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

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40
votes
4answers
3k views

Can I simplify an expression into form which uses my own definitions?

This seems like a simple thing to do, but I couldn't find anything relevant from Mathematica documentation. So suppose I have an expression: a*b/(a + a*Cos[a/b]) ...
1
vote
1answer
54 views

FullSimplify fail with general assumption

Assume I want to simplify this: -a^(-1) ** b^(-1) + (b ** a)^(-1) given assumption: $\frac{1}{b\_\text{**}a\_}=\frac{1}{a\_}\text{**}\frac{1}{b\_}$ Then it ...
10
votes
1answer
274 views

How to prevent simplification?

I have a question about the concept of simplification. I want to explain it with an example. When I write $4/8$ in mathematica, output is 1/2. How can I return ...
3
votes
3answers
132 views

How to obtain this expression in terms of real functions

I know that this expression (2 (ArcCot[E^(-((I ϕ)/2)) r] + ArcCot[E^((I ϕ)/2) r]))/π is real, because is the sum of a real series, in particular: ...
3
votes
3answers
447 views

Simplify big numbers in a second order equation

How can I simplify big exponents like $10^{39}$ in the solution of a second order equation: ...
0
votes
0answers
53 views

Handling Inequality with condition

I have verifying inequality using Mathematica using Simplify command For Example I want to check whether inequality a<f ...
0
votes
1answer
36 views

Complex number simplifications

My Mathematica notebook is not simplifying some expressions which do look trivial. I mean that one of my outputs contains: ...
0
votes
1answer
37 views

Option for Simplify command in mathematica

What does Simplify[%[[1]], %[[2]]] mean in following code? I mean [[1]] and [[2]] exactly what does refer to? ...
1
vote
2answers
83 views

Double sum in mathematica

It may look like a stupid question, but I was really confused by how double sums works in mathematica: After simplification, the function actually has nothing to do with n2? Also, when I manually ...
0
votes
1answer
55 views

Simplify assuming $x$ is small [closed]

I would like to assume that $x$ is small so that values of the order $x^2$ (and higher orders) are negligible. For example, I would like Mathematica to return $1-2m$ when I ask it to simplify $(1-x)^...
4
votes
2answers
604 views

Simplifying expressions involving Sum

I am trying to use Mathematica to simplify a symbolic expression involving Sum. The expression is defined as follows: ...
0
votes
3answers
60 views

how to take complex conjugate of a real variable

I have a function defined as follows: g[θ_] := 1/k (Exp[-I δ0] Sin[δ0] + 3 Exp[I δ1] Sin[δ1 Cos[θ] + 5/2 Exp[I δ2 (3 (Cos[θ])^2 - 1)) and I compute ...
1
vote
2answers
49 views

Simplify Expressions used to define Region

For example, RegionPlot[{x + y > 1, x - y > 1, y - x > 1, -x - y > 1}, {x, -2, 2}, {y, -2, 2}] can be somehow written as: ...
2
votes
1answer
101 views

Mathematica doesn't know about the absorption identity? [closed]

The well-known binomial absorption identity states that $$n\binom{n-1}{k-1} = k \binom{n}{k}$$ However, Mathematica gives ...
0
votes
1answer
52 views

Inverse of a Fourier matrix [closed]

I am trying to find the inverse of a Fourier matrix but I am getting confusing results. If R is a Fourier matrix, then ...
0
votes
2answers
106 views

Solving recursion relation from power series

I am interested in solving differential equations in the form of power series. Let's say we have following equation: $$f^{\prime \prime} (\rho) + \left( \frac{2 e^{-k \rho}}{\rho} - \varepsilon \...
8
votes
2answers
144 views

Collect/Factor a fraction

Is there a way to tell Mathematica to factor things only containing a specific combination of a fraction, example: $$\tag{1}f = \frac{a+m\cdot a+b+n\cdot b+c+k\cdot c+d+e}{ab}$$ Is there a way to ...
0
votes
0answers
50 views

Force expression in certain form

Is there a function in Mathematica to force an expression to be transformed into a given form. For example f[x] is a function of ...
2
votes
4answers
93 views

How to fix unsimplifed Sqrts?

