Questions tagged [simplifying-expressions]
Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
2,034
questions
0
votes
0answers
25 views
problem in returning relations with unified format
first of all I didn't know what could be the proper title for this question, you may edit it if you find better, thanks.
I am making some relations dynamically, relations will return based on two type ...
0
votes
0answers
30 views
Result of a series of long arithemitic operations
Let us consider the following expression:
$$((x-y∗(a-(B+3)))^2-(f-1)^2∗(2a∗(B+3)-(B+3)^2-1)^2)^2+(g-(2a∗(B+3)-(B+3)^2-1))^2+(w-(B+3+h))^2......(q)$$
I want to make the following steps:
(1) Expand and ...
0
votes
0answers
26 views
Simplify complex vector expression - ratio of quadratic forms
There are two vector expressions:
$F_1=\dfrac{\frac{(v \times w)^T}{(v \times w)^Tu}\Omega}{\frac{(v \times W)^T}{(v \times W)^Tu}\omega}\tag{1}$
$F_2=\dfrac{(v \times w)^T \Omega}{(v \times w)^T\...
2
votes
0answers
74 views
FullSimplify gives erroneous answer
FullSimplify gives a wrong expression when simplifying Hypergeometric functions:
f = Hypergeometric2F1[1/2 - n, -n, 1 - 2 n, -4 a];
g = FullSimplify[f];
The ...
1
vote
0answers
55 views
Avoid Hyperbolic functions during FullSimplify
I am working with a particularly complicated set of equations in continuum mechanics that I have found solutions for analytically. I am now using Mathematica to recheck my work, as well as to find ...
0
votes
0answers
47 views
Assuming in Piecewise [closed]
I have just found Mathematica, and I have a simple problem. In a Piecewise function, I'm Assuming the range of values of $x$. In ...
0
votes
0answers
55 views
Manipulation of expression
Let
ss2 = (γ + ν)/β;
is2 = ((γ + ν)/β) (β/((γ + ν)) - 1);
I wish to do the following computation but want to keep the output in terms of ss2 and is2:
...
1
vote
0answers
55 views
Expand, simplify, and get rid of Abs[] of a multi-variable polynomial [closed]
Given a polynomial that $poly = ((-1 + t_1^2) (-1 + t_2^2) (1 - t_2^2 + t_2^4))/(\sqrt{t_1^2} \cdot(t_2^2)^{3/2})$. I would like to expand and simplify this polynomial into the form $poly = \sum_{i\in ...
0
votes
0answers
56 views
Simulatneously replacing variables of an expression [closed]
How do I simultaneously apply a set of substitutions on an expression? I have tried $/.\{{\text{replacement1}, \text{replacement2}, \ldots}\}$, however, it still seems that only the first one is ...
1
vote
1answer
51 views
How to 'define' value in Assumptions but not let Simplify replace it? [closed]
I want to let Simplify know the exact value of a symbol, to resolve logical statements, but don't want it to actually replace it. For instance, I would like ...
1
vote
1answer
98 views
Finding rotated function on a sphere in Mathematica
I'm trying to rotate a scalar valued function $$f(\theta,\phi)$$ on a sphere. Following
this post, I get
$$ \begin{pmatrix}
f'(\theta',\phi')\sin\theta'\cos\phi'\\
f'(\theta',\phi')\sin\theta'\sin\phi'...
0
votes
2answers
48 views
How to FullSimplify/Simplify an inequality while keep a variable isolated
I have an inequality as follows
2^(1/2 (1 + 1/n)) > 0 &&
t <= (2^(1/2 (-1 - 1/n) + n/2) n^(1 + 1/(2 n)) \[Pi]^((1/2)/n))/E
I want to simplify the <...
10
votes
5answers
861 views
Simplify radical expression (a + b - Sqrt[a^2 - b^2])/Sqrt[a + b]
I have the following expansions:
$\frac{a+b-\sqrt{a^2-b^2}}{\sqrt{a+b}}$ and $a>b>0$
Obviously we can simplify it further by hand $\sqrt{a+b}-\sqrt{a-b}$, but Mathematica doesn't know how to ...
0
votes
1answer
57 views
Solve cannot return NOT[A==B] in equations results
can you help me to return NOT[A==B] for Solve operation. in below code it does not return zP!=14
...
