Questions tagged [algebraic-manipulation]

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

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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 ...
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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
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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
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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: ...
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1answer
39 views

Not able to multiply the output of the code below

It is the output of the code given below ...
6
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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
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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
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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 ...
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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^...
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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
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1answer
22 views

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

I have a somewhat complicated inequality expression like this: ...
0
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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
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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 ...
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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
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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
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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
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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 ...
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1answer
37 views

Terms not cancelling properly [closed]

I have defined ...
2
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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 ...
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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 ...
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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
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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
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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 ...
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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 ...
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3answers
44 views

Storing solution of equation and performing operation

I have the following equations which I solve to find a and b. ...
0
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 $$...
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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
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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
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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
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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
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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
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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
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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
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2answers
815 views

Mathematica can't simplify some logarithmic expressions

When I simplify some logarithmic expressions in Mathematica, it just returns the expression ...
3
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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 ...