# Questions tagged [simplifying-expressions]

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

1,595 questions
Filter by
Sorted by
Tagged with
49 views

### Completely expand and simplify logical expressions?

Consider a logical expression such as expr = (a == b + q - w || c == d) && (q + c - d == w || e == r); I wonder if there is a function that would ...
44 views

### How to speed up xTensor simplification?

I need to compute a variation of the 4th rang symmetric tensor. I've written a code that successfully computes it, but when I use the resulting tensor to compute the second variation the ...
46 views

### FullSimplify not finding trig substitution with other terms present

Consider the following: FullSimplify[Cos[x - y - z] + Cos[x + y + z] + 1] Mathematica simply returns the exact expression with no simplification. However, if I ...
93 views

### Fullsimplify output depends on variable order

Bug introduced in 5.2 or earlier and persisting through 12.0 or later Mathematica 11.3.0.0 (used on a Mac) seems to give different results when using FullSimplify. ...
88 views

### Make assumption for function with variable argument

I would like to assume that a>t[b_] for any b, such that e.g. Simplify[a>t[c]]==True. ...
45 views

### Substituting variables in an equation

I wanted to see what would happen if I took ...
51 views

### Convert Part of an Expression Using ExpToTrig

I'm wondering if there's a nice way to convert only parts of an expression, say exponential functions of varible $\theta$ to trig. The motivation is best descripbed by the following example. ...
72 views

### Time spent on a transformation exceeded 300 when solving the optimization problem

I have the code which shows below to solve an optimization problem, but it will show that it's over the time constraint of 300 seconds. Is there anyone who could help me solve it. Thanks. ...
58 views

### How to show the sign of an algebraic expression?

I defined a long expression ...
99 views

### How to simplify a three variables expression with Simplify?

I want to calculate the value of $\nabla\cdot\frac{1}{(x^2+y^2+z^2)^{1.5}}(x\hat{x}+y\hat{y}+z\hat{z})$. I used the following syntax: ...
73 views

### How do I force this simplification?

I am trying to calculate:$$\epsilon_{ijk}n^iM1^j\epsilon^{lmk}n_lM2_m$$ Defining the vectors as: M1={M1x,M1y,M1z} M2={M2x,M2y,M2z} n={nx,ny,nz} and using ...
23 views

### Optimizing and Parallel Computing for Large Dyadic Intervals

I need help with the efficiency of my code i.e. less time so I can compute for large range of values. My function n[x] takes in a number x and outputs the ...
377 views

### How can I automate this tensor computation?

I am doing this work by hand, but it takes a lot of time and I make several calculation errors, so I was thinking to make Mathematica to calculate this for me, but I am stuck at the very beginning. I ...
63 views

### Simplify the cubic root of cube assuming real and positive variable

I know this is very simple but I couldn't find a reasonable solution for it in the archive. It seems that my Mathematica does not take into account the assumptions when it wants to simplify the ...
100 views

### Why are some of my assumptions ignored?

In my opinion Mathematica should be able to further calculate and simplify the output of G1[...]. ...
39 views

### Complex number manipulation

I want to simplify a complex expression like y * x * Conjugate[x] where y is a real number. Now mathematica is giving output as y x conjugate[x]. how can I get the answer as y abs[x]^2. "FullSimplify" ...
95 views

### Combining ArcTan's like in Maple

It seems to me there is no simple way to combine ArcTan's with complex arguments symbolically in Mathematica as it is in Maple (https://www.maplesoft.com/support/help/Maple/view.aspx?path=combine%...
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; ...
139 views

### How can I simplify a super long expression? [closed]

I am a brand new to using Mathematica, and currently using it for my thesis. Essentially I have a really long expression made up of lots of parameters. I am trying to reduce the size of the ...
58 views

### Factoring Algebraic Expressions [closed]

Say I have an expression $$x = L-(L-N)y^2(1+AB)$$ is there a way I can use mathematica to put the expression into the form $$x = M(1+\sigma B)$$ where $M$ and $\sigma$ are lumped terms?
31 views

### Sum over powers of roots of unity gives only partial answer

Mathematica seems to be unable to handle sums over roots of unity. For example, Simplify[Sum[Exp[2 Pi I a b/m], {a, m}], {b, m} \[Element] Integers] yields ...
32 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 ...
37 views

### FullSimplify does not simplify at all

I have some problems simplifying things with FullSimplify. Suppose a matrix ...
469 views

### How can I simplify $\lim_{n\to \infty } \, \int_0^n e^{-x} \left(1-\frac{x}{n}\right)^n \, dx$?

How can I simplify $\lim_{n\to \infty } \, \int_0^n e^{-x} \left(1-\frac{x}{n}\right)^n \, dx$ ? Limit[Integrate[(1 - x/n)^n/E^x, {x, 0, n}], n -> Infinity] ...
53 views

### Finding closed forms for various addition laws on elliptic curves, FullSimplify fails even with assumptions?

I would like to get Mathematica to do some tedious algebra for me, but I have been unsuccessful so far, and I don't know whether I am not using it correctly or whether it is simply not sophisticated ...
26 views

### Creating a function in which certain conditions exist

I am trying to create a function for which it is known that certain conditions exist on the argument. I want this to be a simplified version of the function. For example, if I wanted to create a ...
94 views

