Questions tagged [simplifying-expressions]
Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
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How to find output response of filter circuit if transfer function is too complex?
I want to find unit step response of this transfer function. But I think, there is a problem, mathematica is not given any solution. Can anybody give me suggestion how to get the output response?
<...
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Simplify or FullSimplify doesn't work on Gamma function [migrated]
I have this expression:
Gamma[n - 0.691 + 2.35 I] Gamma[n - 0.691 - 2.35 I]
which returns real values for all $n$. However, neither Simplify nor FullSimplify can ...
user91875
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Can I define relations without explicit transformation rules?
Is there an alternative way to use Mathematica for symbolic algebra, where instead of defining explicit transformation rules into 'canonical form', I can instead 'gently inform' Mathematica about ...
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Series expansion using binomial theorem in Mathematica
The series expansion of $\displaystyle\left(1-\frac{a}{x}\right)^{1/3}$ using the Binomial theorem is given by
$$\displaystyle\left(1-\frac{a}{x}\right)^{1/3}=1-\frac{a}{3x}-\frac{a^{2}}{9x^{2}}-\...
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How to preserve the order of expressions in the asymptotic expansion?
I have a complicated expression involving logarithms.
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How to convince Mathematica to give zero instead of zero to some exponent [closed]
I was using some replacement rules when I got a surprising output. When I have the expression
(r - rm)^((-I m Sqrt[rm] Sqrt[rp])/(rm - rp)) /. r -> rm
I didn't ...
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Simplify complex conjugation and force joining of exponentials
I define the following piecewise functions.
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Subtituting kronecker deltas for products in simplification
I have a problem where I have some vector, $a = (a_1, a_2, \ldots, a_n)^T$ that I want to have a Kronecker delta multiplication rule, $a[i]a[j] = \delta_{ij}$ (these are basically basis vectors, but ...
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How to convert the result of the complete square form under the quadratic radical into the form of absolute value? [closed]
such as：
Sqrt[(c + a x0 + b y0)^2/(a^2 + b^2)]
How can we get the following results?
Abs[c + a x0 + b y0]/Sqrt[a^2 + b^2]
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How to get Mathematica to give me a specific alternate form? [closed]
I have a lot of equations of a form similar to
$$\frac{x(\frac{4}{3} + 4x^4)}{(x - \sqrt{\frac{2}{3}}e^{i\pi/4})(x - \sqrt{\frac{2}{3}}e^{-i\pi/4})}.$$
All of these equations can for non-zero ...
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How to print particular cases with Integrate?
I would like to perform the following simplification:
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Getting the terms containing rational exponents to zero in an expression
I have some expressions. For example:
expr=f[x]^(7/3) + 2*f[x]^(2 + 2/(3*n)) + f[x]
where n is an integer.
I want to get the terms containing rational exponents ...
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Expression of trigonometric function
I have a complicate expression with a lot of trigonometric functions. And I want to express the function just in the form of $\cos(\theta)$ and $\sin(\theta)$ instead of something like $\cos(2\theta)$ ...
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Simplifying an expression to a sensible conic section polynomial
I have an expression which represents an intersection of the unit sphere and a cone, projected to two-dimensional plane:
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Making an "unsafe" simplify that ignores the validity conditions of simplifications
Mathematica will never make assumptions you don't tell it to make, and will state all conditions under which the answers it gives are valid. While this is overall a good thing, this often leads to ...
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Simplify with equals; can't move terms from one side to another
I am doing symbolic manipulations to get some equations. After generating the equations I want to put them into a more readable form. I am doing this by hand; moving terms from one side of an equals ...
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Simplifying an equation over the domain of natural numbers
How can an equation like this be simplified in Mathematica where q,a,b,...
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Use two derivative rules and iterate several times to get the simplest expression of higher derivative
I have 2 rules of recursive relation of the derivative, I want to use it several times get the higher derivative on [\Theta] of ...
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What is the right way to simplify a tensor expression (with many indices, but no derivatives) in Mathematica?
After not finding the desired capabilities in base Mathematica, I am trying to use xAct`xTensor package. It appears that I do not need most of it capabilities ...
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FullSimplify does not simplify involving `ResidueSum`
Consider the following code involving ResidueSum:
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How to properly factorize expression with respect to specific combinations of terms?
This is something that I have never been able to properly do in Mathematica so I wish to learn how to do it once and for all.
I have the following expression in Mathematica:
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Simplifying $a_1^k\times a_2^{k+2}+a_3^k\times a_4^{k+2} \to a_2^2\times (a_1\times a_2)^k+a_4^2\times (a_3\times a_4)^k$
Consider the following expression that Mathematica returned me after a calculation:
Res=1/77 (-107 3^(1 + k) 7^k + 199 2^(1 + k) 49^k)
As you can see, Mathematica ...
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Evaluating a simple limit in Mathematica
Consider the function
$$M = \frac{\left[(f^{\prime})^2 - 2ff^{\prime \prime} - f^{\prime}_H~f^{\prime}\right]}{2f}$$
where $f \equiv f(r)$, and the primes are derivatives with respect to $r$. $f'_H$ ...
