Questions tagged [assumptions]
Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].
448
questions
0
votes
1answer
49 views
0
votes
2answers
62 views
Triple integral: How do I include assumptions and conditions?
I would like to solve the following integral:
$$I=\int_{0}^{a} \int_{0}^{y} \int_{0}^{z} e^{(a-x)^{3}} d x d z d y$$
with the condition that:
$$a>0$$
So I tried to input the equation like below ...
5
votes
2answers
181 views
Why Mathematica is not assuming real variable as real?
I am dealing with the situation where despite of specifying my variables b1 and c to be greater than zero, Mathematica still ...
0
votes
1answer
81 views
how can I modify this function to convert to polar form for any complex expression?
The function from another post is to convert a complex number to polar form.
polarForm = Expand[# /. z_?NumericQ :> Abs[z] Exp[I Arg[z]]] &
Now if I apply ...
1
vote
1answer
45 views
How to generate assumptions automatically for definite integrals？
In Mathematica, a trick to speed up the process of definite integrals is by adding assumptions. For example, the following codes run faster if we add such assumptions:
...
3
votes
0answers
75 views
$Assumptions causing problems in Mathematica 12.3 vs. 10.4 [duplicate]
I would like to use $Assumptions to add global restrictions to the parameters in my notebook (Mathematica 12.3). I tried exactly this in Mathematica 10.4 and it ...
2
votes
1answer
89 views
Symbolic Mean and Variance Calculations
I need a tutorial that gets me started on basic symbolic calculations with random variables. My naive attempts did not get me far.
...
1
vote
1answer
89 views
FullSimplify is giving a condition that is implied by the assumptions
I've been trying to understand why FullSimplify is giving a condition that is implied by the assumptions (otherwise the set is empty). However, I couldn't ...
1
vote
0answers
62 views
Why is this integrand not integrating to a Bessel function? [duplicate]
I know from the identities of Bessel functions that the following is true:
$$
J_{m}\left( x \right) = \frac{ 1 }{ 2 \ \pi \ i^{m} } \int_{0}^{2 \pi} \ d\phi \ e^{i \left( x \cos{\phi} \ - \ m \ \phi \...
1
vote
1answer
76 views
Using Simplify and Reduce with Assumptions when the inequality is already one of the assumptions
I am using the Simplify and Reduce functions to reduce inequalities, but somehow the function Simplify does not consistently give "True" when the inequality happens to be one of the ...
1
vote
2answers
51 views
Assuming r0 ≈ r1 && r0 ≈ 0 && r1 ≈ 0, to discourage division by near-zero
I’m using Mathematica for some conceptually simple algebra, that will ultimately land in Excel or a compiled language.
...
0
votes
1answer
59 views
Solving an equation, and verifying that it is correct
I want to solve the equation
Solve[e == 1/2 (-2 ef + hvk - Sqrt[9 hvk^2 + 4 j^2]), hvk]
I then obtain the solutions
...
3
votes
1answer
65 views
Solve yields complex Root even if the domain is Reals
I want to solve $x^3=a^2$ for $x$ where $a>0$ and $x$ is real. The answer I want is
$$x=a^{2/3}.$$
On Wolfram Cloud, I tried
...
0
votes
0answers
19 views
How to assume that an unknown function of many variables and all its derivatives is real?
I'm working on modified theories of gravity and I extensively use Mathematica to derive differential equations starting from the general covariant expressions of field equations of a theory. For ...
5
votes
2answers
169 views
Help solving this differential equation
I am trying to solve this differential equation
$$ y^{''}(x) + \frac{6}{x} y^{'}(x) +14 y(x) = -4 y(x) \; \ln(y(x)),\; x > 0$$
subject to the boundary conditions $y(0) = 1,\;y^{'}(0) = 0$. The ...
0
votes
0answers
30 views
Assume some expression is false
I need to Reduce a complicated function and I want to exclude some conditions A and B. How do I assume that the expression A is ...
