Questions tagged [simplifying-expressions]
Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
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Why do Resolve and ForAll fail with trigonometric expressions?
Why Resolve is not able to solve this problem? Similarly Solve and Reduce are not able to do ...
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Sum of sinusoids at the same frequency but with different amplitudes and phases
Three sinusoids at the same frequency are superimposed:
Cos[3.1 - t] + 5 Cos[π/4 + t] + 2 Sin[0.3 + t]
How can the resulting oscillation be stated in the following ...
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Strange result simplifying higher order BesselJ
Consider the following integral:
$$\int_0^1 Z_n^m(r)\ J_m(\rho r) r dr$$.
The solution of this should contain a single Bessel function:
$$(-1)^{(m-n)/2}\ J_{n+1} (\rho)/\rho$$ (see https://www.osti....
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Expanding Pochammer symbols/Gamma function for simplifying expressions
TLDR: How to expand gamma functions or Pochammer symbols in an arbitrarily long product?
Some context
I am trying to find out a closed-form expression for $\langle r^\alpha\rangle$ for the non-...
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Why can't Mathematica simplify $\left(e^{t/m}(gm)^{1/k}\right)^{-k}$? [duplicate]
It seems Mathematica can't simplify this
Simplify[(e^(t/m)*(g*m)^(1/k))^(-k)]
The result is
I think it should be
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1
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More intuitve way to simplify a simple expression involving two exponential factors
Is there a way to ask Mathematica to simplify expressions it generates, like:
$e^{-\frac{A t}{v^3}-\frac{v^2}{2 w^2}} \left(-1+e^{\frac{A t}{v^3}}\right)$
into a more readable form by taking out the ...
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Using Reduce to simplify (not solve) system of equations
I'm dealing with a Mathematica program that generates a set of coupled non-linear equations involving an unknown function and its derivatives with respect to at least one independent variable. My goal ...
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3
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Why does assuming f[_] > 0 does not work while Element[f[_], Reals] does?
Refine works with symbols in either way:
Refine[Sqrt[x^2], Element[x, Reals]]
(* Abs[x] *)
Refine[Sqrt[x^2], x > 0]
(* x *)
...
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PiecewiseExpand fails to address assumptions
PiecewiseExpand seems to ignore more complex assumptions. Here's an example:
...
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How to factorize $x+y$ in this kind of example?
Consider the following simple polynomial in two variables 5 + 2x + 2y. Suppose I want to simplify it to 5+2(x+y). I have no idea ...
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How to make ReplaceAll recognize what to be replaced in a situation like this?
I'm a bit confused on how ReplaceAll works. For example
ReplaceAll[2x+2y, x+y -> 1]
just gives ...
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2
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Simplify inverse of function
This would be a noob question, but I need help simplifying the inverse of an expression
...
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How to make MMA distinguish between symbolic coefficients and variables when doing factorization? [closed]
I what to factor a polynomial with complicated symbolic coefficients
Factor[p0^2 + k^2 r^2 \[Tau]^2 - 2 k p0 r \[Tau]^2 \[Omega] + p0^2 \[Tau]^2 \[Omega]^2]
In ...
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How to collect specific terms in an equation and set them to new parameters?
I have this equation
...
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Long outputs manipulation
does anyone know how to get the expressions of this shortened form? when I try to use "show all" my mathematica collapses
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Simplifying symbolic expression using replacement rules
I am trying to carry out a linear stability analysis of a two PDE system. I start by defining the equations and then define the perturbation along with the replacement rules required. I then use a ...
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How to force Mathematica to simplify in terms of half angles?
By basic trigonometric identities, the expression $\frac{\sinh(x)}{\sqrt{2}\sqrt{1+\cosh(x)}}$ simplifies to $\sinh(\frac{x}{2})$. But Mathematica seemingly don't perform this simplification. I tried ...
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RuleDelayed with Simplify?
I have the Rule
yRule = y -> Function[{l,m,x},x^(l + 1) Exp[-((2 I m)/x)] Hypergeometric1F1[1 - l, -2 l, (2 I m)/x] ]
Is it possible to replace and simplify ...
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Limit giving indeterminate result
I have a function $r_h(v)$ given by,
$$r_h (v) = \left(\frac{m_0}{2 g} e^{-g v_f} \left(-1+e^{-g(v - v_f)} \right) \right)^{1/5}$$
where $m_0$ and $g$ are just numbers. I want to take the limits of ...
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2
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How to simplify logical expression?
I would like to simplify
(a == c && c != 0) || (a == 0 && c == 0)
to
a == c
How can I do that?
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How Not to Simplify Exponential of Log?
I have the expression
Power[x,I y]
Both $x,y$ are real. Now I want to write this expression in term of Exponential of Logarithm. The expression can be rewritten as
...
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Evaluation gives different results before and after simplifying expression
I am trying to evaluate $h(z)=\frac{f(z)}{g(z)}$ at points $z$ close to 0. Here I have taken an example value of $z=\texttt{z1}=10^{-7}$ for demonstration. I notice that evaluating the fraction before ...
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How to prevent evaluation without simplification?
I am trying to compute a sequence of terms, which have a form similar to $g(z)$ at different points $z$. For $z$ close to 0, I have observed that the terms are evaluated as 0/0 (indeterminate form) ...
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Why doesn't Mathematica recognise two integrals as equal?
