Questions tagged [simplifying-expressions]

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

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0answers
39 views

A question about simplifying

From basic examination, the following expression Integrate[Abs[a - x], {x, 0, n}] appears to simplify fully to 5 n - n a + a^2 ...
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1answer
49 views

Remove specific terms from Mathematica output

I have a very complicated output from Mathematica - which may run to several pages - and I want to keep only some of the terms. The expression I am working with is a double summation. It results in (...
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2answers
147 views

How do I write Sqrt[x] as x^(1/2)

Sometimes it is needed to keep the powers as the fractional form. However Mathematica tends to write x^(1/2) as Sqrt[x]. How do ...
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1answer
37 views

How can I get a matrix valued function to act like a matrix instead of a scalar?

A small example illustrating the issue: If p:={{1,0},{0,0}}; q:={{0,0},{0,1}}; a[t_]:=Piecewise[{{p,t<=0},{q,t>0}}]; And I then define ...
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1answer
37 views

Addition of matrices not working as intended with piecewise definition

A somewhat minimal working example: I define p:={{1,0},{0,1}}, q:={{2,0},{0,2}}, and finally ...
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2answers
108 views

Map a function at one "part" of each term in a multivariate polynomial

I have polynomials in several variables x[i] and y[j], and I am using First@SymmetricReduce@ ...
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2answers
507 views

Simplify 1+Sqrt[2]I-Complex[1,Sqrt[2]]

The expression 1+Sqrt[2]I-Complex[1,Sqrt[2]] should be zero. In fact, N[1+Sqrt[2]I-Complex[1,Sqrt[2]]] yields ...
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0answers
68 views

Result not simplified

The following script gives not the simplest result. What should be the right command to get the simplest result? ...
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0answers
73 views

How can I simplify a symbolic tensor expression?

My question is about simplifying tensor expressions. If I have $(a+b)\otimes (c+d)$ The function TensorExpand gives $a\otimes c + a\otimes d + b\otimes c + b\otimes ...
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2answers
170 views

How to check linear independence

I want to check linear independence in Mathematica. But I don't know to how to use this. My question is as follows: I want to check whether $\sin (m \pi x) \sin (n \pi y)$ where $m, n =1,2, 3 \cdots$ ...
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0answers
43 views

Binomial Expansion on Mathematica [duplicate]

Why when I typed Expand[Binomial[m-1,6]], it gives me Binomial[-1 + m, 6] instead of ...
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1answer
102 views

How to Simplify safely

Mathematica often writes simplied expressions with -1 first followed by any variables (eg. -1+x). However I want to write it as ...
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1answer
55 views

Integration shows RootSum and really long expressions

I am doing this integration and when I use $C_\alpha(T)$ as just constant numbers(...
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1answer
72 views

limit of an expression including BesselK function

i want to calculate the limit of the following expression when 'w' tend to zero. I have used the Limit function, it takes a lot of time for running without any result. could you please help me how to ...
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5answers
1k views

Calculating commutators in quantum mechanics symbolically with the help of Mathematica

Say I have a hamiltonian $H=p_x^2+p_y^2+x^2+y^2+x^4+y^4$, and I want to calculate the commutator $\left[A,B\right] \equiv AB-BA$ of arbitrary operators $\mathcal{O}=x^ap_x^by^cp_y^d$, where $a,b,c,d\...
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0answers
50 views

Problem in FullSimplify with assumptions:

For the vector $\psi = \{ 0,F1,\alpha ,0,\beta ,0,0,F2\} $, I am trying to simplify ${\left\| \psi \right\|^2}$ where $\alpha = \cos (\theta )$, $\beta = \sin \left[ \theta \right]$, $F1 = {{\cos ...
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0answers
57 views

Reduce only generically correct?

While it is clearly said in the Mathematica documentation that functions like FullSimplify yield only 'generically correct' results, I have found no mention of such restrictions for Reduce. However, ...
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2answers
100 views

Mathematica not Simplifying?

The function ...
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0answers
76 views

How to sum the KroneckerDelta[] in equation?

How to sum the KroneckerDeltas in following equation? k, p1, ...
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0answers
78 views

Exponent combinations

How can I have Mathematica represent the product of two different bases and exponents as a single power (where possible)? For example, see the product below can be expressed below: ...
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0answers
51 views

How can I use a replacement rule as part of a simplification?

I am using Mathematica to symbolically calculate the likelihood for a simple linear regression model. As part of this I want to substitute ...
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1answer
205 views

Is it possible to combine the following pattern?

I want to simplify the following pattern Cases[Permutations[Range@3], {___, 2, 3, ___} | {___, 3, 2, ___}] into something like (but it does not compile). ...
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1answer
50 views

How to continually simplify derivatives of function defined in a system? [closed]

For example, if I input something like b'[t_] = a[t]; a'[t_] = -Sin[b[t]]; a''[t] it outputs just a''[t]. Is there a way to ...
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2answers
180 views

Conjugation with real elements

Suppose I have an expression, such as A = 5 t^2 + 3 t + 4; I want to define the variable t to be real, therefore I can write ...
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1answer
43 views

Exponents manipulation

When I type(a^2)^s Mathematica does not give me $a^{2s}$ instead it gives ${(a^2)}^s$. Is there a way to make it print $a^{2s}$. It made some real difference where ...
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1answer
122 views

Pushing Mathematica's FullSimplify to a global complexity minimum

Original: Is there any way to control Mathematica's inner simplification algorithm? I have seen several instances where FullSimplify does not yield the most optimal ...
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1answer
72 views

Derivatives of trigonometric functions

Let's use the following sample case Clear["Global`*"]; t1 = ArcTan[y/(x - x1)]; f = (3*(Cos[t1])^2 - 1); der = D[f, x] which gives ...
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0answers
29 views

TimeConstrained with absolute timing

Due to backwards compatibility issues, I am using Mathematica 8.0 and it seems to have an issue with TimeConstrained. I am using this function to set a limit to the ...
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0answers
28 views

Directed Infinity vs Indeterminant in this output

When I evaluate ...
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2answers
63 views

How to find the max of two functions?