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Refine not able to simplify for PositiveReals
If I type in Mathematica
Refine[d^2 == a^2, {a ∈ PositiveReals, d ∈ PositiveReals}]
I get
d^2 == a^2
Why don't I get ...
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Checking if a sum of expressions is smaller than its upper bound?
Let \begin{equation} A+B+C+D \leq \frac{\Lambda}{\mu},\end{equation}
be always true.
Now, define the following:
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How to simplify an expression with simple symbolic integrations with the same boundaries?
I am new to Mathematica and I am trying to simplify an expression with symbolic integrals as below
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Prove linearity of integration [duplicate]
I'd like to prove the linearity of integration over one real variable ($x$).
Integrate[f[x] + b g[x], x] == Integrate[f[x],x] + b Integrate[g[x],x]
which I was ...
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How to give an approximation expression of a complicated expression using Mathematica?
I came across a very complicated expression as the first following picture shows, it makes normal processing such as coordinate conversion difficult, so I thought it would be nice to use an ...
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Why can't the denominator be rationalized for such a result?
The root formula of the output is rational for denominator, and the result of FullSimplify output is the same.
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Replace x + I y by z in complex expression
Say I define
z = x + I y;
Then I calculate
-2 Im[z] + 3 + I(2 Re[z]) // ComplexExpand
which gives
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Eliminate variable with partially documented Solve feature Solve[eqns,vars,elims]. Robust?
The Eliminating Variables section on Manipulating Equations and Inequalities documentation quotes an otherwise undocumented feature for Solve
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The different solution compare to the book solution?
On a book I found an integral with its solution I'm trying to solve it as well in Mathematica 13.2.0 but They are very different?!!!! If anyone can help it out!(integral : Sqrt[(3 x)/(x + 2 d)] d/(x -...
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How to calculate the integral only in real domain?
I have the following integral:
Integrate[1/(Sqrt[2] + Cos[4 X] + Sin[4 X]), X,
Assumptions -> Element[X, Reals]] // Simplify
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Collect with symbolic exponents does not simplify any further
I am trying to simplify a symbolic expression. Here is an example:
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Issue recognising Abs[w]*Sign[w]=w equality [closed]
Mathematica was unable to validate the first identity here, even though I believe it is correct, and even though it is able to validate the second one.
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How can I verify that the function $f$ and its simplified version are same?
I have the function $f=f(x,y,z)$ and rewrite it in the PolynomialForm and TraditionalOrder ; then, I try to verify the result by ...
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Collect and simplify coefficients of functions (Exp[a x])
I have a quite cumbersome expression in Mathematica and browsing through it I can identify that it could be written as
$$f(t) = A e^{a t} + B e^{b t}+ C e^{c t} ...$$
I wanted to be able to use ...
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How to convert this Root expression in to a normal algebraic form?
I need to convert this root expression in to a normal form
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Looking for the asymptotics of an asymptotics
I am trying to polish my second answer to this question in Mathematics Stack Exchange.
The problem is to find the asymptotics of $t$, solution of the implicit equation
$$\color{blue}{\left(1-2 x^2\...
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Simplify Expression with Positive and Negative Powers
I am trying to simplify expressions as follows
expr2 = a^(-2b)*c^(2b) * (a + b)^(-3e/(f + g))*(c + d)^(3e/(f + g))
which I would like to become like
...
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Is it possible to express the number $\;\arctan \left(\sqrt{7-4 \sqrt{2}}\right)-\arctan \left(\sqrt{4 \sqrt{2}+7}\right)$ in a compact form?
I obtained this number in Mathematica:
$$\text{number}=\arctan \left(\sqrt{7-4 \sqrt{2}}\right)-\arctan \left(\sqrt{4 \sqrt{2}+7}\right)$$
I would like to write it in a more compact form (if possible);...
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Trying to solve a 4D system that gives me an error: Equations may not give solutions for all "solve" variables
When I try solving for all other combination of states aside from q (like e,p,i) I am able to solve; however when I include q, I can a {}
Any suggestions on how I ...
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Finding the (symbolic) eigenvalues of a matrix with some assumption
I have the following 3$\times$3 symmetric matrix with symbolic entries.
Meff =
\begin{array}{ccc}
2 \beta \text{c12}^2 \text{c13}^2 \text{$\eta $11} \text{m1}+\alpha \text{c13}^2 \text{D31} \text{...
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How to get the real part of a complex function with some real coefficients?
I want to get the real part of the function n3[t] (see below) which is the solution to a differential equation.
Solve the differential equation. (Suppose ...
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FullSimplify-ing automatically
Is it possible to make Mathematica FullSimplify all expressions automatically? I am performing symbolic computations and I am trying to avoid writing ...
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Why does side relation work differently in these two cases?
I am not able to figure why this replacement using side-relation works in one case but not the other in the following
...
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Unexpected behaviour from Simpify with Complexity Function and Transformation Rules
While massaging an expression in Mathematica I get terms of the form $(-((-1 + z) z))^{-1 + \epsilon}$. However, $z$ is between $0$ and $1$ and thus I would prefer $((1 - z) z)^{-1 + \epsilon}$. Just ...
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