1
vote
1answer
66 views
1
vote
0answers
42 views
Intervals v.s. Domains: when to use which and why?
or: How to use Interval correctly?
Mathematica provides these constructs for various symbolic deductions tasks. Among those constructs are symbolic number sets ...
1
vote
1answer
58 views
Real part of complex exponential
How do you obtain the real part of a complex exponential? For example, Mathematica gives $Re[e^{ik}]$ instead of $\cos(k)$, see figure.
...
2
votes
1answer
63 views
Display assumptions of a variable
If I restrict a variable x to x>0 via $Assumptions=x>0, is there a way I can get ...
2
votes
1answer
79 views
Can Limit take limits of unknown functions?
For example, when I input this
f[0] = 0;
Limit[f[x], x -> 0]
, it does not output 0.
Is there a way to get it to output <...
2
votes
0answers
67 views
Unexpected results with Integrate/AsymptoticIntegrate with assumptions
I am quite disturbed by the result provided by Mathematica, and I am not sure if I understand perfectly its behavior.
What I want to do is to check the asymptotic form of the function $I(\tau)$ with $\...
0
votes
0answers
54 views
How to assume a number to be a half integer?
For integer x $\left(\cos 2\pi x\right) ^2=1$ and I can check this as follows
...
0
votes
2answers
100 views
1
vote
0answers
80 views
How reliable is AsymptoticIntegrate?
In new mathematica 12 there is a new function AsymptoticIntegrate. However, it seems that it gives me incorrect results in some cases. To be completely honest, it ...
14
votes
2answers
393 views
Behavior of Solve with $Assumptions changed in 12.2
Something changed with Solve between versions 12.1 and 12.2.
12.1:
...
2
votes
3answers
344 views
How can I write in Mathematica that 2*x is an integer? [closed]
I have to maximize $h/k^2$, where $h/k^2 < 0.1974$ and $k$ is an integer, and $2\cdot h$ is an integer, $h>0$, $k>0$.
How can I write this problem in Mathematica?
0
votes
0answers
77 views
Issue with several replacements in a function under certain conditions
I am trying to define a function (reduce[x]) which does several substitutions, depending on the values of certain parameters. Concretely, consider an expression x, which contains an arbitrary number ...
0
votes
1answer
53 views
How do I give assumptions to Simplify or Solve? [closed]
I've have the expression:
q2sol =
(Sec[2*a1]*Tan[a1]^3*(-7 + 6*Cot[a1]^3*Sqrt[Tan[a1]^2]))/(6*Sqrt[Tan[a1]^2])
I know that a1...
0
votes
0answers
19 views
Assumptions with piecewise problem?
I am trying to apply the assumpion of 0<s<1 throughout the calculation however the piecewise condition does not accept it automatically. Is there any way to avoid the manual choice of x>0.
...
1
vote
0answers
64 views
Assuming a monotonic function
I'm trying to tell Mathematica that a function is increasing. More specifically, I would like at least one of the following statements to report 'true'.
...
0
votes
2answers
57 views
Expression simplification
I have this term
Sqrt[(B Bc)/(A^2-B Bc)]Sqrt[B Bc+A(-A+Sqrt[A^2-B Bc])]Sqrt[-B Bc+A(A + Sqrt[A^2-B Bc])],
which actually can be simplified to B*Bc. However, it ...
2
votes
1answer
73 views
Trouble evaluating this definite integral, either directly or with indefinite + limits
I have the function
$$
\Sigma(x) = \frac{\sqrt{R^2-x^2}(\left| R\right| -1)}{\left(R^2-1\right) \left(x^2-1\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{R^2-x^2}}{\sqrt{R^2 \left(1-x^2\right)}}\right)-\...
0
votes
0answers
32 views
Simplify with Assumptions: Puzzle for 4 variables [duplicate]
I have a rather specific question about Simplify[] (hope this is not off-topic).
The puzzle I have is that Simplify[] with ...
