Questions tagged [simplifying-expressions]
Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
1,977
questions
2
votes
0answers
55 views
Analytical Cross-Correlation between two time lagged Sinc functions gives complicated result
I'm trying to calculate the analytical Cross-Correlation between two time-lagged Sinc functions, i.e.,
\begin{align} R(\tau) = \int_{-\infty}^{\infty} \overline{\textrm{sinc}\left(\pi f \left(t - d_1\...
0
votes
0answers
36 views
How can I isolate a specific variable to one side in an equation?
Firstly, I will integrate the equation using Simpson's 3/8 Rule since it is quite long to do analytically. All the variables
(x, y, r, n, ps, k) are unknowns. I want to make r as the subject.
I tried ...
5
votes
3answers
196 views
Mathematica can't simplify asymptotic expressions containing constant symbols
I want to calculate simple asymptotic expressions involving positive constant symbols ($a > 0$), such as
$$\lim_{x\to\infty} \operatorname{sech}(a x) \sim 2 e^{-a x}$$
Surprisingly, the ...
3
votes
1answer
71 views
Solution for inequality equation - “Cannot be solved with the methods available to Reduce”
I am trying to solve the following inequality for $v$: $b>e^{\frac{-v}{\alpha}}\cdot \alpha + v$.
(Where I know: $b>0$, $v \in [0, 1]$, and $\alpha >0$).
However the following doesn't work: <...
0
votes
0answers
34 views
Small problem with TensorReduce
Given:
$eq=-\frac{1}{2} \text{$\varpi $1}^T.\text{J1}.\text{$\varpi $1}-\frac{1}{2} \Omega^T.\text{jp}.\Omega+\frac{1}{2}\left(\text{Jp}+\text{Jp}^T\right)^T.\Omega$
where $J1$, $jp$ and $Jp$ - $3 \...
2
votes
2answers
451 views
Getting False for an equality that I know it is true
I am getting false for an equality that I know it is true(I proved it by hand and I used sagemath to see that it is true) however when using Mathematica it is giving false although I used ...
0
votes
1answer
87 views
How to simplify complex Trigonometric expression in mathematica? [closed]
The expression which I need to simplify in mathematica into simplest form
...
0
votes
0answers
39 views
Simplifying hypergeometric function 4F3
I am trying to make Mathematica simplify the following expression below.
...
0
votes
1answer
55 views
How to ask Mathematica to simplify an expression in terms of a particular variable?
With the following matrix where there are relations between different variables a,b,c,...
0
votes
0answers
25 views
Issues in expanding expressions with formal sums
I have a very long expression involving formal sums to infinity, unfixed functions and several variables.
In this very long expression, I need a typical term, like
$\frac{6 A \sigma \sum _{n=0}^{\...
0
votes
0answers
20 views
How to rearrange terms in an expression to a particular form (e.g. A/w-> A*(1/w)
I have a huge expression for which the numerators are a big mess, involving numbers, variables, formal sums and unevaluted function, let's call the numerators Ai, with i=1,2,...n
This "beast"...
0
votes
2answers
55 views
How to get a result in a form without complex numbers?
How can I get rid of the complex numbers in this result? The actual result is obviously real, but Mathematica gives me this inconvenient complex form.
...
1
vote
2answers
47 views
How to reorganize a polynomial including exponents to the simplest form?
I want to reorganize a polynomial including exponents as the following Figure 1 to the form showing as Figure 2. Failed to realize it after several times trying such as Figure 3. Can you help me to ...
0
votes
1answer
55 views
How to arrage the expression in asscending powers of the variable
It seems that FullSimplify is not working here. I want to arrange the expression in ascending powers of x
...
2
votes
2answers
54 views
Removing transient part in equation and solving for a general form
I have the following code that I run:
...
0
votes
1answer
41 views
Reduce coefficients from constraints in a set of equations
Total beginner here. I am chaining 4 quadratic equations $f_i(x)$ at 4 knots $k_i$ (where $0 < k_i < 1$ and $k_{i+1} > k_i$) on a wrapped unit interval (i.e. $0 \leq x \leq 1$):
$$ f_i(x) = ...