Suppose I have a parametric function like f(v)=max{v-x,-y} where 0<=v<v_max, and ...
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3answers
258 views

How to simplify one side of an inequality with a lot of square roots that are the same

Mathematica seems to refuse to simplify the following inequality, even though it is obvious there are things that can be done ...
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1answer
43 views

Simplifying expression

I have the following expression: (1 - a) (H - 3 L*r + L) and I would like to `simplify' this to (1 - a) (H - L(3 r +1)) I ...
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2answers
62 views

How can I use FullSimplify output in function construction without having to re-FullSimplify? (Doubts about my workaround)

I have an expression that I want to use in a function definition. For concreteness let's take Gamma[k + 4]/k!. I know this can be simplified to ...
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2answers
119 views

How to efficiently simplify using PowerExpand

I am tying to simplify the following expression using Simplify, FullSimplify, Expand and <...
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0answers
33 views

How to make the variable on the lhs stay after eliminate?

I had a following list of variables, {x''[t] == -x[t]+x'[t], x'''[t] == -x'[t]+x''[t], x''''[t] == -x''[t]+x'''[t]} after performing Eliminate to simplify the ...
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0answers
41 views

Check equality of two expression "With Conditions"

I want to check if these equation holds if only if $t>0$ $$\frac 1t\left(-\gamma+\operatorname{Chi}(t)-\ln(t)-\operatorname{Shi}(t)\right)=\frac 1t\left(-\gamma+\operatorname{Ei}(-t)-\ln(t)\right),\...
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1answer
45 views

Simplifying this relationship A*B + conj(A) conj(B)

How can I force Mathematica to simplify the $A B + A^* B^*$ relationship so that it takes the following form: $$ A B + A^* B^*=2Re[AB] $$
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1answer
78 views

Symbolic Integration with trigonometric functions

I have this trigonometric integral which takes forever to evaluate $\int dx \frac{4 \left(\cos \left(p_1 x\right)-\frac{\sin \left(p_1 x\right)}{p_1 x}\right) \left(\cos \left(p_2 x\right)-\frac{\...
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1answer
51 views

Simplifying expressions after expanding

I am totally new to Mathematica, so if this is a simple googleable question, I am sorry I have this expression: $\left(e^{i \text{p1} x}-e^{-i \text{p1} x}\right) \left(e^{i \text{p2} x}-e^{-i \text{...
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2answers
242 views

How can I compare two equations in Mathematica , to check whether they are mathematically same or not?

Let's say expr1= Sin x expr2 = e^x -e^-x/2j Now we know they are the same mathematically, how will I come to know expr1=expr2 and they are the same? Let's say I have these two equations and have code ...
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2answers
77 views

Simplifying Simplify[Conjugate[Sqrt[a^2 - b^2]], {a < b}]

How can one simplify the following Simplify[Conjugate[Sqrt[a^2 - b^2]], {a < b}] Edit: I want to add that in my case $a$ and $b$ are real and I expect ...
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0answers
25 views

Fullsimplify works on one, not the other

Exp[x] is less than 1 if x<0. Both of the following should simplify, only the first does. ...
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1answer
110 views

Is simplify giving a "not always" correct answer here?

A result like this appears as one of the terms when I compute coefficients in a Fourier Series: expr =(Sin[n*Pi])/((-4 + n^2)) If I simplify all my terms, this ...
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2answers
217 views

FullSimplify completely changes result

I have a function that when I operate FullSimplify on, produces widly different results depending on if the parameters are left symbolic or values are substituted ...
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0answers
71 views

How to assume a number to be a half integer?

For integer x $\left(\cos 2\pi x\right) ^2=1$ and I can check this as follows ...
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1answer
58 views

Understand a result of FullSimplify

FullSimplify[((Sqrt[5] - 1)/(2*2^(1/4)))*Sqrt[Sqrt[2]*5^(1/4) - Sqrt[Sqrt[5] - 1]]] returns ...
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2answers
79 views

Approaches to expression reduction

I am still learning how to use Mathematica more efficiently, but something that I keep bumping into is problems with it reducing formulas. Often, I'll ask it to compute a certain formula (take a ...
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0answers
73 views

Converting Tensor product to Matrix

I have a basic question regarding matrices and tensor product forms. Given $N > 0$, I am interested in the tensor product series $\sum_{i}^{N} X_i$, where $X_i$ is the Pauli $X$ spin operator at ...
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1answer
34 views

Perform Eliminate, Solve and Format at once in Mathematica

I have a series of equations where I use eliminate to get a new equation with desired variables. This equation is then solved for a specific variable and then the result is presented in a specific ...
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1answer
95 views

How to simplify the following integral to be in terms of Bessel functions?

I have evaluated the following integration using Mathematica. I obtained a solution in terms of Meijer G function. I wonder if it can be simplified to be in terms of Bessel functions. ...

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