1
vote
1answer
37 views
How to remove the domain of variables in result relation?
this is my relation and it returns me xP [Element] Integers. I do not want any kind of these information. for example, I just need to see for every relation, yp-> x+1 - xp , thanks
...
2
votes
2answers
120 views
Is it possible to simplify this expression in Mathematica?
Let us consider an expression $$\frac{\sqrt[3]{\sqrt{2-x^2}+x} \sqrt[6]{1-x \sqrt{2-x^2}}}{\sqrt[3]{1-x^2}}.$$
Its plot
...
0
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0answers
63 views
Use cases for PiecewiseExpand applied to If or Which?
As indicated by its name, PiecewiseExpand's most natural application is to Piecewise expressions but nonetheless, it is still ...
4
votes
2answers
166 views
Get rid of a certain variable in a fraction's numerator
Consider expression $\frac{a - b}{a + b}$. When I apply $FullSimplify[\frac{a - b}{a + b}]$, I get $-1 + \frac{2a}{a+b}$, effectively getting rid of $b$ in the numerator. However, I want to get rid of ...
1
vote
2answers
66 views
how to get the result without conditional expressions
I am working with JAVA API and send a relation to kernel, then receive the returned solved result. Although I explicitly mentioned in my relation to have Integer Elements, the returned expressions ...
1
vote
2answers
136 views
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0answers
62 views
Identifying variables that are implicitly hidden in an expression
I am given an expression that is a sum of exponentials :
$\frac{1}{6} \big( e^{-2 \pi i (z_1-2z_2)} + e^{2 \pi i (z_1-2z_2)} + e^{2 \pi i (2z_1-z_2)} + e^{-2 \pi i (z_1+z_2)} + e^{2 \pi i (z_1+z_2)} + ...
0
votes
0answers
63 views
Mathematica can FullSimplify general but not specific case of a square root
FullSimplify[
Sqrt[(M^2 + A^2 - B^2)^2],
M^2 + A^2 - B^2 > 0
]
outputs the desired:
A^2 - B^2 + M^2
I've followed the ...
1
vote
1answer
95 views
Simplifying special functions via substitution
We have a well-known identity
$$B(a,b) = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)}$$
between beta function and gamma function.
I have a complicated expression involving the terms in the form $\frac{\...
0
votes
1answer
39 views
Trigonometric simplification .Correct syntax? [closed]
I cannot simplify this expression any further, which should result in 7.
Could you please provide me with the correct syntax, I have tried several without success.
$$Assumptions[A + B + C == 0 ,
...
3
votes
2answers
97 views
Spherical harmonics and Laplace operator
The spherical harmonic function $Y_l^m(\theta,\phi)$ is defined to be an eigenfunction of the angular part of the Laplace operator with eigenvalue $-l(l+1)$. In other words, it solves the PDE:
$$\...
1
vote
1answer
42 views
Prevent automatic simplification of trigonometric functions with complex argument
I would like to prevent automatic simplification of some trigonometric functions involving complex numbers.
The option AutosimplifyTrigs does the trick with 1/Cos[z], but not with Cos[I z].
...
0
votes
1answer
50 views
Simplify an expression with assumptions connected with OR
Mathematica doesn't seem to have any problem with these commands:
...
1
vote
1answer
89 views
Rewrite a variable in terms of another variable
I have two variables
t = 1/Sqrt[2] (Sqrt[1 + Cos[a]] + Sqrt[1 - Cos[a]] +
Sqrt[1 + Cos[b]] + Sqrt[1 - Cos[b]] + Sqrt[1 + Cos[c]] +
Sqrt[1 - Cos[c]])
and
<...
0
votes
3answers
134 views
How to show that two expressions are the symbolically the same
The following two expressions are the same when checked numerically.
...
1
vote
1answer
67 views
FullSimplify fails with simple assumptions
I have a list of relations of the form
x[1] x[2] + y[1] y[2] - z[1] z[2] == 0
and I want Mathematica to simplify certain expressions using these relations.
I have ...
1
vote
1answer
26 views
Globally set a time constraint for simplifications
I am using a differential geometry package (the now discontinued Atlas) which repeatedly calls the Simplify functions in its computations, which in some cases leads to extremely long (days? In the end ...
0
votes
0answers
51 views
Mathematica not performing simplifications with units with ScientificForm
I've run into a little problem, and I think in my research I've run into a dead end. I'm trying to perform some basic calculations with units, but Mathematica refuses to simplify the most basic ...
