Questions tagged [simplifying-expressions]

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

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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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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 ...
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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\...
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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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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 ...
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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 ...
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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: ...
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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 ...
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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 ...
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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 ...
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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'...
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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 <...
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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 ...
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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 ...
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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 ...
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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 ...
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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
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 ...
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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
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)} + ...
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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 ...
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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{\...
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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
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: $$\...
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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
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 ...
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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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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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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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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
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 ...
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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
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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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 ...
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60 views

How to simplify expression

What are some ways to simplify the following expression? ...
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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 ...
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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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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
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 ...
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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   $f(x,t)=t+x^2$...
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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 ...
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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 ...
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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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