2
votes
2answers
62 views
Solving an Algebraic Equation with Constraints on Multiple Parameters
Suppose we have the following equation to solve (with respect to $x$):
$$
\frac{m\omega^2x^2}{2} + \frac{m\alpha x^3}{3} = E,\quad\text{where }m,\omega,\alpha,E>0\text{ and } E < \frac{m\omega^6}...
0
votes
0answers
30 views
Why a complementary inequality for function values does not simplify to False?
I have a general assumption of a function to be positive. The direct inequality (f[x]>0) does simplify to True, but a complementary one (f[x] < 0) does not simplify at all despite the fact that ...
0
votes
1answer
66 views
How can I get rid of Abs?
In the following code, the functions WP[t] and WS[t] are real. Time also is a positive parameter. As you can see, MATHEMATICA enters Abs in the calculations. Including Abs only complicates the next ...
2
votes
1answer
94 views
Mathematica and its default assumptions
I am a bit surprised that evsluating
Integrate[Exp[I n x],{x, 0, Pi}]
gives
$\qquad \frac{-i(e^{in\pi}-1)}{n}$.
What if $n = 0$? I didn't assume anything about $n$ ...
1
vote
1answer
54 views
Use the fact that $u(t)\cdot u'(t)=0$ for $u\in\mathcal{S}^2$
If for all $t$, $u(t)$ is a point on the unit sphere $\mathcal{S}^2 \subset\mathbb{R}^3$, $u'(t)$ is orthogonal to $u(t)$, because $u'(t)$ is in the tangent plane of the sphere.
I have large ...
1
vote
3answers
338 views
Problems with solutions involving Lambert W function of transcendental equation
Solve and Reduce fail here with rational parameter l, but succeed when I plug in a value
<...
8
votes
1answer
111 views
Why does Simplify work diferently for (a+b)/e versus (a+b+c)/e?
I am playing around with Simplify amd assumptions. I noticed that:
Simplify[x > (a + b)/e, x < (a + b)/e]
...
1
vote
1answer
62 views
How to evaluate a multidimensional NIntegral in a range where certain conditions must be satisfied by the variables
I have a function f which looks similar to this :
f[a_, b_, c_] := NIntegrate[sigma[a, b, c], {a, -valueA, valueA}, {b, -valueB, valueB}, {c, -valueC, valueC}]
and ...
2
votes
1answer
83 views
0
votes
1answer
55 views
Specifying assumptions at the start of a piece of code
I am aware of the use of 'Assumptions' or 'Assuming' to attach to certain operations (e.g. integrals) to aid Mathematica. Is there a way of listing asssumptions at the beginning of a piece of code ...
0
votes
1answer
67 views
How do I introduce an assumption when defining a piecewise function?
Define m as an integer. I want to specify a Piecewise function f[x,n] that takes value ...
3
votes
1answer
65 views
NMinimize with assumptions gives result that does not satisfy assumptions
I am trying to determine if a function is always positive given a set of assumptions. I am using NMinimize following the advice of previous posts in this site. ...
0
votes
0answers
41 views
Regarding “Assumptions” under “Integrate”
Sir,
I tried to integrate the following in mathematica
...
0
votes
1answer
36 views
Need help understanding the results of the unit function
I want to get Limit of the following function at $T\to 0$.
$$
Eig=\frac{8 (\eta +J \sinh (2 \beta \eta ) \sinh (2 \beta J)+\eta \cosh (2 \beta \eta ) \cosh (2 \beta J))}{\eta Z^2}
$$
where $Z=2 (...
3
votes
1answer
75 views
Solve an equation with real parameters
I am trying to solve
$$
\left(\eta ^2-1\right) \cosh ^2(\beta \eta )+2 J^2=2 \eta (J \sinh (\beta \eta ) \sinh (\beta J)+\eta \cosh (\beta \eta ) \cosh (\beta J))
$$
for $\eta$. Where, $\beta, ...
0
votes
1answer
65 views
Problem with DiracDelta evaluating to zero
I am having an issue (in Mathematica 11.2.0.0) where the following integral evaluates to zero:
...
