# 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
Filter by
Sorted by
Tagged with
60 views

### 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 ...
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): $$\sum_{i=1}^{n-k+1} i \binom{n-i}{k-1}$$ ...
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)...
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 ...
85 views

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] ...
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; ...
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 ...
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 ...
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 ...
48 views

### How to simplify Log expressions using rules

I have the following expression, ...
53 views

### Possible bug involving square roots simplifications?

I have the following code: ...
30 views

### Specify “Simplify” output to see steps

I have the equation: $$w=\frac{b(r+s)+\theta q(\theta) \lambda p}{r+s+ \theta q(\theta) \lambda } + \lambda \left(p - \frac{b(r+s)+\theta q(\theta) \lambda p}{r+s+\theta q(\theta) \lambda}\right)$$ ...
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., ...
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 ...
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 ...
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 ...
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 $(-\frac{1}{2},\frac{1}{2})$:- ...
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} ) ...
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: ...
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 ...
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. ...
61 views

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 ...
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. <...
60 views

### FullSimplify weird behavior

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

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

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