The following code produces two values for the variable p. But the results contain Sqrt[k^2]. This should just be reduced to k, because the sign ambiguity is ...
1
vote
0answers
57 views

Output in FunctionExpand for function of Gamma

I used of this code: α Gamma[α] // FunctionExpand and get output: Gamma[1 + α] Also I used of this code: ...
0
votes
1answer
51 views

Two Variable First Order Approximation [duplicate]

I found that using Series and Normal command, I am able to approximate the first order of x or y, but If I also get rid of x*y (cross term), Series command does not work any more. Let's define some ...
3
votes
0answers
71 views

Can Mathematica reliably determine the equality of any two constructible numbers?

A constructible number is any number which can be expressed with only natural numbers and the operators $+$, $-$, $\times$, $/$, $\sqrt{}$ (square root only). Is Mathematica's ...
1
vote
1answer
388 views

Collect and simplify both the coefficents and the matched patterns

(This is a far tighter version of a previous question I asked) The problem with Collect is that while Collect[exp, pattern, Simplify] will simplify the coefficients,...
2
votes
0answers
45 views

How to remove parentheses from algebraic expression? [closed]

Suppose I have an expression like $x+x+y(x+y(x+y))$. I used Simplify command and get $y^3+x(2+y+y^2)$. How to remove parentheses to get every summand explicitly? $$...
3
votes
2answers
189 views

How can I get Mathematica to simplify this i * sqrt expression

In[11]:= FullSimplify[I Sqrt[-1 + w^2], Element[w, Reals], Assumptions -> 0 <= w <= 1] Out[11]= I Sqrt[-1 + w^2] Is it possible to have Mathematica ...
2
votes
2answers
57 views

Expanding and simplifying expressions

I have some complicated expression, for example: (-a^3 (-1 + b^2) - 3 a b^2 (2 + b^2) d c)/(b^2 (d c)^(3/2)) All variables are positive. I want to expand it and ...
3
votes
1answer
101 views

Simplifying a complicated expression (with no variables)

I am trying to obtain some exact analytical results without resorting to numerical approximations, and I ended up with a pretty huge expression that Mathematica is really struggling with. It has no ...
-1
votes
2answers
104 views

linear system equation ( trying to solve ) [closed]

I am trying to solve this system 3.7 x1+51.5 x10+71.3 x11-84. x2-16. x3-57.7 x4+89.7 x5-54.9 x6-85.8 x7+57.8 x8-51.3 x9==-36.8 -86.3 x1+5.7 x10-0.2 x11-39.9 x2+52.6 x3-45.6 x4+78. x5+90.7 x6-86.2 x7-...
-1
votes
2answers
109 views

Square root of a square root [closed]

Calculate square root of: Sqrt[3] Sqrt[3 - Sqrt[5]] (Sqrt[15/2] + Sqrt[3/2]) The response of the square root is 6. Edit: Can anyone go? http://prntscr.com/...
0
votes
2answers
57 views

Put a trigonometric equation in the form A*cos(theta)+B*sin(theta)+C=0 [closed]

eq = (Cos[Θ[t]]cf - Cos[γ1[t]] mf + Cos[γ2[t]] mf)^2/cf^2 + (Sin[Θ[t]]cf + Sin[γ1[t]] mf - Sin[γ2[t]] mf + xP1[t] - xP2[t])^2/cf^2 Can you help me to simplify and ...
7
votes
0answers
83 views

Need explanation on strange behavior of Simplify under given assumption

This is quite surprising to me. Simplify[a == b, {a == {1}, b == {1}}] a == b does not evaluate the equality, while <...
2
votes
1answer
93 views

How to estimate the running time of a programme on mathematica [closed]

I am solving a system of 6 linear equations containing six unknowns using mathematica. It is taking too much time and still running after 3 hours. can I estimate the approximate running time? Is there ...
3
votes
0answers
89 views

How to force Series[] to compute expansions by considering non commutative multiplication?

