Questions tagged [algebraic-manipulation]
The art of manipulating an algebraic expression into the desired form.
0
votes
0answers
28 views
CoefficientRules for huge expressions
Is there some idea to get the coefficients for a very complicated, huge, and explicit polynomial expression to avoid insufficient memory problem? I am trying to use GroebnerBasis`DistributedTermsList ...
0
votes
3answers
68 views
Expand and Simplify do not work for NonCommutativeMultiply
Expand and Simplify do not work for NonCommutativeMultiply[] then how do we expand an expression like
(a+b)**(a-b) ?
2
votes
1answer
44 views
Is there a method to preserve order when matrix multiplying in Mathematica?
I know that commutativity can be preserved in Mathematica by using
**
i.e.
a*b can get printed as b a
but if I use a**b then it will always be printed as a b.
However, I am not able to implement ...
5
votes
1answer
77 views
Defining rules for anti-commutative multiplication
I am trying to create products following an anti-commutative rules using the binary operator **. I define my rules the following way:
...
0
votes
1answer
39 views
6
votes
2answers
82 views
Get the intermediate steps of FullSimplify
I have this expression:
Log[i] > (i Log[i])/n + Log[n - i] - (i Log[n - i])/n
And I attempt to simplify it and get this:
...
2
votes
0answers
31 views
How to Simplify/Factorise symbolic non-commutative expressions?
It always strikes me as odd, that Mathematica seems to have a hard time with non-communative multiplications.
I can use the horrible TensorExpand (or more performant Distribute) to get
...
1
vote
1answer
48 views
Parametric solution of a system of polynomial equations
I have the following system of equations,
1+x+y+z==0, 1+x*y+y*z+x*z==0
which I want to solve in the extension field of GF(2), the algebraic closure of GF(2) for ...
0
votes
1answer
61 views
Approximate Simplify (or factorization) [closed]
Suppose I have
$$(2+2a+a^2)(RC)^2 + RC(5+2a)t+t^2$$
I can factor $(2+2a+a^2) = 1+(1+a)^2$. When I assume $a \gg 1$ then $1+(1+a)^2\approx (1+a)^2$. Then I can write:
$$(a+1)^2(RC)^2 + 2RC(5/2+a)t+t^...
0
votes
2answers
37 views
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 ...
1
vote
1answer
22 views
Trying to apply Jensen's inequality to a complicated symbolic expression
I have a somewhat complicated inequality expression like this:
...
0
votes
2answers
41 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 ...
1
vote
1answer
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 ...
0
votes
2answers
49 views
Factor not factoring quadratic polynomial [closed]
I'm using version 11.3
Expand[(Sqrt[2] - t)^2]
2 - 2 Sqrt[2] t + t^2,
but
...
2
votes
0answers
83 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 ...
1
vote
0answers
154 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 ...
1
vote
1answer
50 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 ...
0
votes
1answer
37 views
2
votes
2answers
95 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 ...
0
votes
0answers
29 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
...
0
votes
2answers
108 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
...
2
votes
2answers
98 views
Vector calculus with index notation
How would you calculate this in Mathematica?
$$\sum_i\partial_i\partial_i G_{jk}$$
$$G_{jk}=\bigg(\frac{\delta_{jk}}{r}+\frac{(x_j-y_j)(x_k-y_k)}{r^3}\bigg)$$
where $r=|\boldsymbol{x}- \boldsymbol{...
2
votes
2answers
39 views
Defining a differential operator that acts on a non-commutative basis
Given a non-commutative basis ${x_0,x_1,x_2}$ I'd like to define a differential operator that acts as so
$$ \Delta_i (\sum_{n=0}^\infty c_n x_i^n) = \sum_{n=1}^\infty c_n x_i^{n-1}, \quad \Delta_i ...
0
votes
0answers
35 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
44 views
Storing solution of equation and performing operation
I have the following equations which I solve to find a and b.
...
0
votes
1answer
43 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
33 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
43 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 ...
4
votes
1answer
132 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
80 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
314 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}{...
6
votes
1answer
75 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
95 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
37 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
53 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
66 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
99 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
46 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
$$...
0
votes
0answers
34 views
Manipulating Equations: Substracting two equations
I was wondering why I fail to substract two equations using thread, while it works properly, as described here for additions.
Example: Let a system of equations be given:
...
1
vote
1answer
38 views
Output of Apart as a list?
I have a rational funtion of one variable that I know will always have a simple partial fraction decomposition of the form
$$\sum_{n=1}^N\frac{\alpha_n}{z- \beta_n},$$
but I do not know the values ...
0
votes
3answers
86 views
Finding the integer terms of a binomial expansion [closed]
What functions can I use to find how many integer terms the following expression has?
$$\left (\sqrt[19]{19}+\sqrt[95]{95}\right )^{1995}$$
Edit 1
In the development of that binomial, at some point ...
1
vote
3answers
75 views
Eliminating radicals from denominator or numerator of an expression
I need to find the limit when r2 tends to r1 of the following expression:
...
0
votes
0answers
22 views
Pauli matrix dot momentum in _feyncalc_
So I want to perform a dot product of a Pauli matrix (vector form) and momentum (also a vector) in feyncalc. How would I do that?.
And next question is: Can feyncalc show gamma matrices in terms of ...
4
votes
1answer
99 views
rational parameterization of a plane curve
Say one has a plane curve defined by a polynomial equation
$$P(x,y)=0$$
and one knows that the curve has genus 0. Is there an implementation in Mathematica of a (proper) rational parameterization, i.e....
2
votes
1answer
49 views
FindInstance for all real values satisfying a condition
I seek at least one instance of positive fractions $p,q,r$ where $p,q,r \in \mathbb{Q}^+$, for which
$$\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
38 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
815 views
Mathematica can't simplify some logarithmic expressions
When I simplify some logarithmic expressions in Mathematica, it just returns the expression
...
3
votes
2answers
114 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
43 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 ...
