Questions tagged [simplifying-expressions]

Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.

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1answer
35 views

How to 'define' value in Assumptions but not let Simplify replace it?

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 ...
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1answer
47 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'...
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0answers
31 views

Simplifying equation using other equations [closed]

I have a large expression involving terms of the form $p[i,j]$, and I would like to simplify this expression as much as possible using a set of equations that are relations of the particular $p[i,j]$. ...
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2answers
45 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 <...
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5answers
783 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 ...
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1answer
55 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 ...
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1answer
36 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 ...
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2answers
119 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 ...
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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 ...
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2answers
165 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 ...
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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 ...
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2answers
111 views
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0answers
61 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)} + ...
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0answers
62 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 ...
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1answer
93 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{\...
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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 , ...
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2answers
96 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: $$\...
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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]. ...
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1answer
50 views

Simplify an expression with assumptions connected with OR

Mathematica doesn't seem to have any problem with these commands: ...
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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 <...
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3answers
134 views

How to show that two expressions are the symbolically the same

The following two expressions are the same when checked numerically. ...
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1answer
65 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 ...
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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 ...
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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 ...
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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: ...
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3answers
186 views

Mathematica not simplifying expression with square roots

With x, y, z all positive, how can one simplify the following expression: ...
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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 ...
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1answer
25 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 ...
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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 ...
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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: ...
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0answers
16 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 ...
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0answers
60 views

How to simplify expression

What are some ways to simplify the following expression? ...
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0answers
46 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 ...
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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: ...
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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 ...
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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 ...
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5answers
504 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 ...
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0answers
59 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   $f(x,t)=t+x^2$...
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1answer
62 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 ...
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1answer
108 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 ...
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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[] ...
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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 ...
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0answers
35 views

Simplification based on Kronecker Product Properties

I am trying to simplify some algebraically intensive expressions that involve inverses and Kronecker products. One simple example of such an expression is $$(1) \quad \quad \quad Z'(I_n\otimes\Sigma+Z\...
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1answer
70 views

How to refine polynomial which has a constraint condition to perfect square?

The expression : 1 + 4 p2^4 + 4 p2^2 (-1 + p1^2 - p3^2) - 4 p3^2 (-1 + p1^2 + p3^2) has a constraint condition: ...
7
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1answer
744 views

Why is Mathematica returning Abs[-1+x] even with assumption x<1?

With the following Simplify[Abs[-1 + x], {-1 + x < 0}], I expect Mathematica to return 1-x, but it instead gives the same <...
3
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0answers
81 views

Mathematica cannot simplify a rather simple expression with only one term

I run this code on Mathematica 11.2, Simplify[1/x^2,Assumptions->(1/x^2==1)] and hope to get 1, but Mathematica returns me ...
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2answers
65 views

Formal substitution of exponential factors in an expression

Assume that we have some complex algebraic expression, like Exp[(a t + b s)/w] ( t Exp[ q t] w + q Exp[q s] Exp[-2 s] + a^2 Exp[3 s] + s t + 1 ) Now, this is just ...
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3answers
135 views

How to get rid of {{ }} from scalars?

I am confronted with the situation where a scalar appear within curly brackets like a = {{2}} (as example) and the subsequent operation involves multiplying ...
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1answer
44 views

Mathematica not simplifying an expression!

I have the following matrix which can be checked to be zero by putting different values of parameter x. However, on applying FullSimplify, the desired result (zero ...
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0answers
38 views

Simplification of discrete recursive expression

I'm very new to Mathematica and I'm looking to simplify an expression where there are relations between discrete functions. Suppose(this simplified expression): ...

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