I wish to compute the Taylor series expansion of the following iteration method $x_{k+1}=x_k-f'(x_k)^{-1}f(x_k)$ up to four terms of error ($e_k=x_k-\alpha$). When this is a scalar iteration, I very ...
3
votes
1answer
58 views

Simplifying a trigonometric function with arctan

Why is this trigonometric expression with $\arctan$ not simplified ? ArcTan[Tan[γ[t] - θ[t]]]
0
votes
2answers
89 views

Expression of an integral

I am doing the following integral in Mathematica with $a>0$: $$\iint e^{-\frac{(x_{1}+x_{2}-2b)^2}{4a}}dx_{1}dx_{2}$$ My code is ...
1
vote
1answer
58 views

Using Collect to group derivatives together

Is there a way to combine derivatives that are a result from the product rule back together using Collect. For example, I'd like to collect x Dt[y,b] + y Dt[x,b] ...
2
votes
1answer
88 views

Getting wrong result when Integrating under an assumption [duplicate]

The simple integral $$\int_0^b \cos\left(\frac{2\pi m(y-\eta)}{b}\right) \cos\left(\frac{2\pi \eta}{b}\right)\mathrm{d}\eta$$ can be easily evaluated by Mathematica as, ...
0
votes
1answer
60 views

How to evaluate and simplify series expansions of long partial derivatives involving trigonometry?

I have 4 maps defined on a plane, i.e. on $\mathbb{R}^{2}$. Let's call them $F,G,H,J$. Let $(s,t) \in \mathbb{R}^{2}$. Define $F(s,t) = (f_{1}(s,t), f_{2}(s,t)).$ Likewise, in components, write $$ G(...
0
votes
0answers
31 views

Simplify expression?

Suppose I have expressions that involve terms like: p1.p1+p2.p2+p3.p3+p4.p4 p1, p2, p3, and p4 are all elements of an array: ...
6
votes
1answer
119 views

How to Collect a variable multiplied by a constant?

I'd like to use Collect to get terms that have a variable multiplied by a constant. For example I'd like: Collect[x + b x, b x] ...
1
vote
2answers
134 views

Express roots of quadratic equation in a specific form [closed]

By solving this equation, I got two roots as follows: Solve[1 + Subscript[a, 1]*s + Subscript[a, 2]*s^2 == 0, s] Is there a way to express it in the form below ...
6
votes
1answer
142 views

Faster way to perform SameQ[Reduce[…], Reduce[…]]

I'm have some expressions that I need to confirm the equality of. SameQ[Reduce[...], Reduce[...]] works like a charm for the more simple expressions, however when ...
25
votes
4answers
415 views

FullSimplify wrongly reduces expression to zero

Bug introduced in 9.0 and persisting through 10.4 I get the following output with a fresh Mathematica (ver 10.0.2.0 on Mac) session ...
4
votes
0answers
69 views

strange FullSimplify result, why zero? [duplicate]

This came up looking at this How to speed up calculation of this equation (FindRoot). Is there some sense to why FullSimplify gives zero here? ...
4
votes
2answers
123 views
0
votes
1answer
76 views

Simplify Re[z] in equation to more “natural” form [closed]

If you have a triangle in the complex plane with vertexes {a,b,c} (all complex numbers), the length of the altitude from A to the side BC can be computed as: ...
0
votes
1answer
112 views

Understanding the symbolic solutions of a system of differential equations

I'm trying to solve a simple system of differential equations but get outputs i just cant grasp, they seem way overkill. Someone said it might be because mathematica interprits the constants as non-...
3
votes
1answer
350 views

How to simplify to form without imaginary unit

I have an integral that I compute with Mathematica and as a result I get a seemingly complex expression (i.e. the expression contains the imaginary unit, $i$, at some places). However, if I try to ...