latest version of Mathematica, D can compute derivatives of symbolic order, that is, the $n^{\text{th}}$ (partial) derivative, returning an expression ...
4
votes
3answers
498 views

Writing System of Equations == 0

I have a system of equations and would like to retrieve the Jacobain w.r.t. to some variables. Now I see that this would be best done if I wrote the equations in a form == 0. Is there an easy way to ...
3
votes
4answers
180 views

How to separate integers and radicals from a term?

If I have a variable such as r = 1 + Sqrt[2] + Sqrt[13] how can I separate that into two separate variables with the rational and irrational parts? i.e. ...
0
votes
1answer
23 views

Keeping terms separate without combining it especially with multiplied random numbers

Suppose I have an expression where random numbers in exponentials are multiplied and this expression will keep on iterating such that more of such terms will occur. But I need to keep those terms as ...
0
votes
1answer
31 views

Threading Functions Specifying the Head and Level

I'm trying to thread a function only on the second level of an expression. For example Thread[(a * b) ** (c * d),Times] gives (a ** c) * (b ** d) However Thread[2(a * b) ** (c * d),Times] ...
4
votes
1answer
63 views

Distribute NonCommutativeMultiply over Times

Is there a method to transform (a1 * a2) ** (b1 * b2) into (a1 ** b1) * (a2 ** b2) I am trying to transform non-...
1
vote
1answer
40 views

How to force Refine to use a specific form

I have an assumption relating three variables and Simplify (and all functions that use assumptions) seem to take preference on one of these variables. For example: ...
0
votes
1answer
148 views

FindRoot fails 100 iteration precision

I am attempting to find roots of a complex equation that involves exponential functions and small approximation values. I have had success using FindRoot for values ...
3
votes
3answers
187 views

Construct approximation by eliminating algebraic terms of small magnitude

Let's suppose that for the following expression: $\qquad \alpha\,\beta +\alpha+\beta$ I know that $\alpha$ and $\beta$ are of small magnitude (e.g., 0 < $\alpha$ < 0.02 and 0 < $\beta$ < ...
1
vote
1answer
37 views

LogicalExpand with AlgebraicNumber present puts variables into the right hand side

Consider the following two test-cases: Reduce[{a^3 + 1 == 0, b^15 - b^3 + 1 == 0}, {a, b}, Backsubstitution -> True] Gives an output roughly: ...
1
vote
0answers
81 views

Why does the equation Sqrt[x] Sqrt[x] == -1 have a solution? [closed]

When I try to solve the following equation, Mathematica gives a solution for which the equation is not defined: Reduce[Sqrt[x] Sqrt[x] == -1, x] x == -1 and ...
15
votes
2answers
1k views
4
votes
0answers
86 views

Continued fraction expansion of a rational function

Maybe I'm missing something, but what would be a good way to calculate the continued fraction expansion of a rational function $Z(s) = N(s)/D(s)$? The built-in function ...
1
vote
0answers
31 views

Solving some constraints on a subgroup of a Lie group [closed]

Let $M$ be a rank-3 matrix, I am interested in searching all the group elements $g \in$ SU(3) Lie group, such that, $$ g^T M g =M. $$ Example 1. Let $$ M[1]= \left( \begin{array}{ccc} 0 & 1 &...
1
vote
1answer
55 views

Picking out terms according to proportionality in expressions

I am trying to figure out how to pick terms proportional to $x$ (or any other expression). I have the following problem: I want to pick out $(1+2y) x$ from a polynomial of the form $(1+2y)x + e^xx +...
1
vote
3answers
102 views

Command for approximating a function in variable limit?

The function $ f(T) = 1/T^2 Exp(1/T) [Exp(1/T) + 1]^{-2} $ in low $T$ limit is $ f(T)=Exp(-1/T)$ and in high $T$ limit $(T)=1/T^2$. Is there a command in mathematica to find the the function in ...
0
votes
3answers
71 views

How to factor out and cut off a parameter

In an exemplary expression expr = -6 3^(1/3) c1 kL^4 L^2 (δ^3/L^3)^(1/3) all parameters are real, especially L > 0. ...
0
votes
3answers
54 views

Is it possible to evaluate this algebraic expression ?

a +b == Subscript[q,1]n + Subscript[r,1] b + c == Subscript[q,2]n + Subscript[r,2] Subscript[r,1] + c == Subscript[q, 3]n + Subscript[r,3] Expand[a+b+c] I want to ...
0
votes
0answers
29 views

simplification of ordered ratios (lists) of linear polynomials in many variables

Let us work with variables $x_m$ with $m=1,\ldots,k$. Consider a fraction $f=N/D$ where both $N$ and $D$ are collections (for my purposes, the order matters) of simple factors, more precisely $N$ is a ...
0
votes
1answer
32 views

Define nonstandard expansion rule for lists

I have defined my own algebra using the unused operators $\oplus$ and $\otimes$. During evaluation, lists pop up which have the structure ...