Questions tagged [algebraic-manipulation]
The art of manipulating an algebraic expression into the desired form.
0
votes
0answers
29 views
Factoring explicit quantities
I'm wondering if there is a way I can explicitly factor an equation into separate chunks. For example, if I have
...
0
votes
3answers
22 views
Storing solution of equation and performing operation
I have the following equations which I solve to find a and b.
...
0
votes
1answer
34 views
Changing variables to obtain derivatives of new variables [duplicate]
Let's say that I have some symbolic expression of a function $x(t)$, and would like to obtain its derivative $x'(t)$.
However, I also have the following two identities, $\xi = \omega t$, and $\eta = ...
0
votes
1answer
30 views
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
...
1
vote
2answers
40 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 ...
3
votes
1answer
124 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 ...
1
vote
1answer
71 views
How to distribute rules?
For example i want to have following equation :
Det[A B C]=Det[A] Det[B] Det[C]
What is the simplest way to distribute automatically?
2
votes
5answers
302 views
Reconstructing a polynomial from its coefficient array
A polynomial coefficient matrix:
mat =
CoefficientList[3 + 5 x^3 + 4 y^3 + 2 x + 6 x^2 y + 7 x y^2 + 8 x y, {x, y}];
\begin{equation}
\left(
\begin{array}{...
4
votes
1answer
54 views
Computing the seven roots of a polynomial
This question was originally asked by @fsrong70 six months ago.
The OP deleted it shortly after posting and has not returned to this site since. I had just figured it out when it was deleted. I ...
0
votes
0answers
45 views
Commutator of differential operators
Let $P_x = \frac{\hbar}{i}\frac{d}{dx}$, after specifying the commutator relation symbolically $[X, P_x] = i\hbar$, I can ask Mathematica to calculate commutator algebra. My question: is there a way ...
0
votes
1answer
32 views
Solving an equation
I need to solve the following equation (expr = 0) for "A", but looks like Solve and Reduce struggle. All parameters are positive, and "expr" is given below. (I suspect the issue might be due to powers ...
0
votes
1answer
49 views
Compare algebraic equivalence (regardless of term order) without having to simplify? [closed]
I know that in order to find the equivalence of say $ a+b $ and $ b+a $, then:
FullSimplify[a + b == b + a]
is sufficient. However, suppose I want to compare ...
1
vote
1answer
62 views
List from algebraic expression?
Consider an algebraic expression
exp = a x^2 -b x +c
I want to create a list from its element:
list = {a x^2, -b x, c}
Is ...
1
vote
0answers
76 views
Surprising result using operator form of FoldList [closed]
I was trying to implement some Graph related functions in Functional form and came accross this result which I found surprising.
I want a function that does various operations on a graph.
The ...
3
votes
2answers
106 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
41 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
$$...
0
votes
0answers
31 views
Manipulating Equations: Substracting two equations
I was wondering why I fail to substract two equations using thread, while it works properly, as described here for additions.
Example: Let a system of equations be given:
...
1
vote
1answer
37 views
Output of Apart as a list?
I have a rational funtion of one variable that I know will always have a simple partial fraction decomposition of the form
$$\sum_{n=1}^N\frac{\alpha_n}{z- \beta_n},$$
but I do not know the values ...
0
votes
3answers
83 views
Finding the integer terms of a binomial expansion [closed]
What functions can I use to find how many integer terms the following expression has?
$$\left (\sqrt[19]{19}+\sqrt[95]{95}\right )^{1995}$$
Edit 1
In the development of that binomial, at some point ...
1
vote
3answers
52 views
Eliminating radicals from denominator or numerator of an expression
I need to find the limit when r2 tends to r1 of the following expression:
...
0
votes
0answers
20 views
Pauli matrix dot momentum in _feyncalc_
So I want to perform a dot product of a Pauli matrix (vector form) and momentum (also a vector) in feyncalc. How would I do that?.
And next question is: Can feyncalc show gamma matrices in terms of ...
3
votes
1answer
93 views
rational parameterization of a plane curve
Say one has a plane curve defined by a polynomial equation
$$P(x,y)=0$$
and one knows that the curve has genus 0. Is there an implementation in Mathematica of a (proper) rational parameterization, i.e....
2
votes
1answer
46 views
FindInstance for all real values satisfying a condition
I seek at least one instance of positive fractions $p,q,r$ where $p,q,r \in \mathbb{Q}^+$, for which
$$\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
36 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
786 views
Mathematica can't simplify some logarithmic expressions
When I simplify some logarithmic expressions in Mathematica, it just returns the expression
...
3
votes
2answers
111 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
41 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
74 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
82 views
0
votes
2answers
42 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
187 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
104 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
301 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
57 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
56 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
137 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
70 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
85 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
53 views
Simultaneous solving of three equations with nested, complicated expressions
I have the following variables s1, s2, and r1 defined as
...
5
votes
1answer
94 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
500 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
182 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
24 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
72 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:
...
