Questions tagged [simplifying-expressions]
Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
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2answers
26 views
Simplifying polynomials
I have noticed a strange behaviour in Mathematica regarding simplifying polynomial expressions.
Take the following polynomials
pol1=3-8s+4s^2
pol2=(2s-1)(2s-3)
...
5
votes
1answer
39 views
How to make Orthogonalize simplify each new vector before using it to orthogonalize the next one?
I'm trying to construct a set of orthogonal polynomials, starting from a specially-prepared initial polynomials:
...
0
votes
0answers
36 views
Mathematica cannot simplify this expression to trigonometric function
We are trying to simplify expression (-1)^(6/7) (1+(-1)^(2/7)), which is actually -2 Cos[π/7], using different methods. None of ...
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0answers
41 views
Simplify conjugate of square root of a positive function [closed]
I am trying to simplify the following conjugate expression with assumptions.
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0
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0answers
40 views
Integrating Logarithms [closed]
I am having trouble to understand why these two lines give different answers.
...
1
vote
2answers
61 views
Cancel opposite terms, and only that [on hold]
I have the following problem: I have a formula which looks like
$$A = \sum \frac{1}{p_1 p_2 p_3 \dots},$$
where the $p_i$ are linear expression in some variables X.
In the sum there are many opposite ...
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votes
3answers
47 views
Simplifying polynomial Roots with assumptions
I have acquired the following root from a minimization problem:
...
0
votes
1answer
53 views
Reduction of differential operators
Suppose my code outputs the expression
$$\frac{f^{(0,2)}(r,\phi )+r \left(f^{(1,0)}(r,\phi )+r f^{(2,0)}(r,\phi )\right)}{r^2}$$
This is simply the Laplacian $\nabla^2f(r, \phi)$. Is there a way ...
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votes
0answers
26 views
2
votes
1answer
50 views
Choose a branch cut using assumptions
I understand Sqrt function won't simplify expressions such as $\sqrt{x^2}$ unless there is an assumption that $x \in \mathbb{R}$. In my computation, I get an output containing an expression like this ...
0
votes
1answer
25 views
Simplify function with a derivative
This may be a very simple question: how can I substitute out a term involving a derivative in Mathematica?
I have the following derivative:
...
3
votes
1answer
94 views
“Smart” substitution of subexpressions
I have the following question.
An expression, which I want to simplify contains several subexpressions which appear quite frequently all over the place. To optimize simplification I would like to ...
0
votes
1answer
48 views
Compare algebraic equivalence (regardless of term order) without having to simplify? [closed]
I know that in order to find the equivalence of say $ a+b $ and $ b+a $, then:
FullSimplify[a + b == b + a]
is sufficient. However, suppose I want to compare ...
3
votes
1answer
47 views
Simplifying symbolic integration with trigonometric functions
I am using DSolve to verify a multitude of definite integrals I have done by hand, and things have gone perfectly until this integral,
$$ \int_0^t \frac{\mathrm{d}...
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votes
1answer
66 views
Simplify DSolve solution with products of square roots
The following code solves a simple 2nd-order linear differential equation with all real parameters.
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3
votes
3answers
84 views
DSolve returns incorrect solution by automatically assuming positive parameters?
The following code solves a simple 2nd-order linear ODE with real parameters $a,b$.
...
0
votes
1answer
39 views
Usage of simplify with If and Sum [duplicate]
I have a question related to this post I made : Why is the function assuming not taken in consideration?
Consider the following code :
...
1
vote
1answer
59 views
Why is the function assuming not taken in consideration?
In the following code, I assume that my variables are strictly positive. However, mathematica doesn't take this in consideration when it evaluates the If : the If is still in a non simplified form.
...
1
vote
1answer
56 views
How to judge whether a relation is true or false
$x$ is a real number, how to judge $x+1>x$ is true using Wolfram.