### FullSimplify doesn't know simplify an obvious expression

expr=(2 (x1-x3) (x2^2-x3^2+y2^2-y3^2)+2 (x2-x3) (-x1^2+x3^2-y1^2+y3^2))/ (4 (x3 (y1-y2)+x1 (y2-y3)+x2 (-y1+y3))); Through[{Simplify,FullSimplify,Cancel}[expr]] ...
37 views

### Interesting output in Integrate [closed]

I found interesting behaviour, best illustrated in the following example. When trying to evaluate Integrate[1/(d^2 - 1), d] Mathematica 11.3 gives the following ...
104 views

### Simplify $w^{3n}, w^{6n}, w^{3 + 3n}, w^{4+3n}$, etc. using $w^3=1$

I having an expression containing terms that are powers of $w$. How can I simplify these terms using the assumption $w^3=1$? ...
55 views

I have ...
47 views

### Mathematica doesn't evaluate/simplify arithmetic expression in its output [closed]

I have two matrices, A := {{1, 2, -4}, {2, -2, -2}, {-4, -2, 1}} and ...
97 views

### How to simplify an expression by substitution?

Sometime Solve and DSolve give a finial form of the solution, which is fine in may applications. However, in some cases, one may ...
68 views

### Computing Definite Sums of Rational Functions

I am attempting to compute a rather complicated sum, $S_n$, that in the end satisfies the relation $(S_n + T_n) = (\frac{(n+1)^2 - 1}{n+1})m^3 + O(m^2)$. I should note that $T_n$ is also unknown. ...
67 views

### Simplify multiple summations involving Kronecker deltas

Sorry if this has been asked before, but I couldn't find a specific answer to it. These work, i.e. they simplify: ...
60 views

### Why is this false? [closed]

In:= TrueQ[Gamma[2 z] == (2^(2 z) Gamma[z] Gamma[z + 1/2])/(2 Sqrt[\[Pi]])] Out:= False Can someone explain why the ...
1k views

### Why does Sin[b-a] simplify to -Sin[a-b]?

As I understand it, Mathematica often uses alphabetical order when simplifying expressions. For example, b-a simplifies to -a+b. ...
80 views

### Summation and product term expressed in Mathematica [duplicate]

I have the following term which I would like to express correctly in Mathematica: $$\sum_{i=1}^{m}\frac{1}{\prod_{j=1,j\neq i}^m(\rho_i-\rho_j)}$$ This means that for $m=3$ for example you should ...
43 views

### On simplification of polynomials in several variables

Let us consider a polynomial expr = Expand[(x - 2*y + 1)^9 - x*(x + y)^8]; Mathematica does her best, simplifying it by ...
139 views

### How to write down a product with omitted terms?

I have the following term which I would like to express correctly in Mathematica: $$\prod_{j=1,j\neq i}^m(\rho_i-\rho_j)$$ Can you please help?
65 views

### FullSimplify does not work well (require answer in terms of a particular variable)

(new to Mathematica) I am trying to simplify the Schwarzian derivative of f w.r.t. u.(In). Here f is prime of Weierstrass function (In) which has some constraints (In) ...
46 views

### Reduction of certain trigonometric functions

There is a trigonometric function: Cos[m x]^2 Cos[n y]^2 Sin[m x] Sin[n y] I want to transform it to the next form: ...
149 views

### How to simplify (square) roots in expressions?

e.g. it doesn't notice Sqrt[9 C^2 + 8 w^2 - 3 C Sqrt[9 C^2 + 16 w^2]] = (-3 C +Sqrt[9*C^2 + 16*w^2])/Sqrt The only way I found so far was doing it myself via ...
97 views

### Simplify the equation in terms of function and coefficients?

I have two fourth order differential equations and eight boundary conditions. I want to get my result in terms of function (Y) and coefficients (let say P1, P2 and so on). I used Dsolve to get the ...
34 views

### TensorReduce causes “inhomogeneous dimensions” error [closed]

I want to use TensorReduce to realize the following property of wedge: ...
40 views

### Finding common terms in an expression to simplify further? [duplicate]

Writing a big expression into one line is always hard. I usually simplify the expression further by manually finding some common terms (numerator and denominator) and give it some name. However, this ...
90 views

### Keeping specific terms in Mathematica output

Update: After solving an equation I came up with a complicated expression, is it possible to only keep some specific terms of an expression ? As an example, if the expression is: How can I keep only ...
37 views

### FindRoot for a transcendental function (PolyLog)

I am trying to solve an equation involving polylog using FindRoot, I am not sure how to give the initial guess as I want to solve the equation for a variety of parameters. Here is my code: ...
34 views

### Kernel crash when simplifying piecewise function

So the kernel appears to just die whenever you try to simplify a piecewise function containing "Nothing". For example: this appears to kill the kernel \text{Simplify@}\begin{array}{cc} \Bigl[\...
### How to simplify $(x^{1/y})^y$?
I would like Mathematica to be able to simplify the expression $\left(x^{1/y}\right)^y$ to $x$. However, running Simplify[(x^(1/y))^y] does not accomplish the ...
### 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 ...