Questions tagged [simplifying-expressions]

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

238 questions with no upvoted or accepted answers
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Simplify (or Reduce) a system of inequalities intelligently

I have the following system of inequalities of 4 real variables 3 (a + b) + 4 (d + c) > 0 && 2 (a - d) + 3 (b - c) > 0 The system can be written as ...
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64 views

How to evaluate $\sum_{i=1}^{n-k+1} i \binom{n-i}{k-1}$ to get $\binom{n+1}{k+1}$?

I evaluate the following summation using mma (Version: 11.2.0.0): $$\sum_{i=1}^{n-k+1} i \binom{n-i}{k-1}$$ ...
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105 views

Simplify expressions by automated substitution of repeated terms

I would like to know whether there is a way in Mathematica to simplify an expression including the introduction of symbols for repeated terms, like so: SimplifyWithSubstitution[(a+b)^7+(a+b)^3+(a+b)...
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79 views

How does Simplify resolve SimplifyCount ties?

The expressions a (b + c) + b c and a b + (a + b) c are equivalent and equally complex as measured by ...
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0answers
85 views

How to ComplexExpand Jacobi elliptic functions?

It seems that Mathematica cannot expand Jacobi $\text{sn}, \text{cn}, \text{dn}$ functions. For example, A&S 16.20.1-3 say that for real $y$ $$ \operatorname{sn}(i y \mid m) = i\operatorname{sc}(y ...
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142 views

Power Series Expansion of Infinite Product

I've defined a function which I call $F$ below, requiring an infinite product. Ultimately, the function $G$ I'm interested in is a finite sum of products and ratios of the infinite product function. ...
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72 views

How do I remove the symbolic GCD of an expression?

In an expression like expr = 2 g Pi - (2 I) G Pi - (2 I) Pi V0; obviously $2 Pi$ is some sort of symbolic GCD. In such a simple case I could eyeball it and ...
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391 views

Simplifying symbolic multiple sums

suppose I have a multiple sum with an unspecified number of indexes: $$\sum_{i_1=1}^n \ldots \sum_{i_k=1}^n x_{i_1}\otimes\ldots\otimes \hat{x_{i_j}}\otimes\ldots\otimes x_{i_k}$$ with $x_{i_j}$ ...
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207 views

Simplify large fractions

Hi i'm quite new with Mathematica and i'm experiencing some problems with Simplify and FullSimplify. I'm dealing with a sistem ...
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118 views

A better way to simplify with rules than this?

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85 views

Building a ComplexityFunction based on the size of the expression output

I am experimenting with the ComplexityFunction of Simplify and came up with this one: ComplexityFunction->Function[e,Rasterize[HoldForm[e],"BoundingBox"][[1]]] ...
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262 views

Problems with Simultaneous Equation Solving

Let me first explain what I am doing and then I will explain the problem that I can't figure out. I am basically trying to solve 2 equations for 2 unknowns (a1 and <...
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40 views

Simplification of expression under symmetry conditions

How to simplify the following expression: ...
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33 views

What options should I feed to FullSimplify to make it strongly prefer elementary functions?

I want that FullSimplify strongly preferred all elementary functions as opposed to all non-elementary. Can I do it?
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62 views

Find all pattern in expression

Consider this problem: I have a functional $\mathcal{F}$ acting on some function $n(t)$ such that $$ \mathcal{F}[n(t)]=0 $$ $$ \mathcal{F}[n^*(s)n(t)]=\alpha(t,s) $$ $$ \mathcal{F}[n(s)n(t)]=0 $$ ...
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49 views

Change a single letter changes the result

these two codes give different result. FullSimplify[a-b,Assumptions->a==1+y&&b==1+y-x] this give x ...
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40 views

Why does Mathematica miss some solutions for my integral?

When computing the integral of two orthogonal sine functions $\qquad \sin(n\,\pi\,x)\,\sin(m\,\pi\,x)$, where $n,\,m$ are integers > 0 Mathematica seems to miss the solution where $n=m$. I don't ...
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49 views

Efficient application of the fundamental theorem of calculus

How can the following definite integral be computed with Mathematica? $$ -\frac14\int_1^{\infty}\!\!\frac{\sqrt{-4 x^4-4 x^2 z-(y^2+z)^2}}{x (x^2+z)}\theta\!\left(-4 x^4-4 x^2 z-(y^2+z)^2\right)\...
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55 views

Assumptions with conditions

How does one specify the assumption that a function is real for real arguments? Compare Simplify[Re[I f[x]], Assumptions -> f[x_] ∈ Reals] ...
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53 views

How to get results in terms of vector operations?

Is there a simple way to simplify an expression in terms of vector operations? For example, when I evaluate this; ...
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31 views

Inverse fuction of TensorExpand

Is there a way in mathematica to factorize/simplify a dot product? I.e. I have something like a.b + a.c (obviously more complicated expressions) and I would like to factorize terms like ...
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74 views

How can I get Mathematica to recognize that $ab^* + ba^* = 2\Re(ab^*)$?

Mathematica understands that $z + z^* = 2\Re(z)$, FullSimply[z + Conjugate[z]] (* output: 2 Re[z] *) However, Mathematica does not simplify the expression ...
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37 views

Make a function invariant under a permutation of the arguments

The output of my current notebook contains expressions that look as follows (V[{k,q},{s,t}] + V[{-k, -q}, {t,s}]) In my specific application these two functions ...
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48 views

How to simplify Log expressions using rules

I have the following expression, ...
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53 views

Possible bug involving square roots simplifications?