2
votes
0answers
41 views
Superfluous un-simplifiable condition returned by Reduce
No real "problem" here, just wondering why this is happening and how one might force Mathematica to simplify this. Consider:
...
2
votes
3answers
186 views
Mathematica not simplifying expression with square roots
With x, y, z all positive, how can one simplify the following expression:
...
0
votes
0answers
60 views
Simplify simple symbolic expression with KroneckerDelta
In short, my question is about finding a method for performing an automatic substitution f[a]/.{a->b}, where b depends on the ...
1
vote
1answer
26 views
Want to realize this operation (multiplication of divergent integrals of polynomials) in Mathematica [closed]
I am currently researching divergent integrals.
Definition. An extended number is an expression of the form $\int_a^b f(x)dx$, where function $f(x)$ is defined almost everywhere at $(a,b)$. Generally ...
0
votes
0answers
52 views
Techniques for simplifying expressions
I am hoping to get techniques to use when faced with expressions I think may be simplified.
From two symmetrical looks at a problem I ended up with two inequalities. With excess stuff removed and ...
3
votes
0answers
58 views
What is the ComplexityFunction used by FullSimplify in Mathematica 12? [duplicate]
I was surprised to see FullSimplify make my expressions numerically unstable. The result can be summarized below:
...
0
votes
0answers
17 views
Strategy tips for time consuming FullSimplify, crashing FullSimplify, and strange behavior of TimeConstraint
I am trying to simplify a complicated integration result containing both error functions and MeijerG - I give the full expression below. A simple FullSimplify[expression,{x>0,y>0,z>0}] would ...
1
vote
0answers
60 views
0
votes
0answers
48 views
How to eliminate dummy indices in Package-X
I'm using a package called Package-X that computes things involving summation over dummy indices (using Einstein summation conventions). In the output of the computation the dummy indices sometimes ...
1
vote
1answer
57 views
Is this behavior of the Series function correct
While series expanding a function, I got an unexpected result, which seems like an error to me. I have boiled it down to this minimum (non) working example:
...
0
votes
0answers
34 views
FullSimplify including Sum or Product and related functions
I am searching for a function that can simplify or compress an expression. FullSimplify does an excellent job, however, it doesnt exploit ...
1
vote
1answer
42 views
How to re-arrange an expression based on an integration
I have an expression that includes some integrations. I find the derivative of the expression which results in a long-expression. I wanna rewrite the result based on one of the integrations. I would ...
5
votes
5answers
510 views
Combination several If conditions in a loop
I have a Do loop with several conditions:
Do[If[i < 20, a[i] = i; If[i == 19, a[i] = i + 1], a[i] = i + 3], {i,1, 100}]
How ...
1
vote
0answers
60 views
Simplifying a numerical integral involving a variable integration limit
I have a one-variable function basically consisting of an integral whose limits depend on the variable —I mean, something like this:
$F(x)=\int_0^{L(x)}{f(x,t)}dt$
with
$L(x)=5x$ and $f(x,t)=t+x^2$...
1
vote
1answer
63 views
Evaluate $c_k = \frac{1}{k!}\Big\{ \Big(\frac{d}{dz}\Big)^{k-1} f(z)^k \Big\} \Big|_{z=0} $ for $k=1,2,\dots$
I would like to compute
$$c_k = \frac{1}{k!}\Big\{ \Big(\frac{d}{dz}\Big)^{k-1} f(z)^k \Big\} \Big|_{z=0} $$
for $k=0,1,2,\dots$,
where
$$ f(z) = \frac{z[\cos( \alpha z ) +\sin(\alpha z)]}{\sin(\alpha ...
-1
votes
1answer
109 views
Did Mathematica make a mistake or was it me?
I'm having a little trouble with Mathematica. There are two expressions that should be equal over a given region. Each of which consists of three terms that should be equal individually:
term1 of ...
0
votes
0answers
40 views
Difference between Assuming[] and Refine[]
I'm trying to find the limit of a root. I've found that the limit is undefined if I use Refine[]
...
0
votes
1answer
33 views
Simple Question: Cut Number in Transfer function
Given transfer function:
$W=\frac{10 (s+100)}{2 s^4+219 s^3+1909 s^2+900 s+1000}$
W=(1000 + 10 s)/(1 (1000 + 900 s + 1909 s^2 + 219 s^3 + 2 s^4))
Which command to ...