Questions tagged [algebraic-manipulation]
The art of manipulating an algebraic expression into the desired form.
475
questions
2
votes
1answer
24 views
Definition of a general rule
By defining:
rule = Sqrt[expr_^2] :> expr;
and writing:
Sqrt[x^2] /. rule
I get:
x
which is what is desired (...
1
vote
2answers
35 views
Simplify expression with non-commutative products
I am using NCAlgebra but I am open to any solution. I would like to simplify some expressions with many terms (a few dozens) using:
the fact that each term is a ...
3
votes
1answer
50 views
How to find noncommutative product of two expression
I have the following function
$$
B(n)=x \alpha ^n-y \alpha ^n q^n
+ \epsilon \left(x \alpha ^{n+1}-y \alpha ^{n+1} q^{n+1}\right). $$
Here, I want to find the product $B(n)^2$ or $B(n)*B(n+1)$ ...
6
votes
4answers
366 views
A problem with `Eliminate`.`
Consider this expression:
Eliminate[a x + b y == 0 && c x + d y == 0, {x, y}]
Mathematica returns ...
1
vote
1answer
49 views
How do I expand expressions involving complex numbers?
I am trying to do the following:
Expand[(A g + n)^2 Conjugate[A g + n]^2, Element[{A, g, n}, Complexes]]
The goal is to expand and get all the terms of $(A g + n)...
0
votes
2answers
107 views
How can I decompose polynomials in a certain way?
I' ve learned that the following examples can be used to decompose a
factor in this way
...
1
vote
3answers
656 views
How would I solve this math problem on Mathematica?
$(3t^2 + 5t + a ) (4t^2 + bt - 2) = 12t^4 +26t^3 - 8t^2 - 16t + 6$
What is a + b?
The answer would be:
$6=-2a$
$a=-3$
$-16t=(5t\cdot-2)+a\cdot bt\Longrightarrow-16t=-10t+(-3)bt\Longrightarrow b=...
0
votes
1answer
31 views
Making substitution to an expressions with a list of numerical data [closed]
Suppose I have an expression similar to this: y=23.23*(h[x]^2)*(D[h[x],x])*(D[h[x],{x,3}])/(13.2+Cos[0.245x]) The actual expression is a lot more complicated, but ...
3
votes
3answers
89 views
isolating a specific variable to one side in an equation
I am trying to do a simple operation of manipulating an equation of multiple variables (say, $x,y,z$), so that I can get one of the these variables on the LHS and everything else on the RHS. It should ...
1
vote
2answers
64 views
Replacing value by another value
My question is that in Mathematica notebook when I write replacing commands, it didn't replace.
In[1]:= 2*x+y+1/.(x+y)->0
Out[1]:=1+2x+y
or
...
4
votes
1answer
117 views
How to get DAE representation from equations?
Update2: Thank you for all of your answers.
I would like to clarify the question as I did a bit of research on DAE representations and their applications in software.
There are 2 representations used ...
0
votes
1answer
64 views
Finding ODE series solution coefficients
I am trying to solve an ODE by subbing in a series form and then looking individually at the coefficients of different powers of the variable. I'm looking at a general form of equation:
$$\frac{\...
3
votes
0answers
87 views
How to invert Expand
How do I invert Expand?
I have
lis={1 + x^2, 2 + 2 x^2 + x^4, 5 + 8 x^2 + 8 x^4 + 4 x^6 + x^8}
and want to get
...
1
vote
1answer
62 views
Can Mathematica check if I correctly applied an algebraic transformation?
Mathematica has tons of functions to perform algebraic manipulations. But is there a way to use it to check if I didn't make mistakes in my own algebraic manipulations.
As a real world example:
[...
1
vote
1answer
67 views
Factoring after polynomial long division [closed]
I have gotten the code to do polynomial long division, but I want my students to also factor the solution if possible.
4
votes
1answer
143 views
Pattern matching expressions that have been simplified
I run into this type of issue frequently when trying to apply known identities to complicated expressions: some of my expressions will have their forms simplified by mathematica in such a way that ...
1
vote
1answer
202 views
Simplifying solution to a third-order Boundary Value problem
I have been trying to solve a physical problem during which I reach the following third-order, Linear O.D.E.
The solution I get using this expression is really messy. Is there any way to simplify it ...
0
votes
0answers
51 views
Dealing with positive power variables in Taylor expansion and assumptions
I would like to compute the Taylor expansion of monomials whose powers are nonnegative rational variables.
First, here is a function which encodes the multivariate Taylor expansion at the points <...
0
votes
2answers
36 views
Check whether a given quantity is negative
Given four numbers $n0, n1, n2, n4$ such that $n1+n2+n3+n4 = 1$. How can we check the sign of $A - 2 B$ (where $A$ and $B$ are defined below), i.e., whether this quantity is positive or negative?
<...
8
votes
3answers
251 views
How can I check if a function can be written as $a * \sin (b * x + c) + d$?
I want to write a function that takes another function, say $f(x)$ and a variable $x$ as input and return True it this function can be written in the form ...