I have the following code: ...
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30 views

Specify “Simplify” output to see steps

I have the equation: $$w=\frac{b(r+s)+\theta q(\theta) \lambda p}{r+s+ \theta q(\theta) \lambda } + \lambda \left(p - \frac{b(r+s)+\theta q(\theta) \lambda p}{r+s+\theta q(\theta) \lambda}\right)$$ ...
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64 views

Efficient evaluation of real/imaginary parts of long expressions

I have the following, rather compact, but complex, expression (see below). I simply want the real part of this. Now, when I do the usual, i.e., ...
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97 views

Finding general forms of sums in Mathematica

A general form can be obtained for some sums with binomial coefficients. Mathematica is able to find these general forms for some of the simplest sums. For others the output contains for instance ...
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1answer
95 views

Simplify rules with variable number of arguments

Problem How to simplify the following rules? The rules simplify (single, double, triple ...) summations of Kronecker delta. Replacement should occur if any summation and the Kronecker delta share an ...
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43 views

Expression simplified for explicit int values, but not with FullSimplify/FunctionExpand and Assuming. What formula does Mathematica use?

I have a $_4F_3$ hypergeometric function (Mathematica 11.3) HypergeometricPFQ[{1, 3/2 + n, 1 + 2 m + n, 1 + 2 m + n}, {2 + n, 2 + n, 3/2 + 2 m + n}, z] If I ...
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41 views

How to force the output to be in terms of a specific function?

I have a rectangular function rect[t], which is a window function with values of $ 1 $ in the interval $ (-\frac{1}{2},\frac{1}{2}) $:- ...
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117 views

Simplify rational function with removable singularity

In this example I consider a rational function f ( {n \[Element] Integers, n > 0, v \[Element] Reals, 0 < v < 1} ) ...
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104 views

“Simplify” or “Evaluate” an expression until it is expreseed in terms of some other variables

Let's say we have the following relation between different variables: ...
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59 views

Collect/Expand with D

I am new to MMA and have a basic question. I am trying to separate the derivatives of an expression for simplification. E.g. on doing ...
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101 views

Cauchy product (sum multiplication)

I want to apply Cauchy rule (attached) to the following. I tried but in vain to code it using Mathematica. Any help to define this rule is highly appreciated. ...
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61 views

How to convert Piecewise into KroneckerDelta form by FullSimplify?

The question comes from the last example of this topic in the Wolfram documentation. SeriesCoefficient[E^x^2, {x, 0, n}] However, my (v11.1) output is $\begin{...
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114 views

Simplify exponents

Consider the following expression Var = ( m^((a + b + c)/(3 n + j + d)) k^(a + b))^(f/(a + b)); Then, I take the ratio ...
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91 views

How to work out sums symbolically?

Intro Consider these two equal expressions of the variance $$\frac{\sum _{i=1}^n x(i)^2}{n}-\frac{\left(\sum _{i=1}^n x(i)\right){}^2}{n^2}$$ and $$\frac{\sum _{i=1}^n \left(x(i)-\frac{\sum _{i=1}...
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46 views

How to control pre-simplify (part 2)

For example, if you enter Reduce [a == 0 && x == Root [a * # ^ 3 + # &, 1]] The output is x == 0 && a == 0...
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170 views

Simplifying special functions in Mathematica?

This question is a continuation of another question of mine, in an attempt to gain more understanding on how to use Mathematica to simplify special functions. Consider the expression: ...
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86 views

Coefficients are extremely high

I'm currently doing eigenvalue decomposition of a function. The answer given by Mathematica contains strange coefficients, on the outside is a factor of 10^-11 and on the inside are several factors ...
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51 views

How to run the command 'Distribute' on large product of multivariable polynomials without simplifying it

I am new to Mathematica, so pardon if question is trivial. I am trying to expand (i.e multiply out the factors) an polynomial expression $d$, with many factors, obtained as a result of taking ...
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77 views

FullSimplify versus Reduce applied to set of inequalities

I have a complicated expression Expr describing a bunch of inequalities and I am trying to reduce it to a manageable subset that facilitates ready interpretation. I ...
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61 views

Solving this system of two algebraic equations

I'd like to find symbolically the common roots of two polynomial of second order in X and Y. Though this is not possible in general, with the present coefficients, MMA manages to output a result. <...
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60 views

FullSimplify weird behavior

FullSimplify gives me two different results for similar expressions ...
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83 views

Simplify an integer expression involving Ceiling and Root[] of third degree polynomial

I would like to simplify the following expression Ceiling[ToRadicals[Root[90 - 6 num + 65 #1 + 12 #1^2 + #1^3 &, 1]]] with ...
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45 views

When inequality exists, why variables are still complex number?

I remember when inequality exists, we can think variable is real number. Reduce[Exp[x] < Exp[3], {x}] Why this is not the case here. We need add Reals ...
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65 views

What prevents Factor from Working also on Arguments of Sqrt in Expressions?

Consider this example (intersection of a line and a sphere): ...
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103 views

Simplifying expressions containing derivatives of the assumptions

I want to Simplify expressions with terms like these: D[f[x,y],x]-D[g[x,y],x]+... but when i use ...
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54 views

Simplifying an exponent using a constant rule

How do I use mathematica to simplify an exponent by breaking it up into its constituents and setting one of them equal to a constant? For instance, E^(k - 1/x) ...