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0answers
61 views
Evaluate higher order derivative at some point under some assumptions
I need to evaluate the $k^{\rm th}$ order derivative
D[w[t] w'[t], {t, k}]
which is actually equal to
...
1
vote
1answer
72 views
why does this simple ratio of products not simplify?
Why does this ratio of products not Simplify to a[n]?
Clear[a,k,n]
$Assumptions={n>1}
Simplify[ Product[a[k], {k, 1, n}] / Product[a[k], {k, 1, n - 1}] ]
...
0
votes
0answers
33 views
How to perform delayed evaluation containing function with Mathematica
I was wondering whether there is a way in Mathematica to evaluate an expression in the most simple form, without any simplifying. For example if we define:
...
2
votes
0answers
38 views
Speed up Mathematica's Simplify and ComplexExpand functions
I am trying to simplify an expression and taking the real part only. However Mathematica use ages to run the command (if it is able to do so in the end). The problem is that the expression I am ...
2
votes
1answer
74 views
Fullsimplify with two Diracdelta functions
I am having a problem with the FullSimplify and DiracDelta functions. When I run the following line in mathmatica:
...
3
votes
2answers
104 views
Replace $ z z^* $ by $ |z|^2 $
I have a long expression involving different complex numbers. I want to force Mathematica to replace z Conjugate[z] by Abs[z]^2 ...
0
votes
1answer
30 views
PDE's numerical integration: simplify output: get rid of $[t,r]$'s and ${}^{(0,1)}$'s
When numerically integrating PDE's systems mathematica output can be chaotic and therfore time-consuming or even impossible to understand and use.
A major source of confusion are the $[t,r]$'s and ${...
0
votes
1answer
43 views
How can I simplify an Irrational Fractional Expression in Mathematica
The expression is:
$$\frac{4\surd3 + 5\surd2}{\surd48 + \surd18}$$
and its simplification is:
$$\frac{3}{5} + \frac{4\surd6}{15}$$
How can I perform such simplification in Mathematica?
1
vote
1answer
57 views
Can Mathematica factor out constrained functions when it simplifies? [closed]
For example, distributions in the exponential family take a likelihood function of the form $$f(x)g(\theta)e^{\phi(\theta)^{T}u(x)}$$. Given some ugly algebraic expression, can I tell mathematica to ...
1
vote
1answer
74 views
Simple case for FullSimplify doesn't work
Newbie question, couldn't find an exact dupe.
I'm expecting that with these assumptions
...
3
votes
2answers
57 views
How do you define a TransformationFunctions for Simplify?
I'm trying to change the form of some electrical engineering expressions. One transformation that can help add insight is noticing when two resistances are in parallel. The equation for this would be:
...
0
votes
0answers
27 views
Simplifying expressions: factorization: reverse distributive property
Is there any Mathematica of the type Factor, FullSimplify, etc. that fully reverses distributive property?
I mean, is there a simple way to turn the expression
$$ e^{x(t,r)}+e^{x(t,r)+y(t,r)}+e^{x(t,...
1
vote
2answers
39 views
FullSimplify applied to equations: not simplifying though apparently it should
I tried to Fullsimplify
$$ e^x(1-x)=0$$
to the equation
$$1-x=0$$
However the command
FullSimplify[E^x (1 - x) == 0]
just ...
11
votes
3answers
244 views
Simplifying Cosh[a] + Sin[a] + Sinh[a]
Why does FullSimplify[Cosh[a] + Sinh[a] + Sin[a]] not return Exp[a]+Sin[a]
?
Is this some bug in Mathematica or am I being ...
2
votes
2answers
71 views
FullSimplify Nested radicals
I'm trying to simplify this expression with Mathematica.
$\sqrt{2-a^2-2\sqrt{1-a^2}}, 0<a<1$
It can be simplified as
$\sqrt{1+1-a^2-2\sqrt{1-a^2}}=\sqrt{(1-\sqrt{1-a^2})^2}=1-\sqrt{1-a^2}$
...
