Questions tagged [assumptions]
Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].
459
questions
0
votes
0answers
57 views
This expression isn't simplifying [closed]
Consider:
expr = -(((s β - γ - ν) (s (β - γ) -
i γ - ν))/(s β));
I tried:
1)
...
1
vote
1answer
51 views
How to 'define' value in Assumptions but not let Simplify replace it? [closed]
I want to let Simplify know the exact value of a symbol, to resolve logical statements, but don't want it to actually replace it. For instance, I would like ...
0
votes
0answers
63 views
Mathematica can FullSimplify general but not specific case of a square root
FullSimplify[
Sqrt[(M^2 + A^2 - B^2)^2],
M^2 + A^2 - B^2 > 0
]
outputs the desired:
A^2 - B^2 + M^2
I've followed the ...
1
vote
0answers
41 views
0
votes
1answer
50 views
Simplify an expression with assumptions connected with OR
Mathematica doesn't seem to have any problem with these commands:
...
4
votes
1answer
228 views
0
votes
0answers
37 views
0
votes
0answers
22 views
Test domain assumption of a variable
Using $Assumptions to define the domain of variable is straightforward, i.e. $Assumptions = Element[x, Reals]. Nevertheless, it'...
0
votes
0answers
40 views
Difference between Assuming[] and Refine[]
I'm trying to find the limit of a root. I've found that the limit is undefined if I use Refine[]
...
4
votes
3answers
742 views
How can I specify the assumption 'a' is much greater than 'b' (a>>b) in Mathematica?
I want to evaluate an expression of type 1/(r-2 m), assuming r >> 2 m. This is regarding black hole physics and r = 2 m is the Schwarzschild radius. But I am working on something where I need to ...
1
vote
0answers
42 views
Piecewise and Assumptions [closed]
Assumptions sometimes work as expected with Piecewise, for example
Simplify[Piecewise[{{A, a + b >= c}, {B, True}}], Assumptions -> a + b > c]
correctly ...
0
votes
1answer
62 views
0
votes
2answers
67 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
185 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
83 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
47 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
76 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
95 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
97 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:
$$
J_{m}\left( x \right) = \frac{ 1 }{ 2 \ \pi \ i^{m} } \int_{0}^{2 \pi} \ d\phi \ e^{i \left( x \cos{\phi} \ - \ m \ \phi \...
1
vote
1answer
82 views
Using Simplify and Reduce with Assumptions when the inequality is already one of the assumptions
I am using the Simplify and Reduce functions to reduce inequalities, but somehow the function Simplify does not consistently give "True" when the inequality happens to be one of the ...
1
vote
2answers
51 views
Assuming r0 ≈ r1 && r0 ≈ 0 && r1 ≈ 0, to discourage division by near-zero
I’m using Mathematica for some conceptually simple algebra, that will ultimately land in Excel or a compiled language.
...
0
votes
1answer
60 views
Solving an equation, and verifying that it is correct
I want to solve the equation
Solve[e == 1/2 (-2 ef + hvk - Sqrt[9 hvk^2 + 4 j^2]), hvk]
I then obtain the solutions
...
3
votes
1answer
67 views
Solve yields complex Root even if the domain is Reals
I want to solve $x^3=a^2$ for $x$ where $a>0$ and $x$ is real. The answer I want is
$$x=a^{2/3}.$$
On Wolfram Cloud, I tried
...
0
votes
0answers
20 views
How to assume that an unknown function of many variables and all its derivatives is real?
I'm working on modified theories of gravity and I extensively use Mathematica to derive differential equations starting from the general covariant expressions of field equations of a theory. For ...
5
votes
2answers
174 views
Help solving this differential equation
I am trying to solve this differential equation
$$ 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
31 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
68 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
70 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
68 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
82 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
70 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
59 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
122 views
1
vote
0answers
82 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
426 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
347 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
79 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
26 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
66 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
58 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
74 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
33 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
66 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
31 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
80 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
100 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
57 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 ...