3
votes
1answer
51 views
Expression should vanish under assumptions. How can I use Mathematica to simplify this type of of expression (and similar)?
This is maybe the worst type of question because it is super specific, but I am hoping that some Mathematica function or rule exists (built-in or custom) that can be helpful for simplifying a somewhat ...
0
votes
0answers
29 views
Getting the coefficients of an expression with Solve
I have a very lengthy expression (600+ terms) with derivatives of several functions, which I want to write in a compact way. I would like to get the coefficients of terms I know exist in this ...
2
votes
0answers
35 views
Why doesn't this KroneckerDelta simplify?
When I take D[Sum[a[x[0], x[j]], {j, 1, nsp}], x[0]] I get
I would expect that the KroneckerDelta[0, j] would automatically ...
0
votes
1answer
44 views
How to simplify for a ratio of two variables
Say I have an equation like
$$2 z \ln[\frac{a v_{2}^{2}}{b_{2}}]+(v_{1}-2v_{2}) - z \ln[\frac{a v_{1}^{2}}{b_{1}}]\geq0$$
...
2
votes
3answers
167 views
0
votes
3answers
87 views
How to extract a factor from equation and rearrange the equation?
I want to extract a factor from the equations, it's not a common factor, just a factor defined by myself, like this:
(ac+b) --> c(a+b/c)
I have tried Factor,<...
0
votes
2answers
49 views
How to find and apply variable substitutions that simplify an expression?
I have a simple matrix expression.
...
5
votes
2answers
181 views
Why Mathematica is not assuming real variable as real?
I am dealing with the situation where despite of specifying my variables b1 and c to be greater than zero, Mathematica still ...
2
votes
1answer
111 views
Checking a solution of PDE
I'm having trouble verifying solutions for complex PDEs including conjugate and absolute value.
For Example:
I have a complex PDE:
where superscript * denotes conjugate of the unknown function ...
2
votes
3answers
111 views
How to collect a polynomial with a specific power
Suppose I have got this polynomial
u=x^12-3x^8-x^4+3
Now, I am trying to collect this polynomial with x^4 terms.
I need to write it like this: (-1+x^4) (-3 + x^4) (1 + x^4)
To evaluate it, I used
...
0
votes
2answers
44 views
Approximating giant polynomial expression
Suppose I have a giant polynomial expression analogous to
$$
F=a_1xX^6+a_2x^2X^5+a_3x^3X^4+a_4x^4X^3+a_5x^5X^2+a_6x^6X
$$
and it is true that $X \gg x$. Let it be enough for me to approximate this ...
1
vote
0answers
56 views
How to intelligently use FullSimplify and FunctionExpand to simplify complex sums
I am trying to find a compact form of some sums which is related with some Bayesian probability factor (not so relevant, if required further explanation please ask). The point is that I know that the ...
0
votes
1answer
50 views
How can I take numerator of an expression? [closed]
How can I take numerator of the expressions?
-((2 (r^2) )/E) + (2 a)/E^3 + r \[Lambda] ==
0 && -2 r^2 Subscript[a, 1] + (6 Subscript[a, 1])/E^2 == 0
6
votes
3answers
313 views
Express MeijerG as integral
For definite integrals MMA gives identities in terms of Meijer G-functions, e.g.
$\begin{align}\sqrt{\pi}\int_0^\infty \textrm{e}^{-4x/t^2-t}\ \textrm{d}t &=
G_{0,\,3}^{3,\,0} \left( x\left.
\...
0
votes
2answers
42 views
Simplifying expressions involving Sqrt[] inside ComplexConjugate[]
I have a matrix mat with expressions involving square-root with complex-conjugation operation which makes the simplification difficult.
...
8
votes
2answers
2k views
Is there a short way of writing (x==a || x==b || x==c)?
Something like x == (a|b|c) but that doesn't work.
3
votes
3answers
230 views
Solve and Simplify
MMA version 12.3 Windows
Has anybody an explanation why "Solve" gives different results if you use "Simplify" on the argument or not.
Here we create 3 equations (it does not matter ...
0
votes
1answer
46 views
How to simplify square of a Trigonometric function?