0
votes
1answer
31 views
Collect ignoring negative exponential
I have the expression
1 + Exp[-2 x] (-1 - 2 x (1 + x))
I used Expand to get the x's to multiply within the parentheses, this ...
6
votes
1answer
114 views
Generating an efficient way to compute einsum?
Given an einsum like below, how could I generate an efficient computation graph for it?
$$X_{ik} M_{ij}M_{kl} X_{jl}$$
The indices range from $1$ to $d$ and the goal is to minimize computation time ...
1
vote
1answer
69 views
Generating summation formulas for factorized 4th moments
I'm interested in getting summation formulas for the following expression, in Einstein summation notation, with indices ranging from $1$ to $d$ $$c=X_{ik}M_{ijkl}X_{jl}$$
Here $M_{ijkl}$ is ...
0
votes
0answers
36 views
Einstein summation? [duplicate]
Is there something to help me do Einstein summations in Mathematica? I found a couple of Mathematica packages to do this, but not sure how out of date they are.
In Python-land you can do things like <...
4
votes
1answer
85 views
Is it possible to make Decompose work with coefficients containing radicals?
It appears that Decompose works reliably only on polynomials with integer coefficients, although it seems to be not mentioned in the docs. Can I make it work (or ...
1
vote
2answers
54 views
How to replace a sub-expression when it implicitly exists in an expression
In order to make my question clear, I would like to use a simple expression as an toy example.
Suppose we have an expression, which is,
f = a + 2*b + c
Now I ...
1
vote
1answer
39 views
Assuming x real, simplifying or refining Im[1/(x+i)] doesn't yield anything
I think it is straightforward from the title,
Simplify[Im[1/(x+I)], x > 0]
spits out,
Im[1/(x+I)]
while I would have ...
4
votes
3answers
198 views
Eigenvectors in the limit $ \mu\rightarrow 0 $ are not the same as eigenvectors when setting $ \mu=0 $ from the beginning
I would like to find the eigenvectors of a matrix and see what the eigenvectors look like in the limit of $ \mu\rightarrow 0 $:
...
0
votes
0answers
20 views
Expressing Numbers with Rational Denominators (Surd Form) [duplicate]
Is there a command which expresses given real numbers in surd form (when possible)? That is, a form where any rooted terms are placed in the numerator, and the denominator is rational.
Here are some ...
6
votes
3answers
528 views
Factoring the square of this polynomial?
I have a polynomial $$\frac{b^4}{a^4}-\frac{2 b^2}{a^2}+1$$ and I want to complete the square to get this kind of expression: $$\left(1-\frac{b^2}{a^2}\right)^2.$$
I had try:
...
0
votes
1answer
67 views
Get Mathematica to factor constants out of definite integral [duplicate]
Say we have
Integrate[a f[x],{x,-Infinity,Infinity}]
And want Mathmatica to factor out a to get
...
5
votes
3answers
117 views
Optimal way to extract “positive part” of a multivariate polynomial
I've got multivariate polynomials with numerical coefficients, like e. g.
p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3
and ...
1
vote
1answer
43 views
Drop-down menu to globally change definition of a function `t[x]`?
If have a function t[x_] which is used extensively in a long notebook, but which has a variety of definitions, and which is used in a variety of ways. I'm looking ...
0
votes
0answers
43 views
Algebraic manipulation on removing common factor outside
d[i,j] and M[i,j] are elements of size arrays of size 2x2
After some manipulations I get this as Output
...
3
votes
4answers
97 views
Algebraic simplification [closed]
Given,
$$\sqrt{\frac{x}{y}} + \sqrt{\frac{y}{x}}\;\; where \;\; x,y \gt 0 \;\; and \;\; x,y \in \Re \;\; (Expression \;\;1)$$
Somehow, I found that $$\sqrt{\frac{(x+y)^2}{x\cdot y}} \;\; (Expression\...
4
votes
3answers
148 views
Why won't Mathematica give a prettier expression for this really simple algebraic expression?
As a result of some lengthy calculations, Mathematica gave me the following expresssion:
$$
\frac{xy^2+(1 + y)\sqrt{1 + y(2 + y + xy)}}{(1 + y)^2}
$$
I tried all sorts of simplifications, but none ...
10
votes
4answers
513 views
Mathematica function equivalent to MATLAB's residue function (partial fraction expansion)
I am looking for a Mathematica function equivalent to MATLAB's residue function.
If there is no Mathematica equivalent, I would like to write a function that given ...
1
vote
2answers
46 views
Replace rules change dimension
This is absolutely driving me crazy, I don't know if this is a bug or what, but replace rule sometimes change dimension of my data.
Say I have data:
...
1
vote
1answer
148 views
How can I simplify a super long expression? [closed]
I am a brand new to using Mathematica, and currently using it for my thesis.
Essentially I have a really long expression made up of lots of parameters.
I am trying to reduce the size of the ...
0
votes
0answers
39 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
76 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
59 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
112 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
42 views
6
votes
2answers
110 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
35 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
...
0
votes
1answer
81 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^...
3
votes
3answers
73 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
25 views
Trying to apply Jensen's inequality to a complicated symbolic expression
I have a somewhat complicated inequality expression like this:
...
0
votes
2answers
46 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 ...
