Questions tagged [simplifying-expressions]

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

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Simplify expression with assumption that all variables are real

I have an expression in which all variables are real. However when I simplify the expression with appropriate assumptions a 'Conjugate' still remains. How can I get rid of this? Here is my code ...
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1answer
55 views

Why do these results differ?

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1answer
62 views

How can I simplify these formulas?

I got these formulas from computation: ...
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2answers
63 views

How to solve system of equations with complex variables

I'm trying to obtain the solution to the following system of 3 equations and 4 variables: ...
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1answer
119 views

How can we obtain the imaginary part of a too complicated expression with Mathematica?

I would like to obtain the imaginary part of a long expression. All the parameters in the expression are real. Moreover, X and Y are positive. I have used ComplexExpand and tried to simplify the ...
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3answers
2k views

Why doesn't Mathematica know the exact value of some trivial trigonometric functions?

The trigonometric functions for half angles have well-defined and simple rules. For example $$\tan\left(\frac x2\right)=\frac{\sin x}{1+\cos x}=\frac1{\csc x+\cot x}$$ But I can't get the exact value ...
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65 views

How to use an option of FullSimplify on Mathematica or something similar

I solved an equation and now I have this solution but I want to have everything more simple or at least just on Arc or Log! but I can't make them more simple! ...
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0answers
44 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 ...
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0answers
90 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 ...
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0answers
61 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 ...
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56 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: ...
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0answers
57 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 ...
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1answer
52 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 ...
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1answer
101 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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2answers
51 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
878 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
58 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
38 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
127 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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1answer
97 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
193 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
71 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
147 views
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0answers
64 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
99 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
120 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
63 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
92 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
135 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
72 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
32 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
54 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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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
191 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
63 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
29 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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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
61 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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21 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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1answer
140 views

Elliptic Integral simplification

Integrate[Sqrt[(roh^2 - r^2)/(r^2 - rb^2)], {r, rb, roh}, Assumptions -> r > rb \[And] roh > rb \[And] roh > 1] Outputs to: ...
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62 views

How to simplify expression

What are some ways to simplify the following expression? ...
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0answers
54 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
62 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
35 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
44 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
511 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
64 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
65 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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