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
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
0answers
52 views
How do I separate 2 variables to be independent from each other in the equation?
I have an equation namely
...
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 ...
0
votes
1answer
69 views
Reduce the product of two hypergeometric functions to a single hypergeometric function [closed]
I have this product of two hypergeometric functions
...
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
Why it seems that there is no counterpart function as to multiplication, to `Total` as to addition?
Times and Plus have the same grammar, and so do Product and ...
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
...