7
votes
4answers
144 views
Simplifying simple signed expression ( such as $-x(x-1) \to x(1-x)$ ) based on assumptions
Context
I would like to simplify expression involving, say, (x-1) or (x^2-1) when I know that |x|<1 so that the global ...
3
votes
2answers
166 views
Simplify Derivative with Substitution
I try to evaluate:
$$ \frac{\partial}{\partial x} \log{u(x, y, z)}$$
Mathematica gives:
$$ \frac{1}{x+y+z}$$
I want to simplify the expression with my function:
$$ \frac{1}{u(x, y, z)}$$
How to ...
0
votes
0answers
32 views
Simplifying Wigner sums
Rotations of second rank tensors are common in quantum mechanics and Nuclear Magnetic Resonance theory. The sums can often be simplified into simplified real components, but when many sums exist, ...
1
vote
1answer
44 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 ...
1
vote
1answer
43 views
Make Mathematica apply the same rule exhaustively in simplification
Use Case
Mathematica evaluate the partial derivative as:
$$\frac{\partial}{\partial A_{abc}}\sum _{j=1}^J \sum _{k=1}^K \log \left(\sum _{l=1}^L A_{jkl} B_{jkl}\right) = \sum _{j=1}^J \sum _{k=1}^K \...
0
votes
1answer
44 views
Different solution on trigonometric function in mathematica and wolframalpha using Simplify and FullSimplify [closed]
I have this expresion:
-cos(a3) (cos(a2) sin(a1) + cos(a1) sin(a2))
And when I simplify with wolframalpha online, it give me this:
...
1
vote
1answer
58 views
Simplify sum of unnatural conditional functions generated by derivative
I try to use Mathematica to evaluate:
$$\frac{\partial}{\partial A_{abc}} \sum_{j=1}^{J}\sum_{k=1}^{K}\log\left(\sum_{l=1}^{L}A_{jkl}B_{jkl}\right)$$
I get:
$$\sum_{j=1}^J \sum_{k=1}^K \frac{\begin{...
5
votes
3answers
111 views
Simplify sum of Kronecker delta
The following simplification is correct:
$$ \sum_{j=1}^{J}\sum_{k=1}^{K} \delta_{a, j}\delta_{b,k}A_{j,k} = A_{a, b}$$
How to make Mathematica do that?
Try:
...
3
votes
1answer
58 views
Simplify and Sign working only in small expressions
I'm trying to find the sign of some very long expressions, but I don't seem to make it work using Simplify[Sign[...], Assumptions ...]. Here is an example of my problem. I can easily find the sign of ...
0
votes
0answers
63 views
Mathematica can't solve system of equations
I'm trying to solve an admittedly gnarly system of equations:
...
1
vote
0answers
35 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 ...
0
votes
2answers
39 views
Simplifying with restrictions on the whole expression
Suppose, for the sake of keeping things as simple as possible, that I have the following equation that I wish to simplify in Mathematica:
$y = x x$
But suppose further that I also have a restriction,...
0
votes
1answer
54 views
FullSimplify not simplifying expression containing the form Sin[n] where n is an integer [closed]
I have a function f[n] which give 0 for integer input, but FullSimplify doesn't work for it, why?
...
1
vote
2answers
86 views
Simplify product of complex numbers
I am trying to take product of a complex number with its conjugate. When I take
A*Conjugate[A] // FullSimplify
The output is as desired
...
1
vote
3answers
49 views
Eliminating radicals from denominator or numerator of an expression
I need to find the limit when r2 tends to r1 of the following expression:
...
4
votes
0answers
87 views
Integrate under assumptions
I am trying to solve the following integral:
$$\int_0^\infty u^{\sigma-1} \exp\left[-c u^\sigma\right] \mathrm{d}u$$
under the assumptions $\sigma \in (0,1)$ and $c>0$.
I know the result is
$$\...
