Questions tagged [simplifying-expressions]

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

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3answers
99 views

Simplify expression by a known expression substitution

A bit complex than a similar question, below is a minimal example, eqs1 = a b x'[t]^2 - ac x''[t] eqs2 = x''[t] - b x'[t] - c == 0 I want take ...
-1
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1answer
58 views

Simplifying multiplies of sums into a single double sum

I have the following expression: Sum[x^n, {n, 1, Infinity}]*Sum[Log[m, x], {m, 2, Infinity}] How can I Force Mathematica to write this expression in the following ...
-1
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0answers
30 views

Calculating an unsimplified expression containing derivative of an expression which is substituted instead of a function

I have the following expression: Derivative[0, 1][Integrate[E^(-(n*\[Tau]) - I*k*y*Cosh[\[Tau]])*B[\[Tau]], \[Tau]]][x, y] which is created by substitution of a ...
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1answer
28 views

Simplifying an equation in which all the terms are integrals with respect to the same variable

I have an equation in the following form: Integrate[A[x], x] + Integrate[B[x], x] == Integrate[C[x],x] How can I simplify this equation to get: ...
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0answers
31 views

Simplify including dim of matrix as parameter

I want to check that an identity about matrix is true for all dim n. My idea is to view dim n as a parameter and then Simplify the expression. For example,I hope <...
-1
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0answers
38 views

Substituting a two term expression with two rule on one variable with which each of the rules simplify one of the terms

I have two expressions as follows: r (Sin[t]+Cos[t]) and the rules for simplification are: {x == b + x Cos[t], y == r Sin[t]} ...
2
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2answers
146 views

How to express Bessel Functions in terms of Hankel Functions

I have the following expression BesselJ[\[ImaginaryI]*m, k*r] FunctionExpand knows how to transform from ...
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2answers
41 views

Rearrange the parts of formula expression

Below is a minimal example, D[k[θ[t]]*θ[t] == θ'[t], t] // TraditionalForm Output is $$ \theta (t) \theta '(t) k'(\theta (t))+k(\theta (t)) \theta '(t)=\theta ''(t)...
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2answers
51 views

Compare the coefficient in same part of the equations

I want to use Mathematica to do certain calculations. Below is a minimal example, my goal is to solve the equations that result from comparing the coefficients of both polynomials ...
0
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0answers
52 views

Why does Wolfram alpha not understand, that following statements are True? [closed]

Why does Wolfram alpha not return True for following inputs ...
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1answer
57 views

Forcing mathematica not to substitute some terms in an expression

I have an expression c which should be defined before the function and a function f defined as follows: ...
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4answers
41 views

Simplifying an equation by factoring the current coefficients in order to substitute a new coefficients

I have an equation in the following form: a*x + b*y + c*z == d I want to substitute the following constants instead of a,b,c,d: ...
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2answers
52 views

How to help Eliminate simplify simultaneous equations

I have a set of three moderately simple simultaneous equations that I'd like to simplify and eliminate a set of variables for (this is a simple example of a more general class of problem - but I'd ...
3
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1answer
217 views

How to simplify only one side of an equality?

Suppose we have two expressions and == between them. I want to simplify only the right-hand side. What should I do?
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1answer
130 views

How do I avoid the singularities during the calculation of an integral?

I face a serious problem when I try to calculate the following integral. My code is the following: ...
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0answers
51 views

How to evaluate simplify an expression containing derivatives

I have an expression that is a derivative of order 2. I want to assign value to derivatives of orders lower than 2(e.g. the expression itself) which should cause the derivatives of higher order become ...
0
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0answers
32 views

How to simplify half integer gamma functions using ComplexityFunction?

There's a similar question already: Replacing gamma at half integers by double factorial But I wanted to be able to simplify expressions like the following using ComplexityFunction. Equation Source ...
0
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0answers
36 views

How to find all the tree leaves of an expression?

I'd like to better understand what mathematica is doing during simplification, so I tried expression //TreeForm //TreeLeaves to see what it's picking up on. Except ...
4
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1answer
89 views

Cos[sqrt[-x]] == Cosh[sqrt[x]] but not Cos[sqrt[-(x+y)]] == Cosh[sqrt[(x+y)]]?

I have trouble with the following apparent contradiction: ...
1
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0answers
36 views

Simplifying the following expression?

Continuing from this question: How do I simplify the equilibrium point to this simplified expression? We found our equilibrium points. We also define $$\mathcal{R}_0= \frac{[\beta_1 b_3(\epsilon p+b_1(...
1
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1answer
37 views

Simplify function with condition not working [duplicate]

I try to simplify the function Q below: Q[x_] := Sign[x] /; x > 1 Simplify[Q[x], Assumptions -> x > 1] (*return Q[x]*) But it doesn't work. However, if I ...
2
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2answers
212 views

How do I simplify the equilibrium point to this simplified expression?

Install the following package: ...
0
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1answer
43 views

How to remove Wrong relations after LogicalExpand?

I have a complex relation which I need to expand and represnt it clear and nice. So I used LogicalExpand (LE). I know LE does only the simple expansion and nothing further. but it creates some wrong ...
0
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0answers
32 views

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
59 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: ...
1
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1answer
113 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 ...
8
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3answers
1k 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 ...
0
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0answers
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
43 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 ...
3
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0answers
87 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
57 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
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0answers
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: ...
1
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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 ...
1
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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 ...
1
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1answer
100 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
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2answers
50 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
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5answers
874 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
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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 ...
1
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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 ...
2
votes
2answers
124 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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1answer
96 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
167 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
70 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
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2answers
147 views
0
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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 ...
1
vote
1answer
98 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
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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 , ...
4
votes
2answers
116 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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