The following expression
$$\int_{0}^{t} f(t_0) \,dt_0 - \int_{0}^{t} f(t_1) \,dt_1 = 0$$
is zero because it is just a change of integration variable.
Why doesn't Mathematica give zero in this case?
<...
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Is it possible to get rid of the square root in the solutions of the following symbolic quadratic equation?
I have a quadratic equation, which I want to solve, but don't want the square root to appear within the solutions. I tried converting the discriminant into a quadratic form but failed, not sure if ...
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Is there a built-in expression transformation which can perform this simplification?
I have an interval overlap test like this:
...
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Converting expression to quadratic formula
I want to manipulate and represent the following expression in a more presentable way.
...
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Simplifying to remove all imaginary numbers
I have a purely real function (spec[w], where Im[spec[w]]=0), found through
...
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Attempt to find a solution (out of potentially many) to a system of equations with FindInstance runs forever or crashes
I have a system of equations that in principle should have a solution (I would think not a unique one), which I want to solve. I am not interested in all solutions; I just want to locate one, assuming ...
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Simplifying expressions with directional derivative
Suppose I have a function $f(x, y)$ which is differentiable everywhere (but not explicit). When I run a code snippet like:
...
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Strange behaviour of Simplify
MMA version 13.3
Can somebody explain the following behavior:
Here Simplify works as expected:
x1 e[1] + x2 e[1] // Simplify
(x1 + x2) e[1]
However, here ...
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Simplifying fraction containing Abs
The original formula looks like this:
Abs[(b x0^2)/(2 a) - (a y0^2)/(2 b)]/Sqrt[x0^2 + y0^2]
How to get:
...
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Simplifying products of DiracDelta
I want to simplify expressions containing DiracDelta products. For example I want to simplify the expression
$$\delta(z-2)\delta(k-5)\delta(t-z-k-9)$$
to give the answer
$$\delta(z-2)\delta(k-5)\delta(...
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Is there a way to get expressions to output in terms of Log2 instead of Log? [duplicate]
I'm in computer science, pretty much every logarithm I ever encounter is base 2.
Normally, Mathematica wants to convert every logarithm to the natural log Log, so ...
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Get a linear second order differential equation
This question may seems naive, but I still learn calculus: The following equation is a second-order differential equation, since it contains a derivative $h''$, but is it a linear differential ...
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Why would /. Expand rather than replace an expression?
I'm using /., Simplify, FullSimplify, etc. to simplify complicated solutions to a system of differential equations. Part of this is replacing certain expressions by Greek letters, e.g., ...
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Can I get Factor or another command to pull out common factors that appear only in subexpressions of very complicated expressions?
This follows a comment I posted earlier, to which I received several responses but which was then closed. I have used Simplify and FullSimplify with Assumptions to reduce down some very complicated ...
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Series expansion message with special functions
I am trying to expand the following expression in alp,eps. Since the expression involves Hypergeometric2F1, I am using HypExp.
<...
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How do I efficiently define rules for non-commutative algebras, (like differential forms)?
Defining rules seems to be quite troublesome, because whatever rule I make has to have the exact syntax ordering of the expression I want to modify.
For example,
take this differential form
...
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Conjugate symbol
Is there a way to make mathematica display Conjugate[z] as z* or something like that? It gets very verbose when there are multiple conjugates in an expression, it becomes hard to read.
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Don't understand reasons for error messages when trying to get elements of matrix
I am trying to simplify the seemingly very complicated inverse of a 4x4 matrix. "Simplify" resulted in something only somewhat less complicated. So yesterday I started simplifying the ...
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How can I get the determinant of an 8x8 matrix in a particular form?
I would like to get the determinant of a 8x8 matrix with symbolic representation to a particular form. When I used determinant and fullsimply to answer was too long and did not match the form I was ...
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Simplify a summation formula with known identity
I can calculate the formula:
$$\sum\limits_{i,j=0}^{m-1}\lfloor \frac{i\ n_1 +j\ n_2}{m}\rfloor$$
with Hermite identity:
$$\sum\limits_{j=0}^{m-1}\lfloor\frac{j\ n}{m}+x\rfloor=\lfloor m x\rfloor+\...
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How to group terms with the same exponential factor together after Expand?
ET[t] :=
E1*Exp[-I*w1*t] + E2*Exp[-I*w2*t] + E3*Exp[-I*w3*t] +
E1*Exp[I*w1*t] + E2*Exp[I*w2*t] + E3*Exp[I*w3*t];
THGExp[t] = ET[t]*ET[t]*ET[t]//Expand;
I ...
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Alternative to simplification speed-up by replacing an integer with its "non-exact" counterpart
This is a safe setting which assured that all of the equations I want to simplify are actually fully simplified:
...
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Adjustment of AssumptionsMaxNonlinearVariables which avoids both blocking and partial solutions
I write an application which calls Mathematica via API. However, as it turns out, I would need to manually tune
...
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Bessel function identity fails to simplify, but only sometimes
For Bessel functions of positive integer order, it is known that
$(J_{i-1}(\alpha_{i,n}))^2 = (J_{i+1}(\alpha_{i,n}))^2$ where $\alpha_{i,n}$ is the $n$th zero of $J_{i}(r)$. Indeed, Mathematica knows ...
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Using existing conditions to simplify a certain part of polynomial
Here, I want to simplify the polynomial P1
...
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