I have this expression
$a^4 Sin[\phi/2]^4 + 1/2 a^2 b^2 Sin[\phi]^2 + b^4 Cos[\phi/2]^4$.
I expect to get a simple form
$(a^2 Sin[\phi/2]^2 + b^2 Cos[\phi/2]^2)^2$.
However mathematica obtain ...
2
votes
1answer
59 views
0
votes
3answers
95 views
Elimination of the variables
I am trying to get an equation in terms of variable z by eliminating variables g0 and g1 but
Running below code is taking time forever
...
0
votes
1answer
40 views
Simple expression involing Sum[] Mathematica fails to simplify [duplicate]
I have been trying to coax Mathematica to solve some equations involving expressions like Sum[A[t],t], with mixed success. One thing that really surprised me though ...
2
votes
0answers
34 views
Basic simplifications in vector algebra [closed]
Newish Mathematica user here! I just learned about the built-in vector type. To experiment with it I tried to specify that $a,b\in\mathbb{R}^3$ and I hoped that Mathematica would simplify $(2a+3b)\...
1
vote
1answer
86 views
Simplify treats a solution differently when it's formatted as an equation instead of a rule
Solutions returned by Solve are provided as rules:
solnRule1 =
y -> 1/(3 (1 + x)) - (-1 + 2 x)/(6 (1 - x + x^2)) + 2/(
3 (1 + 1/3 (-1 + 2 x)^2));
...
1
vote
0answers
39 views
Simplify system of expressions with cases
I have a system of equations that looks something like this:
...
4
votes
2answers
132 views
Split plus or minus into list [duplicate]
I would like
x= 2 \[PlusMinus] Sqrt[3]
to evaluate to
{x=2+Sqrt[3],x=2-Sqrt[3]}
Including any number of plus or minus symbols, ...
2
votes
1answer
96 views
How can I add conditions to simplify the result?
Here k is an integer number. How can I simplify the result by adding conditions like k is odd or even?
Also why are the 0^k terms not simplified to 0?
...
1
vote
1answer
57 views
Collect Exponential With Pattern
I have some enormous expression with many complex exponentials. Some of these are time varying, others are just phase terms. Here is a small piece of the expression that I hope fully captures the ...
1
vote
1answer
56 views
Inactive and simplify does not work [duplicate]
Consider the following code:
Simplify[Conjugate[Inactive[cn][n, nAvg]],
Assumptions -> Inactive[cn][__] > 0]
If you run it, it will not simplify, i.e ...
1
vote
1answer
89 views
FullSimplify is giving a condition that is implied by the assumptions
I've been trying to understand why FullSimplify is giving a condition that is implied by the assumptions (otherwise the set is empty). However, I couldn't ...
1
vote
0answers
25 views
Reconcile FullSimplify vs Reduce on Simple Problem
Can FullSimplify be coerced to give an answer here? If not, is it easy to say why?
...
2
votes
3answers
76 views
How to expand a rational function as a single fraction
This has been annoying me for a long time. I want a rational function to be represented in the form
$$\frac{a_nx^n+....a_0x^0}{b_mx^m+....b_0x^0}$$
But this seems to be quite difficult. Mathematica ...
0
votes
0answers
19 views
How to deal with multiple conflicting possibilities when using collect
I have some equations that I would like to group according to specified terms.
For example, $x_1x_2x_3+x_1x_2x_4+x_1x_5x_6+3x_1x_2x_3$.
I would like this to be grouped as $3x_1x_2x_3+x_1x_2x_4+...
0
votes
1answer
61 views
Reducing a fraction containing numbers in numerical form
I am looking for a function that would transform a fraction of the form:
$$\frac{1.0\times 10^{-10}}{1.0\times 10^{-11}+1.0\times 10^{-12}\,x}$$
into this:
$$\frac{1.0}{1.0\times 10^{-1}+1.0\times 10^{...
0
votes
0answers
22 views
How do I get actual solutions from MaxValue?
Say I want to calculate the maximum value of a simple function of two variables:
f[r_, t_]:= r Cos[t]^3 (1 + r Sin[t])
with respect to the variable ...
